mathematics

1. STATISTICS & DATA
REPRESENTATION

2. What is Statistics
• Statistics is a science that involves the use of numerical
data.
• It can be defined as “science of collecting, organizing,
presenting, analyzing, and interpreting numerical data to
help in process of making decisions
• The profession that involve statistics is called a “statistician”.
• Statistics use in marketing, accounting, quality control,
and others.

3. Why study Statistics?
1. Data are everywhere
2. Statistical techniques are used to make many decisions
that affect our lives
3. No matter what your career, you will make
professional decisions that involve data. An
understanding of statistical methods will help you
make these decisions efectively

4. Applications of statistical concepts
in the business world
• Finance – correlation and regression, index numbers,
time series analysis
• Marketing – hypothesis testing, chi-square tests,
nonparametric statistics
• Personel – hypothesis testing, chi-square tests,
nonparametric tests
• Operating management – hypothesis testing,
estimation, analysis of variance, time series analysis

5. Types of Statistics
• There are 2 types of
statistics;
1. descriptive statistics
2. inferential statistics.

6. Descriptive Statistics
• Describe the sample data (basic features)
• Provide simple summaries about data and the
measures together with graphical analysis.
• Definition: organizing, presenting, and analyzing
numerical data.
• Used to present quantitative description in
manageable form.

7. Inferential
Statistics
• Involves using a sample to draw conclusions
about a population.
• Estimation
e.g., Estimate the population mean weight using the
sample mean weight
• Hypothesis testing
e.g., Test the claim that the population mean weight is
70 kg
• Inference is the process of drawing conclusions or
making decisions about a population based on sample
results

8. Term in Statistics
• Data consists of
information coming from
observations, counts,
measurements, or
responses.
• A population is the collection
of all outcomes, responses,
measurement, or counts that
are of interest.
• A sample is a subset of
a population.

9. Parameter &
Statistics
• A parameter is a numerical description of a
population characteristic.
• A statistic is a numerical description of a sample
characteristic.
Parameter Population
Statistic Sample

10. Data
• Statistical data are usually obtained by counting or
measuring items. Most data can be put into the following
categories:
• Qualitative - data are measurements that each fail into
one of several categories. (hair color, ethnic groups and
other attributes of the population)
• quantitative - data are observations that are measured
on a numerical scale (distance traveled to college,
number of children in a family, etc.)

11. Qualitative Data
• Qualitative data are generally described by words or letters.
They are not as widely used as quantitative data because many
numerical techniques do not apply to the qualitative data.
• For example, it does not make sense to find an average hair
color or blood type.
• Qualitative data can be separated into two subgroups:
1) dichotomic (if it takes the form of a word with two options
(gender
- male or female)
2) polynomic (if it takes the form of a word with more than
two options (education - primary school, secondary
school and university).

12. Quantitative Data
Quantitative data are always numbers and are the
result of counting or measuring attributes of a population.
Quantitative data can be separated into
two subgroups:
• discrete (if it is the result of counting (the number of
students of a given ethnic group in a class, the number of
books on a shelf,
...)
• continuous (if it is the result of measuring (distance
traveled, weight of luggage, …)

13. Type of Data
• Data sets can consist of two types of data: qualitative data
and quantitative data
Data
Qualitativ
e Data
Quantitativ
e Data
Consists of
attributes,
labels, or
non-
numerical
Consists of
numerical
measurements
or counts.

14. Types of variables
Variables
Quantitative
Qualitative
Dichotomic Polynomic Discrete Continuous
Gender, marital
status
Brand of Pc, hair
color
Children in family,
Strokes on a golf
hole
Amount of income
tax paid, weight of a
student

15. Level of Measurement
• The level of measurement determines which statistical
calculations are meaningful. The four levels of
measurement are: nominal, ordinal, interval, and ratio.
Nominal
Levels
of
Measurement
Ordinal
Interval
Ratio
Lowest to
highest

16. Nominal
Level
Data at the nominal level of measurement are qualitative
only.
Levels
of
Measurement
Nominal
Calculated using names, labels,
or qualities. No mathematical
computations can be made at
this level.
Colors in
the
Malaysia
flag
Names of students
in your class
Textbooks you are
using this semester

17. OrdinalLevel
• Data at the ordinal level of measurement are
qualitative or quantitative.
Levels
of
Measurement
Class standings:
freshman,
sophomore,
junior, senior
Numbers on
the back of
each player’s
shirt
Ordinal
Arranged in order, but
differences between data
entries are not meaningful.
Top 50 songs
played on the
radio

18. Interval
Level
• Data at the interval level of measurement are quantitative. A
zero entry simply represents a position on a scale; the entry is not
an inherent zero.
Levels
of
Measurement
Temperatures Years on a timeline
Interval
Arranged in order, the differences
between data entries can be calculated.
Size of shoes

19. Ratio Level
• Data at the ratio level of measurement are similar to the
interval level, but a zero entry is meaningful.
Levels
of
Measurement
A ratio of two data values can be formed so one
data value can be expressed as a ratio.
Ratio
Ages Grade point averages Weights

20. Summary of Levels of
Measurement
Level of
measurement
Put data
in
categories
Arrange
data in
order
Subtract
data
values
Determine if
one data value
is a multiple of
another
Nominal Yes No No No
Ordinal Yes Yes No No
Interval Yes Yes Yes No
Ratio Yes Yes Yes Yes

21. Source of Data
•There are two source of
data
1. Primary data
2. Secondary data

22. Primary Data
• Specific information collected by the person who is doing
the research
• Data collect through survey, interviews, direct observations
and experiment. Example: Population Census
• Advantage:
1. High Respond rate
2. Accurate
• Disadvantage
1. Lot of time consuming, effort, and cost

23. Secondary Data
• Data that has been collected form other parties. Eg.
Journals, yearly report etc.
• Easily available
• Advantage
1.Convenient and less time effort, and cost
• Disadvantage
2. Produce error
3. May not meet specific needs

24. Presentation of
Data
“Method by which the people
organize, summarize and
communicate information
using a variety of tools such as
tables, graphs, and diagram.

25. Presentation
Data
Tabular
presentation
Visual
presentation
Graphical
Presentation
Diagrammatical
Presentation

26. Uses of Presentation
Easy and better
understanding of the subject
Provides first hand
information about data
Helpful in future analysis
Easy for making comparisons
Very attractive

27. Tabulation
It is a systematic and logical arrangement of classified data
in rows and columns.
”What sport do you play?”
Sport People
Soccer 100
Tennis 45
Gymnas 55
Swimming 80

28. Simple Table
Data relating to only one characteristics
Gender No of Students
Boys 10
Girls 20

29. Double Table
Data relating to only 2 characteristics
Gender Food Habit
Healthy food Non healthy food
Boys 3 7
Girls 5 15

30. Frequency Table
Method of organizing raw data in a
compact form by displaying the
characteristics and frequencies.
Can be used for quantitative (numerical
data) and qualitative data (categorical
data).
For quantitative, there are two type of
table, ie: grouped and ungrouped table

31. Construct Frequency Table
Participant ages at retirement
n = 32
lower class limit of first class – 48
No of classes =
Class width = range/ no of class = (74-48)/6= 4.33~5
56 58 62 62 69 48 70 71 72
56 51 65 64 59 60 61 49 65
66 58 62 67 59 62 64 63 48
54 74 55 70 52

32. Fill in the blank
Class
Interval
Frequency Class Limit Cumulated
frequency
Relative
frequency

33. Histogram
A graphical display of data
using bars of different
heights.
Displays the shape and
spread of numerical data.

34. Bar Graph
Graphical representation that used bars
to compare data among categories.
Can be plotted vertically or horizontally
Difference between histogram and bar
graph
1) histogram represent continuous
variable, bar graph is for discrete
variables.
2) Histogram present numerical
data, bar graph for categorical
data
3) No gap between the bars for
histogram, there are gaps
between bars in bar graph.

35. Frequency
Polygon
A graphical form of
representation of data
Used to depict the shape of
the data and trends.
Usually drawn with the help
of a histogram but can be
drawn without it as well.

36. Ogive
Cumulative histogram that can be used
to determine how many data values lies
above or below a particular value in a
data set.
Is calculated from a frequency table by
adding each frequency to the total of
frequencies.
There are two type of ogive
More than ogive
Less than ogive

37. Pie Chart
Circular statistical graph which
divide into slices to illustrate
numerical proportion.
Usually represent percentage or
proportion or by angle for each
category

38. Stem and
Leaf
A table used to display data.
Stem is on the left displays
the first digit
Leaf is on the right and
display last digit
Is used to presenting
quantitative data to visualize
the distribution.

39. THANK YOU