9012 Investigate life and work related problems using data and probabilities

9012 Investigate life and work related problems using data and probabilities Learner Guide 1
LEARNING UNIT: 9012 Investigate life and work related
problems using data and probabilities
CREDITS: 05
NQF LEVEL: 03
LEARNER MANUAL
LEARNING PROGRAMME
DEVELOPED BY YELLOWMEDIA
PUBLISHERS

Welcome to the programme
Follow along in the guide as the training practitioner takes you through
the material. Make notes and sketches that will help you to
understand and remember what you have learnt.
Take notes and share information with your colleagues. Important and
relevant information and skills are transferred by sharing!
This learning programme is divided into sections. Each section is preceded by a
description of the required outcomes and assessment criteria as contained in the
curriculum. These descriptions will define what you have to know and be able to do in
order to be awarded the credits attached to this learning programme.
These credits are regarded as building blocks towards achieving the Qualification upon
successful assessment and can never be taken away from you!
Programme methodology
The programme methodology includes facilitator
presentations, readings, individual activities, group
discussions and skill application exercises.
Know what you want to get out of the programme from the
beginning and start applying your new skills immediately.
Participate as much as possible so that the learning will be
interactive and stimulating.
The following principles were applied in designing the course:
 Because the course is designed to maximise interactive learning, you are
encouraged and required to participate fully during the group exercises
 As a learner you will be presented with numerous problems and will be required to
fully apply your mind to finding solutions to problems before being presented with
the course presenter’s solutions to the problems
 Through participation and interaction the learners can learn as much from each
other as they do from the course presenter
 Although learners attending the course may have varied degrees of experience in
the subject matter, the course is designed to ensure that all delegates complete the
course with the same level of understanding
 Because reflection forms an important component of adult learning, some learning
resources will be followed by a self-assessment which is designed so that the
learner will reflect on the material just completed.

This approach to course construction will ensure that learners first apply their minds to
finding solutions to problems before the answers are provided, which will then maximise
the learning process which is further strengthened by reflecting on the material covered by
means of the self-assessments.
Different types of activities you can expect
To accommodate your learning preferences, a variety of different types of activities are
included in the formative and summative assessments.
They will assist you to achieve the outcomes (correct results) and should guide you
through the learning process, making learning a positive and pleasant experience.
The table below provides you with more information related to the types of activities.
Icons Type of assessment Description
Formative knowledge
assessment:
This comprises of questions
to assess your knowledge.
You must obtain at least 80%
in each assessment criterion.
Teamwork Self-Assessment
Form
After you completed this
course, you will be required
to assess your own
behaviour regarding team
work.
Work place experience After you completed this
to assess your own
behaviour regarding work
experience.
Project research After you completed this
to assess your own
behaviour regarding
research.

Learner Administration
Attendance Register
You are required to sign the Attendance Register every day you attend training sessions
facilitated by a facilitator.
Programme Evaluation Form
On completion you will be supplied with a “Learning programme Evaluation Form”. You are
required to evaluate your experience in attending the programme.
Please complete the form at the end of the programme, as this will assist us in improving
our service and programme material. Your assistance is highly appreciated.
Learner Support
The responsibility of learning rests with you, so be proactive and ask questions and seek
assistance and help from your facilitator, if required.
Please remember that this learning programme is based on outcomes based education
principles which implies the following:
 You are responsible for your own learning – make sure you manage your study,
research and workplace time effectively.
 Learning activities are learner driven – make sure you use the Learner Guide and
Formative Assessment Workbook in the manner intended, and are familiar with the
workplace requirements.
 The Facilitator is there to reasonably assist you during contact, practical and
workplace time for this programme – make sure that you have his/her contact
details.
 You are responsible for the safekeeping of your completed Formative Assessment
Workbook and Workplace Guide
 If you need assistance please contact your facilitator who will gladly assist you.
 If you have any special needs please inform the facilitator.

Learner Expectations
Please prepare the following information. You will then be asked to
introduce yourself to the instructor as well as your fellow learners
Your name
The organisation you represent
Your position in the organisation
What do you hope to achieve by attending this programme / what are your
expectations?

Information about this module
Overview
9012 Investigate life and work related problems using data and probabilities
.
Scope of the programme
The learning contained within this module will enable learners to:
 Pose questions, collect and organise data.
 Represent, analyse and interpret data using various techniques.
 Use random events to explore and apply, probability concepts in simple life.
Entry Level Requirements
The credit value is based on the assumption that people starting to learn towards
this unit standard are competent in Mathematics and Communications at NQF level
Target group
Mode of delivery
This module will be delivered to you in a four day facilitated workshop. During these four
days you will be required to complete formative activities during class time as well as after
class in your own study time.
Unit standard alignment
Unit standard Number : 9012 Investigate life and work related problems using data and
probabilities
NQF Level :03
Credits :05
Learning time
It will take the average learner approximately 05 learning hours to master the outcomes of
this programme.
Assessment
 Formative assessment will take place during the learning process in class through
means of exercises. You will be required to complete activities as part of a group in
class as well as individual activities. These formative activities will help prepare you
for your final assessment.
 Summative assessment will be conducted at the end of this learning process
through means of a Portfolio of Evidence.
In order to assess whether a learner can actually demonstrate the desired outcomes,

assessment criteria are included in the unit standard. Each outcome has its own set of
assessment criteria.
The assessment criteria describe the evidence that is needed that will show that the
learner has demonstrated the outcome correctly.
It is of utmost importance that the learner fully understands the assessment criteria as
listed in the unit standard, as it is the only way in which the learner will know what he will
be assessed against.
The final or summative assessment is the most important aspect of this training
program. It is during this process that the learner will be declared competent or not yet
competent.
The learner will know exactly how he will be assessed, and when and where he will be
assessed. All of these details must be obtained from the training provider where the
learner enrolled for his program.
Range statements
This unit standard includes the requirement to:
Identify issues suited to resolution by statistical methods
Select a suitable sample
Collect and generate data through the use of questionnaires and suitable
experiments
Calculate statistics and probability values through the use of calculators
Represent data in the form of tables, charts and graphs
Use statistics and representations of data to argue a resolution of an issue
Interpret statistics, the use of probabilities, and representations of data
Determine probability values
Work with probability in practical situations
Use available technology (i.e. whatever is available for working
with data e. g. pencil and ruler, including spreadsheets, graphical calculators) to fit
appropriate curves (e.g., linear, quadratic) to data

More detailed range statements are provided for specific outcomes and assessment
criteria as needed.
Remember: Also included in the unit standard are the range
statements in support of the assessment criteria. The range
statements indicate detailed requirements of the assessment
criteria.
The learner guide
The learner guide is included in this material under various learning units. The
learner guide has been designed in such a manner that the learner is guided in a
logical way through the learning material and requirements of the unit standard.
RPL assessment
The assessment of RPL learners will be conducted in the same way as for those of new
learners. The assessment pack is exactly the same and will therefore be used for new
learners as well as RPL Learners. It must however be noted that learners who are
applying for RPL must provide proof of previous learning and subject related experience
prior to the assessment.
This proof or evidence can be in the format of certified copies (certificates) of previous
learning programs that have been attended.
All the evidence will be assessed and authenticated before a learner will be allowed to
enrol for an RPL program.

Contents
Welcome to the programme.................................................................................................2
Programme methodology.....................................................................................................2
Different types of activities you can expect..........................................................................3
Learner Administration.........................................................................................................4
Learner Support...................................................................................................................4
Learner Expectations...........................................................................................................5
Information about this module..............................................................................................6
Learning Unit 1: .................................................................................................................12
Terminology..................................................................................................................................14
Types of Data...............................................................................................................................17
Qualitative Research versus Quantitative Research .............................................................19
The Research Question..............................................................................................................19
The Hypothesis ............................................................................................................................21
Data Collection Methods ............................................................................................................24
Research Report..........................................................................................................................29
Data Types....................................................................................................................................30
Formative assessment.......................................................................................................33
Role play...................................................................................................................................33
Activity: 01...............................................................................................................................33
Essay –Reflexive ...............................................................................................................37
Learning Unit 2: .................................................................................................................38
The Sample Mean .......................................................................................................................43
The Median...................................................................................................................................44
The Mode......................................................................................................................................45
Role play...................................................................................................................................53
Project.......................................................................................................................................54
Group Activity: 05..................................................................................................................54
Research PROJECT.................................................................................................................55
Activity: 06...............................................................................................................................55
Summative assessment.....................................................................................................56
Simulation................................................................................................................................56
ACTIVITY 02.............................................................................................................................56

Learning Unit 3: .................................................................................................................58
Geometrical Symmetry ...............................................................................................................59
The Properties of a Trapesium..................................................................................................62
Pythagoras Theorem...................................................................................................................63
Role play...................................................................................................................................64
Activity: 07...............................................................................................................................64
Research PROJECT.................................................................................................................66
Activity: 09...............................................................................................................................66
Simulation................................................................................................................................67
ACTIVITY 03.............................................................................................................................67
Essay –Reflexive ...............................................................................................................68
Annexure 1: Growth Action Plan.......................................................................................69
Annexure 2: Words that are new to me.............................................................................70
Annexure 3: Training Evaluation.......................................................................................71
Annexure 4: Evaluation of Facilitator ................................................................................72
2. Bibliography .............................................................................................................73
SECTION C: SELF REFLECTION..............................................................................74
Self-Assessment ..........................................................................................................76
Learner Evaluation Form...........................................................................................77

Learning path:
Pose questions, collect and organise data.
Represent, analyse and interpret data using various
techniques.
Use random events to explore and apply,
probability concepts in simple life.

Learning Unit 1:
At the end of this module learners will be able to:
Introduction
1. Situations or issues that can be dealt with through statistical methods are
identified correctly.
2. Variables contributing to a problem situation are identified and addressed
in data gathering, e.g. crime is related to time of day and location.
3. Appropriate and efficient methods are used to collect, record and organise
data.
4. Data samples are of adequate size and are representative of the
population.
Conclusion
Pose questions, collect and organise
data

Introduction to Statistics and Probability
Wherever you work or whatever job you do, you cannot
escape statistics – very few decisions that we make for
business, industry or government are made without giving
some consideration to statistical data. Such data includes
 financial data,
 population demographics, a
 attitudes and lifestyle choices of people,
 Health statistics, and much, much more.
Below are some examples of statistics:
Think about how stupid the average person is; now
realise half of them are dumber than that.
- George Carlin
47.3% of all statistics are made up on the spot.
- Steven Wright
 About 3000 years ago, most Egyptians died by the time they were 30.
 A toothpick is the object most often choked on by Americans!
 Austria has the highest per-capita rate of deaths resulting from "fall
involving ice-skates, skis, roller-skates or skateboards.
 30% of Chinese adults live with their parents.
 The animal with the largest brain in proportion to its size is the ant. They are the smartest species
of insects with about 250,000 brain cells.

Terminology
In order to make the most of this learning opportunity, it is important that you know and understand
the terminology associated with statistics and probability.
Terminology Meanings
Information Information is the processed form of data.
Mean Average: approximating the statistical norm or average or expected value
Median The middle value of an ordered set of values
Mode The value that occurs the most frequently in a data set or a probability
distribution
Model A standardized representation of data objects used as a container for
transactions, a framework for analysis, and a vocabulary for management.
Population In statistics, population can mean people, but it can also represent any
item or object that is part of the set you are investigating.
Probability Probability is a measure of how likely an event is to occur
Random
sample
A sample in which every element in the population has an equal chance
of being selected
Range The difference between the lowest and highest values. (In {4, 6, 9, 3, 7}
the lowest value is 3, and the highest is 9, so the range is 9-3 = 6.
Ratio A ratio is a proportion - the relation between things (or parts of things) with
respect to their comparative quantity, magnitude, or degree
Sample This is a set of data that you take from the population (usually when it is
too difficult or impossible to include the entire population in the survey)
Statistic A statistic is a summary value calculated from a sample. For example, we
might compute the average age of all respondents.
Statistical
inference
When you use information from a sample to draw conclusions
(inferences) about the population from which the sample was taken, this is
called ‘statistical inference’.

Correlation In statistics, correlation and dependence are any of a broad class of
statistical relationships between two or more random variables or
observed data values.
Data Data is a collection of facts, figures and statistics relating to a topic.
Experiment An experiment is any process or study which includes the collection of
data, the outcome of which is unknown. In statistics, the term is usually
restricted to situations in which the researcher has control over some of
the conditions under which the experiment takes place.
Experimental unit A unit is a person, animal, plant or thing which is actually studied by a
researcher - the basic objects upon which the study or experiment is
carried out.
Statistics or statistic?
A statistic is a quantity (amount) that is calculated from a sample of data. We use the average of
the data in a sample to give information about the overall average in the population from which we
took the sample.
Variable A variable is a characteristic that may assume more than one set of
values to which a numerical measure can be assigned. Height, age,
amount of income, province or country of birth, grades obtained at
school and type of housing are all examples of variables.
Variance In probability theory and statistics, the variance is used as one of
several descriptors of a distribution. It describes how far values lie from
the mean.
The Concise Oxford Dictionary defines statistics as “numerical
facts systematically collected” and statistic as “statistical fact or
item”.
Statistics entails all aspects of information: collecting, organizing,
comprehending, communicating, and interpreting.

It is possible to draw more than one sample from the same population and the value of a statistic
will generally vary from sample to sample. For example, the average value in a sample is a
statistic. The average values in more than one sample, drawn from the same population, will not
necessarily be equal.
Population and Sample
A population is any entire collection (set) of people, animals, plants or things from which we may
collect data. It is the entire group we are interested in, which we wish to describe or draw
conclusions about.
In order to make any generalisations about a population, a sample, that is meant to be
representative of the population, is often studied. For each population there are many possible
samples. A sample statistic gives information about a matching population parameter. For
example, the sample average (mean) for a set of data would give information about the overall
population average (mean).
A sample is generally selected for study when the population is too large to study as a whole.
However, the sample should be representative of the general population. You can usually best
achieve this by random sampling.
Remember that a sample is a group of units selected from a larger
group (the population). By studying the sample you can draw valid
conclusions about the larger group.

It is important that the investigator carefully and completely defines the population before collecting
the sample, including a description of the members to be included.
Parameters
A parameter is a value, usually unknown (and which therefore has to be estimated), used to
represent a certain population characteristic. For example, the population mean (average) is a
parameter that is often used to indicate the average value of a quantity.
Within a population, a parameter is a fixed value which does not vary. Each sample drawn from the
population has its own value of any statistic that is used to estimate this parameter. For example,
the mean (average) of the data in a sample is used to give information about the overall mean
(average) in the population from which that sample was taken.
Parameters are often assigned Greek letters (e.g. ), whereas statistics are assigned Roman
letters (e.g. s).
Types of Data
Categorical Data
Categorical (also called qualitative, and sometimes nominal or ordinal) data is data where what is
being recorded cannot be readily identified with the real numbers. Examples include colours of
cars (red, green, black), size of eggs (small, medium, large), sex (male, female).
One can count the number of cars of various colours, and display that information in a bar chart or
pie chart, but one cannot combine the various cars and conclude that the average car is brown.
(We shall not devote much attention to categorical data because we cannot manipulate it.)
The population for a study of infant health might be all children born in
Mpumalanga in the 1990's.
The sample might be all babies born on 17th May in any of the years (1990-
1999).

Quantitative Data
Quantitative data (also further specified as interval and ratio, the distinction between which is not of
interest for our purposes) is data where what is being recorded can be identified with the real
numbers. Examples include: age, I.Q., weight, height. Identification with the real numbers makes it
easier to organize, understand, and communicate this data.
Statistics is therefore the summary of data gathered from a population of people or things.
Sometimes it is used to generalize the characteristics of that research group to the whole
population. An example would be to say 80% of the sample of people in, for example Upington,
claim that their favourite food is boerewors. Therefore, the researchers conclude, 80% of all
people in Upington’s favourite food are boerewors.
For the research data to be generalized to everybody from the same group, the researchers have
to make sure that they ask enough people, and that they pick a few people from all the areas and
population groups. If the researchers only asked children, or men, or people from the area around
the airport, we could not say that ‘everybody’ in Upington loves boerewors! So researchers try to
use a “random sample” where everybody has an equal chance of being picked. The people they
ask are called the sample, and the whole group that this sample belongs to, is called the
population.
Making Sense of Data
We can count all data, whether categorical or quantitative, the
terms categorical and quantitative refer to the essence of the
individual items which we are counting.

To make sense of all the data that they gather they may want to calculate
 How many people gave a certain answer (for instance, 80% of people liked boerewors
most) – this is called the mode.
 What the average is (e.g. the average birth weight of babies born in the Northern Cape)
– this is called the mean.
 What the correlation is between two or more variables (e.g. whether there is a link
between performance at school and the ability to find a job; or between tallness and
fitness, etc).
Qualitative Research versus Quantitative Research
Qualitative Research Quantitative Research
Researcher is the data gathering
instrument.
Researcher uses tools, such as
questionnaires or equipment to collect
numerical data.
Data is in the form of words, pictures or
objects.
Data is in the form of numbers and
statistics.
Subjective – individuals’ interpretation of
events is important ,e.g., uses participant
observation, in-depth interviews etc.
Objective: seeks precise measurement &
analysis of target concepts, e.g., uses
surveys, questionnaires etc.
The Research Question
The first step in conducting any research is to formulate a research question.
A Research Question is a statement that identifies the phenomenon
to be studied.

The research will answer any question posed. It is therefore important that the research question
is formulated correctly and accurately.
Before a research question can be formulated, a topic must be identified. It is generally stressed
that the topic must be of the right size for the purpose—neither too large nor complex to be dealt
with properly in the time and space available, nor too small for anything much to be done with.
Once a topic has been identified and narrowed to the right size the research question can be
formulated.
There can be three basic types of questions that can be addressed by research projects. These
are:
 Descriptive. This kind study is designed mainly to describe what is going on or what
already exists. Examples can include Public opinion polls seeking only to assess the
number of people who hold various opinions.
 Relational. The purpose of this type of study is to look at the relationships between
various, two or more variables. For example: Does age have an influence on the amount of
health problems that a person encounters?
 Causal. This is when a research study is designed to find out if one or more variables
causes or affects one or more variables depending on them. In other words, these
questions deal with the cause – effect relationship. It usually involves an experiment where
an independent variable is changed or manipulated to see how it affects the dependent
variable. For example: Will increasing the amount of professional development by teachers
increase learner development?
The research question is the purpose of a study summed up in one or two sentences. It is a
statement of what the researcher wants to discover. It can either be a general statement of a
specific hypothesis.
Often the title of a research study will be the research question. The topic sentence is a research
question summarized in one sentence of this form: "What is the effect of something on something
else?" Let's define the terms in the example.
 "Something" - This is a variable. It is the variable that affects another variable.

 "Something Else" - This is another variable. It is the variable that is changed due to the
effects of the first variable.
 "Effect" - This is the process that happens when one variable relates with another.
Here is an example of a Topic Sentence: "As a person gets older the amount of their body that is
muscle mass decreases."
Let's define the components:
 "Something" - "a person gets older." The variable of "aging."
 "Something Else" - "amount of their body that is muscle mass." The variable is the amount
of muscle.
 "Effect" - "decreases." - The effect of aging on muscle mass is predicted.
A Topic Sentence can be a statement or a question.
It is important to be able to identify the research question. The other components of a study grow
from the research question in a logical manner. Once we have a clear research question, the
question leads to specific variables. The variables are the observable phenomena that can be
studied. A variable varies, that is it can be observed to change, or can take on different attributes.
Gender is a variable and it can take on two different attributes, male and female. Knowledge of the
variables allows us to understand the hypotheses of the study.
The hypothesis describes the predicted relationships between the variables.
The Hypothesis
What is a hypothesis?

A hypothesis is a tentative statement that proposes a possible explanation to some phenomenon
or event.
A useful hypothesis is a testable statement which may include a prediction.
A hypothesis should not be confused with a theory.
Theories are general explanations based on a large amount of data. For example, the theory of
evolution applies to all living things and is based on wide range of observations. However, there
are many things about evolution that are not fully understood such as gaps in the fossil record.
Many hypotheses have been proposed and tested.
When are hypotheses used?
The key word is testable. That is, you will perform a test of how two variables might be related.
This is when you are doing a real experiment. You are testing variables.
Usually, a hypothesis is based on some previous observation such as noticing that in November
many trees undergo colour changes in their leaves and the average daily temperatures are
dropping. Are these two events connected? How?
How are hypotheses written?
Consider the following statements:
1. Temperature may cause leaves to change colour.
2. Ultra violet light may cause skin cancer.
All of these are examples of hypotheses because they use the tentative word "may.” However,
their form is not particularly useful.
Using the word may do not suggest how you would go about proving it.
If these statements had not been written carefully, they may not have even been hypotheses at all.
For example, if we say "Trees will change colour when it gets cold." we are making a prediction.
Or if we write, "Ultraviolet light causes skin cancer." could be a conclusion. One way to prevent
making such easy mistakes is to formalise the form of the hypothesis.

Below are some examples of formalised hypotheses:
Notice that these statements contain the words, if and then.
They are necessary in a formalised hypothesis. But not all if-then statements are hypotheses. For
example, "If I play the lottery, then I will get rich." This is a simple prediction.
In a formalised hypothesis, a tentative relationship is stated. For example, if the frequency of
winning is related to frequency of buying lottery tickets. "Then" is followed by a prediction of what
will happen if you increase or decrease the frequency of buying lottery tickets. If you always ask
yourself that if one thing is related to another, then you should be able to test it.
Formalized hypotheses contain two variables. One is "independent" and the other is
"dependent." The independent variable is the one you, the "researcher" control and the
dependent variable is the one that you observe and/or measure the results.
Look at the following examples again:
1. If skin cancer is related to ultraviolet light, then people with a high exposure to UV light will
have a higher frequency of skin cancer.
In this example ultraviolet light can be controlled by the researcher and is therefore the
independent variable while skin cancer is the dependent variable.
2. If leaf colour change is related to temperature, then exposing plants to low temperatures will
result in changes in leaf colour.
1. If skin cancer is related to ultraviolet light, then people with a high
exposure to UV light will have a higher frequency of skin cancer.
2. If leaf colour change is related to temperature, then exposing plants to low
temperatures will result in changes in leaf colour.

In the second example temperature is the independent variable and leaf colour change is the
dependent variable.
The ultimate value of a formalised hypothesis is it forces us to think about what results we should
look for in an experiment.
Testing the Hypothesis or Answering the Research Question
The researcher then carries out the research to answer the research question (or test the
hypothesis). Take note that the research is only valid if it addresses the research question.
Data Collection Methods
Appropriate methods for collecting, recording and organising data need to be used to maximise
efficiency and ensure the resolution of a problem or issue.
You can get Data from:
 Your organisation’s archives – existing statistical data held on file.
 Normal everyday operations of your company – the amount of items produced on a daily
basis, or the number of cars fixed in the workshop every day, for example.
 Research – through questionnaires, surveys, etc.
 Data base information such as – population details obtained from the population census.
The process of collecting accurate data is done through: interviews, questionnaires, and other
methods. Data collection in field settings can be done in a structured, systematic and scientific
way.

Since questionnaires are one of the main ways of obtaining data, we will focus on how to go about
them.
Questionnaires should be short and simple.
Questions should be
 clear and easy to understand
 closed questions that require the person to answer ‘yes/no’
Example:
Are you currently employed? Yes / No
 multiple choice questions where they get to choose an
answer
Example:
Example: Only people with university qualifications should get the
job.
Agree ____ Disagree _______ No Opinion _______
 numerical rating scales where a person is asked to rate
something on a scale of e.g. ‘1-5’, or ‘never – always’, ‘poor
– excellent’
Example:
How would you rate your supervisor?
Excellent (5) Good (4) Average (3) Fair (2) Bad
(1)

Advantages of Questionnaires
 Low cost of posting mail questionnaires
 The can be easily and quickly distributed
 They can reach a large number of people
 You do not have to write your name – so respondents can remain anonymous
 You can eliminate prejudices and biases of an interviewer.
 People can complete the questionnaire when it is convenient for them
 Questionnaires save time for the interviewer and interviewee.
Disadvantages of Questionnaires
 Not everyone who receives the questionnaire will bother to reply
 People might not answer questions properly or leave some out.
 Getting people to reply on time is difficult.
 If the questionnaires are not designed properly they can be unreliable or invalid.
 Questions that are clear to one person might be confusing to another.
 Designing, testing and evaluating a questionnaire takes time.
Guidelines for Compiling a Questionnaire
 Give your Questionnaire a title that states its purpose and that identifies you and your
organisation.
 Provide clear instructions of what you want the respondent to do – tick, circle, choose and
answer, etc.
 Make your questions clear and unambiguous, as well as quick and easy to answer. For
example, to find out how people travel to work, you could ask:

 Use statements which are interpreted in the same way by members of different
subpopulations of the population of interest.
 Use statements where persons that have different opinions or traits will give different
answers.
 Use only one aspect of the construct you are interested in per item.
 Use positive statements and avoid negatives or double negatives.
 Do not make assumptions about the respondent.
 Use correct spelling, grammar and punctuation.
 Avoid items that contain more than one question per item (e.g. Do you like strawberries and
potatoes?).
Questionnaire Administration Modes
Main modes of questionnaire administration are:
 Face-to-face questionnaire administration, where an interviewer presents the items orally.
 Paper-and-pencil questionnaire administration, where the items are presented on paper.
 Computerized questionnaire administration, where the items are presented on the
computer.
 Adaptive computerized questionnaire administration, where a selection of items is
presented on the computer, and based on the answers on those items, the computer
selects following items optimized for the testee's estimated ability or trait.
How do you get to work? Circle the form of transport: car / bus / taxi / train /
bicycle / motorbike / other (say which) ________________.
Rather than, a question like: How you drive to work? (Which is open-ended and
ambiguous.)

Plan how you will score, calculate and evaluate your data. If you can, use a computer to tabulate
your data. Here are some suggestions for tallying your results
Recording Tallies on a Tally Sheet
Use stick figures in groups of four with the fifth stick crossing the fourth when you tally. For
example: IIII IIII IIII = 15
Please tell us what you think of our service by answering this
questionnaire and posting it in the slotted box next to the notice board.
Circle the number that describes how you view our service.
1 = bad, 3 = average, and 5 = excellent.
1. Our staff is friendly and helpful: 1 2 3 4 5
2. We clean the offices well: 1 2 3 4 5
3. Toilets are well cleaned: 1 2 3 4 5
4. We start and finish on time: 1 2 3 4
5
5. We do not disturb office workers: 1 2 3 4 5

Look at the example of a Tally Sheet on the next page.
Research Report
Once the research is complete and the researcher knows the (probable) answer to the research
question, s/he will compile a research report in line with organisational requirements.
Data and information can be presented in various ways:
 Multimedia presentations
 Computer graphics
Ranking: Rate our Service.
1 2 3 4 5
Question 1: III IIII II
Question 2: IIII IIII IIII
Question 3: II III I I
Question 4: IIII III II
Question 5: II III I IIII III
12 8 9 9 18
To summarise the responses, you would add the tallies. The total
tally for each item provides the ranking order. The tally will also tell
you the total number of the respondents. In this example, there
were 46 respondents in total.

The form of the presentation will be determined by:
 The audience
 The purpose of the presentation
 Logistical issues such as space, time, materials and the requirements of the work
environment
Data Types
Before deciding how the data will be represented, it is important that there are different types of
data:
Discrete Data
A set of data is said to be discrete if the values belonging to it are distinct and separate, i.e. they
can be counted. Discrete data is more easily reportable as opposed to non-discrete or unstructured
data.
Examples might include the number of cattle in a herd; the number of patients in a hospital; the
number of flaws in one meter of cloth; gender (male, female); blood group (O, A, B, AB).
Categorical Data
Categorical data is also referred to as frequency or qualitative data. It is a form of discrete data.
Things are grouped according to some common property (ies) and the number of members of the
group are recorded (e.g., males/females, vehicle type).
Each value is chosen from a set of non-overlapping categories.
For example, shoes in a cupboard can be sorted according to colour; the characteristic 'colour' can
have non-overlapping categories 'black', 'brown', 'red' and 'other'. People have the characteristic of
'gender' with categories 'male' and 'female'.
Categories should be chosen carefully since a bad choice can prejudice the outcome of an
investigation. Every value should belong to one and only one category, and there should be no
doubt as to which one.

Nominal Data
Nominal data are values that represent qualities rather than quantities and do so without any
reference to a linear scale (i.e. 'measurement' in terms of names or designations of discrete units
or categories).
Examples include telephone numbers, post codes, or soil types.
Scores on an interval scale can be added and subtracted but cannot be meaningfully multiplied or
divided.
Continuous Data
Data with a potentially infinite number of possible values along a continuum (e.g. age, height).
You can count, order and measure continuous data.
Frequency Table
A frequency table is a way of summarising a set of data. It is a record of how often each value (or
set of values) of the variable in question occurs. It may be enhanced by the addition of
percentages that fall into each category.
A frequency table is used to summarise categorical, nominal, and ordinal data. It may also be used
to summarise continuous data once the data set has been divided up into sensible groups.
A frequency table is constructed by arranging collected data values in ascending order of
magnitude with their corresponding frequencies.
For example, the time interval between the start of the years 1981
and 1982 is the same as that between 1983 and 1984, namely 365
days. The zero point, year 1 AD, is arbitrary; time did not begin
then.

Suppose that in thirty shots at a target, a marksman makes the following scores:
5 2 2 3 4 4 3 2 0 3 0 3 2 1 5
1 3 1 5 5 2 4 0 0 4 5 4 4 5 5
The frequencies of the different scores can be summarised as:
Score Frequency Frequency (%)
0 4 13%
1 3 10%
2 5 17%
3 5 17%
4 6 20%
5 7 23%

Formative assessment
Role play
Activity: 01
Instructions Explain how Situations or issues that can be dealt with through
statistical methods
Method Group Activity
Media Method Flipchart
Answers:
Critical Cross Field
Orgaisation
DEMONSTRATING
Marks 10

Project
Group Activity: 02
Instructions Identify Variables contributing to a problem situation in data
gathering, e.g. crime is related to time of day and location
Answers:
Orgaisation
Communicating
Marks 05

Research PROJECT
Activity: 03
Instructions List Appropriate and efficient methods used to collect, record
and organise data
Method Individual Activity
Answers:
Orgaisation
COLLECTING
Marks 10

Summative assessment
Simulation
ACTIVITY 01
Instructions Data samples are of adequate size and are representative of
the population
CCFO
ORGANISING
Mark 10
Answer:

Essay –Reflexive
Take some time to reflect on what you have learnt in this module and assess your
knowledge against the following pointers. Write down your answers. Should you not be
able to complete each of these statements, go back to your notes and check on your
understanding? You can also discuss the answers with a colleague.
Pose questions, collect and organise data

Learning Unit 2:
Introduction
1. Graphical representations and numerical summaries are consistent with the data,
are clear and appropriate to the situation and target audience.
2. Different representations of aspects of the data are compared to take a position
on the issue.
3. Calculations and the use of statistics are correct and appropriate to the problem.
4. Interpretations of statistics are justified and applied to answer questions about the
problem.
5. New questions that arise from the modelling of the data are discussed.
Conclusion
Represent, analyse and interpret data
using various techniques

A table is both a mode of visual communication and also a means of arranging data. It should be
seen as a container that holds information about like items. For example, an Employees table
would contain the same basic details on each employee: name, title, department and so on.
A table consists of an ordered arrangement of rows and columns and usually organises numerical
information in a grid format. A table can, however also be used to display data in the form of
symbols or pictures.
In a data table:
 The term row has several common synonyms (e.g., record, k-tuple, n-tuple, and vector).
 The term column has several common synonyms (e.g., field, parameter, property,
attribute).
 A column is usually identified by a name.
 A column name can consist of a word, phrase or a numerical index.
 A column is a set of data values of a particular simple type, one for each row of the table.
 The columns provide the structure according to which the rows are composed.
 The intersection of a row and a column is a cell.
The term field is often used interchangeably with column, although many consider it more correct
to use field (or field value) to refer specifically to the single item that exists at the intersection
between one row and one column (in one cell)
For example, a table that represents companies might have the following columns:
 ID (integer identifier, unique to each row)
 Name (text)
 Address line 1 (text)
 Address line 2 (text)
 Columns are arrangements of cells in which are vertical.
 Rows are arrangements of cells in which are horizontal.

 City (integer identifier, drawn from a separate table of cities, from which any state or
country information would be drawn)
 Postal code (text)
 Industry (integer identifier, drawn from a separate table of industries)
 etc.
Each row would provide a data value for each column and would then be understood as a single
structured data value, in this case representing a company.
What is a histogram?
In statistics, a histogram is a graphical representation, showing a visual impression of the
distribution of experimental data. It is an estimate of the probability distribution of a continuous
variable.
The heights of the bars represent observed frequencies.
Histogram Use
Histograms are best used when there is large amount of data presented in a table. Histograms are
like a snapshot as opposed reflecting a process' performance over time.
A histogram makes it easy to see where the majority of values fall in a measurement scale, and
how much variation there is.
The Parts of a Histogram
Column 1 Column 2
Row 1 Row 1, Column 1 Row 1, Column 2

A Histogram is made up of five parts:
Title: The title is a brief description of the information that is contained
in the Histogram.
Horizontal or X-Axis: The horizontal or X-axis indicates the scale of values into which
the measurements fit. These measurements are grouped into
intervals to help you summarize large data sets. Individual data
points are not displayed.
Bars: The bars have two important characteristics—height and width.
The height represents the number of times the values within an
interval occurred. The width represents the length of the interval
covered by the bar. It is the same for all bars.
Vertical or Y-Axis: The vertical or Y-axis is the scale that shows you the number of
times the values within an interval occurred. The number of times
is also referred to as "frequency."
Legend: Legend provides additional information that documents where
the data came from and how the measurements were gathered.
An example of a Histogram is given on the next page.Histograms are used to examine existing
patterns, identify the range of variables, and suggest a central tendency in variables.

The Shape of the Distribution
Symmetry
A distribution of scores may be symmetrical or asymmetrical. Imagine constructing a histogram
centered on a piece of paper and folding the paper in half the long way. If the distribution is
symmetrical, the part of the histogram on the left side of the fold would be the mirror image of the
part on the right side of the fold.
A teacher grades tests and the results are as follows:
Data
Student Grade
Bullwinkle 84
Rocky 91
Bugs 75
Daffy 68
Wylie 98
Mickey 78
Minnie 77
Lucy 86
Linus 94
Asterix 64
Obelix 59
Donald 54
Sam 89
Taz 76
She then creates bins of width 10 points: . . . , 30-39, 40-49, 50-59,
60-69, 70-79, . . . . The number of test scores in each data bin is
recorded and plotted as a bar graph.

If the distribution is asymmetrical, the two sides will not be mirror images of each other. A true
symmetric distribution is referred to as a normal distribution. Asymmetric distributions are more
commonly found.
Skewness
An asymmetric distribution can either be positively skewed or negatively skewed.
A distribution is said to be positively skewed if the scores tend to cluster toward the lower end of
the scale (that is, the smaller numbers) with increasingly fewer scores at the upper end of the scale
(that is, the larger numbers).
A negatively skewed distribution is exactly the opposite. With a negatively skewed distribution,
most of the scores tend to occur toward the upper end of the scale while increasingly fewer scores
occur toward the lower end.
Calculating Statistics
The Sample Mean
Add up all of the data points and divide by the number of data points.

The sample mean is an estimator available for estimating the population mean (average). It is a
measure of location, commonly called the average, often symbolised
The value of the sample mean depends equally on all of the data which may include outliers. It
may not appear representative of the central region for skewed data sets. It is especially useful as
being representative of the whole sample for use in subsequent calculations.
The Median
The Median is the middle number (in a sorted list of numbers). Half the numbers in the list are less,
and half the numbers are greater.
To find the Median, place the numbers you are given in value order and find the middle number.
What is the mean of 2, 7 and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e. we added 3 numbers): 18 ÷ 3 =
6
So the Mean is 6
Let’s say our data set is:5 3 54 93 83 22
17 19.
Find the Median of {12, 3 and 5}. Put them in order: {3, 5, 12}, the
middle number is 5, so the median is 5.

If there are two middle numbers (as happens when there are an even amount of numbers) then
average those two numbers.
With an odd number of data values, for example 21, we have:
Data 96 48 27 72 39 70 7 68 99 36 95 4 6 13 34 74 65 42 28 54 69
Ordered Data 4 6 7 13 27 28 34 36 39 42 48 54 65 68 69 70 72 74 95 96 99
Median 48, leaving 10 values below and 10 values above
With an even number of data values, for example 20, we have:
Data 57 55 85 24 33 49 94 2 8 51 71 30 91 6 47 50 65 43 41 7
Ordered Data 2 6 7 8 24 30 33 41 43 47 49 50 51 55 57 65 71 85 91 94
Median
Halfway between the two 'middle' data points - in this case
halfway between 47 and 49 = 48
It is generally a good descriptive measure of the location which works well for skewed data or data
with outliers.
The Mode
The mode is the number that appears most often in a set of numbers.
Find the Median of {12, 3, 5 and 2}. Put them in order: {2, 3, 5, 12},
the middle numbers are 3 and 5, the average of 3 and 5 is 4, so the
median is 4.
In {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).

Suppose the results of an end of term Statistics exam were distributed as follows:
Student Score
1 94
2 81
3 56
4 90
5 70
6 65
7 90
8 90
9 30
Then the mode (most common score) is 90, and the median (middle score) is 81.
Dispersion
The data values in a sample are not all the same. This variation between values is called
dispersion.
Common examples of measures of statistical dispersion are the variance, standard deviation and
interquartile range. These measures indicate to what degree the individual observations of a data
set are dispersed or 'spread out' around their mean (average).
The Range
Range is the difference between the lowest and highest values.
In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the
range is 9-3. Equals 6.

The range of a sample (or a data set) is a measure of the spread or the dispersion of the
observations. It is the difference between the largest and the smallest observed value of some
quantitative characteristic and is very easy to calculate.
A great deal of information is ignored when computing the range since only the largest and the
smallest data values are considered; the remaining data are ignored.
The range value of a data set is greatly influenced by the presence of just one unusually large or
small value in the sample (outlier).
Inter-Quartile Range (IQR)
It is the highest number and the lowest number in a set of numbers.
The inter-quartile range is a measure of the spread of or dispersion within a data set.
It is calculated by taking the difference between the upper and the lower quartiles.
An outlier is an extreme deviation from the mean.
The range of 65,73,89,56,73,52,47 is: 89 - 47 = 42.
If the highest score in a 1st Year Statistics Exam was 98 and the lowest 48, then
the range would be 98 - 48 = 50.
7, 5, 1, 8, 5, 5, 7, 2, 7, 9.
Range: 1 – 9

Quartile and Percentile
Percentiles are values that divide a sample of data into one hundred groups containing (as far as
possible) equal numbers of observations.
For example, 30% of the data values lie below the 30th percentile.
Quartiles are values that divide a sample of data into four groups containing (as far as possible)
equal numbers of observations.
A data set has three quartiles. References to quartiles often relate to just the outer two, the upper
and the lower quartiles; the second quartile being equal to the median.
Data 2 3 4 5 6 6 6 7 7 8 9
Upper quartile 7
Lower quartile 4
IQR 7 - 4 = 3
Data 6 47 49 15 43 41 7 39 43 41 36
Ordered Data 6 7 15 36 39 41 41 43 43 47
Median 41
Upper quartile 43
Lower quartile 15

Sample Variance
Sample variance is a measure of the spread of or dispersion within a set of sample data.
The sample variance is the sum of the squared deviations from their average divided by one less
than the number of observations in the data set.
To calculate the variance, follow these steps:
 Work out the Mean (the simple average of the numbers)
 Then for each number: subtract the Mean and then square the result (the squared
difference).
 Then work out the average of those squared differences.

Standard Deviation
Standard deviation is a measure of the spread or dispersion of a set of data. The more widely the
values are spread out, the larger the standard deviation. The Standard Deviation is just the square
root of Variance, so:
Standard Deviation: σ = √21,704 = 147
The good thing about the Standard Deviation is that it is useful. Now we can show which heights
are within one Standard Deviation (147mm) of the Mean.
You and your friends have just measured the heights of your dogs
(in millimeters):
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and
300mm.
Find out the Mean, the Variance, and the Standard Deviation.
Step 1: Calculate the mean
Mean =
600 + 470 + 170 + 430 + 300
=
1970
= 394
5 5
so the mean (average) height is 394 mm.
Step 2: Calculate the Variance
To calculate the Variance, take each difference, square it, and then average the
result:
σ2
=
2062
+ 762
+ (-224)2
+ 362
+ (-94)2
=
108,520 =
21,7045 5

Using the Standard Deviation we have a "standard" way of knowing what is normal, and what is
extra large or extra small.
Why square?
Squaring each difference makes them all positive numbers (to avoid negatives reducing the
Variance)
And it also makes the bigger differences stand out. For example 1002
=10,000 is a lot bigger than
502
=2,500.
But squaring them makes the final answer really big, and so un-squaring the Variance (by taking
the square root) makes the Standard Deviation a much more useful number.
Coefficient of Variation
The coefficient of variation measures the spread of a set of data as a proportion of its mean. It is
often expressed as a percentage.
The coefficient of variation (CV) is defined as the ratio of the standard deviation to the mean :

The coefficient of variation is useful because the standard deviation of data must always be
understood in the context of the mean of the data. The coefficient of variation is a dimensionless
number. So when comparing between data sets with different units or widely different means, one
should use the coefficient of variation for comparison instead of the standard deviation.

Role play
Activity: 04
Instructions Graphical representations and numerical summaries are
consistent with the data, are clear and appropriate to the
situation and target audience
Answers:
Orgaisation
DEMONSTRATING
Marks 10

Project
Group Activity: 05
Instructions Different representations of aspects of the data are compared
to take a position on the issue
Answers:
Orgaisation
Communicating
Marks 05

Research PROJECT
Activity: 06
Instructions Calculations and the use of statistics are correct and
appropriate to the problem
Answers:
Orgaisation
COLLECTING
Marks 10

Simulation
ACTIVITY 02
Instructions Interpretations of statistics are justified and applied to answer
questions about the problem
CCFO
ORGANISING
Mark 10
Answer:

Essay –Reflexive
Represent, analyse and interpret data using various techniques

Learning Unit 3:
Introduction
1. Data are gathered, organised, sorted and classified in a suitable manner for
further processing and analysis.
2. Experiments and simulations are chosen appropriately in terms of the situation to
be investigated.
3. Probabilities are determined correctly.
4. Distinctions are correctly made between theoretical and experimental
probabilities.
5. Predictions are based on validated experimental or theoretical probabilities.
6. The outcomes of experiments and simulations are communicated clearly.
Use random events to explore and apply,
probability concepts in simple life

Conclusion
Geometrical Symmetry
The most familiar type of symmetry for many people is geometrical symmetry.
There are 4 types of geometrical symmetry in figures are,
 Reflection symmetry
 Rotation symmetry
 Translation symmetry
 Glide reflection symmetry
These will be discussed in more detail later on.
The Properties of Plane Shapes
A plane shape is a two-dimensional shape that has width and breadth, but no thickness.
A symmetrical shape is one that has similarity in size, shape, and
relative position of corresponding parts

The Perimeter
To find the perimeter of a rectangle, just add up all the lengths of the sides:
Perimeter = L + w + L + w
= 2L + 2w
The Area
To find the area of a rectangle, just multiply the length times the width:
Area = L x w
The Properties of a Parallelogram
A parallelogram is a quadrilateral that has two pairs of parallel
sides.
The perimeter is the total distance around the outside of a shape
Area is defined as the number of square units that covers a closed
figure.

The Perimeter
In the case of a parallelogram, each pair of opposite sides is the same length, so the perimeter is
twice the base plus twice the side length. Or as a formula:
perimeter = 2(a+b)
where:
b is the base length of the parallelogram
a is the side length
The Area
Area = b × h
b = base
h = vertical height
The Properties of a Circle

The Perimeter
𝑃 = 2𝜋𝑟
The Area
𝐴 = 𝜋𝑟2
The Properties of a Trapesium
The Perimeter
Perimeter of Trapesium = a + b + c + d
where
a, b, c, d = sides
The Area
Area = ½(a+b) × h
h = vertical height

Pythagoras Theorem
"Pythagoras' Theorem" and can be written in one short equation:
a2
+ b2
= c2
Note:
 c is the longest side of the triangle
 a and b are the other two sides
If the triangle had a right angle (90°) and you made a square on
each of the three sides, then the biggest square had the exact
same area as the other two squares put together.

Role play
Activity: 07
Instructions Data are gathered, organised, sorted and classified in a
suitable manner for further processing and analysis
Answers:
Orgaisation
DEMONSTRATING
Marks 10

Project
Group Activity: 08
Instructions Experiments and simulations are chosen appropriately in terms
of the situation to be investigated
Answers:
Orgaisation
Communicating
Marks 05

Research PROJECT
Activity: 09
Instructions Probabilities are determined correctly
Answers:
Orgaisation
COLLECTING
Marks 10

Simulation
ACTIVITY 03
Instructions Distinctions are correctly made between theoretical and
experimental probabilities
CCFO
ORGANISING
Mark 10
Answer:

Essay –Reflexive
Use random events to explore and apply, probability concepts in simple life.

Annexure 1: Growth Action Plan
The personal development plan will enable you address any areas of weakness that you
identify during the course and stimulate your desire for personal growth.
Growth Action Plan
I have identified the following as areas in which I need to improve in order to
become competent. List in order of priority.
Actions to
be taken
Resources Completion date Evidence
Learner Name:
Learner Signature:
Facilitator Name:
Facilitator Signature:

Annexure 2: Words that are new to me
Compile a list of words that is new to you and discuss the meaning of the words with your
facilitator.
Term Description
e.g. characteristic
Trait, feature, quality, attribute, etc
Learner Name:
Learner Signature:
Facilitator Name:
Facilitator Signature:

Annexure 3: Training Evaluation
Training Program
Facilitator Name
Date
Ratings:
1 Poor
2 Areas for Improvement
3 Meet the standard requirements
4 Very Good
5 Excellent
Tick where appropriate:
Did the training relate to your job e.g. skills, knowledge? 1 2 3 4 5
Comments:
To what extent will your performance improve as a
result of attending this training
1 2 3 4 5
Comments:
To what extent would you recommend this course to others? 1 2 3 4 5
Comments:
Did this training meet your desired needs? 1 2 3 4 5
Comments:
Was the training material user friendly / easy to understand? 1 2 3 4 5

Annexure 4: Evaluation of Facilitator
Ratings:
1 Poor
2 Areas for Improvement
3 Meet the standard requirements
4 Very Good
5 Excellent
Tick where appropriate:
1 2 3 4 5
Preparation for the training
Knowledge of subject
Handling of questions
Interaction with participants
Voice clarity
Use of training aids (flip charts, handouts, etc)
Facilitator made training exciting
Recommendation of facilitator for future training
Other comments on Facilitator’s delivery of his training

2.Bibliography
Acknowledgements & Reference
The following web-sites have been used for research:
Supplier
Yellow Media Publishers
Senior learning material Developer:
Ms Duduzile Zwane
www.yellowmedia.co.za
dudu@yellowmedia.co.za

SECTION C: SELF REFLECTION
I enjoyed/did not enjoy this module because:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
I enjoyed/did not enjoy this module because:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
I found group work ___________________________________!!!
The most interesting thing I learnt was:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
I feel I have gained the necessary skills and knowledge to:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
______________________________________________________________
______________________________________________________________

Please add the following to this module:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
Some comments from my classmates about my participation in class:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
____________________________________________________________
_____________________________________________________________

Self-Assessment
Self-Assessment:
You have come to the end of this module – please take the time to
review what you have learnt to date, and conduct a self-assessment
against the learning outcomes of this module by following the
instructions below:
Rate your understanding of each of the outcomes listed below:
Keys:  - no understanding
 - Some idea
 - Completely comfortable
NO OUTCOME
SELF
RATING
  
1. Pose questions, collect and organise data.
2.
Represent, analyse and interpret data using various
techniques
3.
Use random events to explore and apply, probability concepts
in simple life.

Learner Evaluation Form
Learning
Programme Name
Facilitator Name
Learner name
(Optional)
Dates of
Facilitation
Employer / Work
site
Date of
Evaluation
Learner Tip:
Please complete the Evaluation Form as thoroughly as you are able
to, in order for us to continuously improve our training quality!
The purpose of the Evaluation Form is to evaluate the following:
 logistics and support
 facilitation
 training material
 assessment
Your honest and detailed input is therefore of great value to us, and
we appreciate your assistance in completing this evaluation form!

A Logistics and Support Evaluation
No Criteria / Question
Poor
BelowStandard
Sufficient
AboveStandard
Excellent
1 Was communication regarding attendance of the
programme efficient and effective?
2 Was the Programme Coordinator helpful and efficient?
3 Was the training equipment and material used effective and
prepared?
4 Was the training venue conducive to learning (set-up for
convenience of learners, comfortable in terms of
temperature, etc.)?
Additional Comments on Logistics and Support
Poor
BelowStandard
Sufficient
AboveStandard
Excellent
B Facilitator Evaluation
1 The Facilitator was prepared and knowledgeable on the
subject of the programme
2 The Facilitator encouraged learner participation and input
3 The Facilitator made use of a variety of methods,
exercises, activities and discussions
4 The Facilitator used the material in a structured and
effective manner
5 The Facilitator was understandable, approachable and
respectful of the learners
6 The Facilitator was punctual and kept to the schedule
Additional Comments on Facilitation

Poor
Below
Standard
Sufficient
Above
Standard
Excellent
1 2 3 4 5
C Learning Programme Evaluation
1 The learning outcomes of the programme are
relevant and suitable.
2 The content of the programme was relevant
and suitable for the target group.
3 The length of the facilitation was suitable for
the programme.
4 The learning material assisted in learning new
knowledge and skills to apply in a practical
manner.
5 The Learning Material was free from spelling
and grammar errors
6 Handouts and Exercises are clear, concise
and relevant to the outcomes and content.
7 Learning material is generally of a high
standard, and user friendly
Additional Comments on Learning Programme
D Assessment Evaluation
Poor
Below
Standard
Sufficient
Above
Standard
Excellent
1 2 3 4 5
1 A clear overview provided of the assessment
requirements of the programme was provided
2 The assessment process and time lines were clearly
explained
3 All assessment activities and activities were discussed
Additional Comments on Assessment

9012 Investigate life and work related problems using data and probabilities

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