STATISTICS AND PROBABILITY GRADE 11 LESSON

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Chapter 1:
Describing Data
Lesson 1: Variation in Data
TIME FRAME: 1 hour session
OVERVIEW OF LESSON
In this activity, students will be asked to provide some data that will be submitted for
consolidation by the teacher for future lessons. Data on heights and weights, for instance, will be
used for calculating Body Mass Index in Lesson 3. Students will also discuss the concept of
statistical questions (in relation to non-statistical ones), then work in groups to discover variation
in data. Students will be asked to imagine that the data they obtained in their groups would now
be collected for much larger groups (the entire class, all grade 11 students in school, all grade 11
students in the district), and to discuss how data could be summarized.
LEARNING COMPETENCIES: At the end of the lesson, the learner should be able to:
 distinguish statistical questions from non-statistical questions,
 recognize that data possess variability,
 identify methods for summarizing data to answer statistical questions, i.e., sort, classify,
and organize data in tabular form and present this into a pictographs, bar charts, etc.
LESSON OUTLINE:
0. Preliminaries
1. Introduction on Statistics as the Science that Studies Data
2. Initial Lesson: Statistical and Non Statistical Questions
3. Main Lesson: Data and Statistics
4. Small Data Collection Activity and Planning for Data Analysis
DEVELOPMENT OF THE LESSON
(A)Preliminaries (for Future Lessons)
Before the lesson and course starts, prepare a sheet of paper listing everyone’s name in class
with a “Student Number” (see next page). The student number is a random number chosen
in the following fashion:
(a) Make a box with “tickets” listing the numbers 1 up to the number of students in class.
(b) Shake the box, get a ticket, and give the number in the ticket to the first person in the
list.
(c) Shake the box again, get another ticket, and give the number of this ticket to the next
person in the list.
(d) Do (c) until you run out of tickets in the box.

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Once the list (see next page) is finished, make sure to inform students confidentially of their
student numbers. Perhaps, when the attendance is called, each student can be provided a
separate piece of paper that lists her/his name and student number. Tell students to
remember their student number, and to always use this throughout the class whenever data
are requested of them. Explain to students that in data collection specific identities are not
required, especially because people have a right to confidentiality, but there should be a way
to develop and maintain a database to check quality of data provided, and verify from
respondent in data collection activity the data provided.
Explanatory Note: These preliminary steps for generating a student number and informing
students confidentially of their student number are essential for the “data collection”
activities to be taken in this lesson and other lessons so that students can be uniquely
identified, without having to obtain their names. In statistical activities, facts are collected
from respondents for purposes of getting aggregate information, but confidentiality should
be protected. This way, respondents can be truthful in giving information, and the researcher
can give a commitment to respondents that the data they provide will never be released to
anyone in a form that will identify them without their authorization.

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Student Name Student Number
1.
2,
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32,
33.
34.
35.

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(B) Introduction
Provide students their “student numbers” and ask them to fill out Activity Sheet 1-01a. After
3-5 minutes, tell students to submit the Sheet to you so you can put all records on the Class
Recording Sheet. Explain to students that compiling all these records from everyone in the
class is an example of a census since data has been gathered from every student in class.
Mention that the government, through the Philippine Statistics Authority (PSA), conducts
censuses to obtain information about socio-economic conditions in the country. This helps
government makes plans, such as how many schools and hospitals to build. Censuses of
population and housing are conducted every 10 years on years ending in zero (e.g., 1990,
2000, 2010) to obtain population counts, and demographic information about all Filipinos.
Mid-decade population censuses have also been conducted since 1995. Censuses of
agriculture, and of Philippine business and industry, are also conducted by the PSA to obtain
information on production and other relevant economic information.
Inform students that the student numbers they were given are meant to identify them without
having to know their specific identities in the class recording sheet (which will contain the
consolidated records everyone provided). This helps protect confidentiality of information.
Mention that the PSA is bound by law to protect the confidentiality of information provided
by respondents. Even market research organizations in the private sector and individual
researchers also guard confidentiality as they merely want to obtain aggregate data.
Ask students what comes to their minds when they hear the term “data” (which may be
viewed as a collection of facts from experiments, observations, sample surveys and
censuses, and administrative reporting systems).
Give them a follow up question about whether data, such as the facts they gave in activity
sheet 1-01a, would be the same or varying from person to person. Even if the data varies,
some numbers may show up more than once in the entire data set. The frequency of a
particular data value is the number of times the data value occurs.
(C)Initial Lesson: Statistical Questions and Non-Statistical Questions
Tell students that data are collected to answer statistical questions, the answers of which can
change depending on who it is asked to, and when it is asked (Non-statistical questions are
questions that anticipate a single answer.)
Give a 5 minute exercise to the students on distinguishing statistical questions from non-
statistical questions.
Ask students which of the following are statistical questions and why:
 How old is student number 3 (in the class list)? (Not a statistical question since only
a particular fact, the age of student number 3, is of interest)
 How old are the people who watch the most recent episode of the television show
“Maalaala Mo Kaya?” (Statistical question since this will require getting data on
ages of all viewers of the tv show)

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 Do dogs eat more than cats? (Statistical question since this will require getting
data on the amount of food eaten by dogs and cats, maybe a sample of them, for
a reference period, say past week, or past month)
 Is the vehicle of the Mayor of our city/town/municipality bigger than the vehicle used
by the President of the Philippines? (Not a statistical question since only a particular
fact, size of mayor’s car in relation to size of vehicle of president, is of interest)
 How many days are there in December? (Not a statistical question since only a
particular fact, number of days in December, is of interest)
 Does it rain more in Cebu than in Davao? (Statistical question since this will
require getting rainfall data on the two cities in a reference period, say past
month, past year)
 Do I have a college degree? (Not a statistical question since only a particular fact,
whether or not I have a college degree, is of interest)
 How much was the Supreme Court Chief Justice’s last paycheck for? Not a statistical
question since only a particular fact, the amount of income received by the SC CJ in
the last paycheck, is of interest)
 Do math teachers earn more than science teachers? (Statistical question since
this will require getting data on income/wages of either all math and science
teachers, or even a sample of these teachers)
 How many searches on Google do residents in Makati City (or some other city
near the school) conduct each day? (Statistical question since this will require
getting data on the frequency of Google searches of residents of Makati or
whatever city of interest)
 What is the weight of Student A, say Ana (or whatever random name you can get
from the list of student names)? (Not a statistical question since only a particular fact,
weight of Student A is being asked)
 What is the proportion of students in class who are underweight or overweight
for their age? (Statistical question since this will require getting data on the
weights of all students in class, comparing these weights to a reference weight for
student ages, and determining the percentage of students that are underweight
or overweight for their age)
(D)Main Lesson: Data and Statistics
Suggest to students that data may be viewed as the facts (counts, measurements, or opinions)
obtained to answer a statistical question.
Define Statistics is a science that studies data, and what we can do with data. Suggest that
this involves processes from collecting, processing (including performing quality checks),
analyzing, interpreting and communicating data.
Trivia: The word “statistics” actually comes from the word “state”— because governments
have been involved in the statistical activities, especially the conduct of censuses either for
military or taxation purposes. The need for and conduct of censuses are recorded in the pages
of holy texts. In the Christian Bible, particularly the Book of Numbers, God is reported to
have instructed Moses to carry out a census. Another census mentioned in the Bible is the

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census ordered by Caesar Augustus throughout the entire Roman Empire before the birth of
Christ.
Inform students that uncovering patterns in data involves not just science but also art, and
this is why some people may think “Stat is eeeks!” and may view any statistical procedures
and results with much skepticism. (See Figure 1-1.)
Make known to students that statistical methods enable us to
 characterize persons, objects, situations, and phenomena;
 explain relationships among variables ;
 formulate objective assessments and comparisons; and,
 make evidence-based decisions and predictions.
and that the main tasks of a statistician include:
 Designing the collection of data to answer statistical questions in a way that
maximizes information content and minimizes bias;
 Verifying the quality of the data after it is collected
 Examining data so that insight and meaningful information can be produced to
support decision making.
Figure 1-1. Cartoon: " ...recommended by 4 out of 5 quacks!"
(Source: http://www.cartoonstock.com)

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(E) Small Data Collection Activity and Planning for Data Analysis
Divide students into groups of five. Tell students to share with each other some opinions and
facts to answer about three questions (that will not yield a “sensitive” response). They may
use questions for Activity Sheet 1-01a:
 What is their height (in cm?) and weight (in kg)? the age of their mother?
 What is their favorite color?
 How do they feel today?
Or other questions (that will not yield a sensitive response):
 Are the five students satisfied with the way the mayor does his/her job? (yes, no,
unsure, no opinion)
 How many hours did the students watch television during the past seven days?
 How many hours did they go on facebook yesterday?
Explanatory Note about Data Collection Activity: The questions listed above are indicative
to help students learn that data has variation. It is crucial to ask questions of interest that are
not culturally sensitive.
After 5 minutes of sharing answers with each other, ask students whether the answers shared
with each other were the same, or whether they varied.
Tell students to imagine that these same questions would now be asked of all grade 11
students in the entire school, or in the entire district.
Ask them how they would summarize the information collected.
Possible Answers:
 Histogram for heights and weights of students
 Histogram for ages of their fathers and for their mothers
 Bar chart or Pie Chart for (Distribution of) favorite color
 Pictogram/Pie chart/Bar chart on satisfaction with the mayor
 Bar chart/Pie chart for hours spent watching television in the past 7 days
 Bar chart for hours spent on facebook yesterday
KEY POINTS
 Difference between a statistical question and a non-statistical question
 The bedrock of statistics (the science that studies data) is data, which is characterized by
variation.
 We can summarizing data collected to answer a statistical question by way of
o Graphs (pictographs, bar graphs)
o Summary numbers (median, mode)

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REFERENCES
Albert, J. R. G. (2008).Basic Statistics for the Tertiary Level (ed. Roberto Padua, Welfredo
Patungan, Nelia Marquez), published by Rex Bookstore.
Workbooks in Statistics 1: 11th
Edition, Institute of Statistics, UP Los Banos, College Laguna
4031
https://www.khanacademy.org/math/probability/statistical-studies/statistical-
questions/v/statistical-questions
https://www.illustrativemathematics.org/content-standards/tasks/703

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ACTIVITY SHEET NUMBER 1-01a
Students should completely fill out the following:
1. Student Number : _________________________
2. Sex (put a check or cross):
________ Male ________ Female
3. Number of siblings : _________________________
4. Weight (in kilograms) : _________________________
5. Height (in meters) : _________________________
6. Age of mother (as of her last birthday in years) : _________________________ (if mother
deceased, provide age if she were alive)
7. Daily allowance in school (in pesos) : _________________________
8. Daily food expenditure in school (in pesos) : _________________________
9. Usual number of text messages sent in a day : _________________________
10. Favorite color (put a check or cross; choose only one):
____White ____Red ____ Pink ____ Orange ____Yellow ____Green
____Blue ____Purple ____Brown ____Gray ____Black
11. Usual Sleeping Time (on weekdays): _________________________
12. On a scale from 1 (very unhappy) to 10 (happiest), how do you feel today? : ____________

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ACTIVITY SHEET 1-01b.
Groups should fill out responses to some questions :
Student ID
Question
1.
2.
3.
Are the responses varying or the same?
How can we summarize the data collected for each of the questions above (especially if we
consolidate the data from the entire class) ?

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CLASS RECORDING SHEET 1-01a (for the Teacher)
(PRINT MORE THAN 1 copy, if necessary)
Student
Number
Sex
( 1=
male; 2
female)
Number
of
siblings
Reported
Weight
(in kg)
Reported
Height
(in m)
Age of
mother
(in
years)
. Daily
allowance
in school
Daily food
expenditure
in school
Usual
number
of text
messages
sent in a
day
Usual
Sleeping
Time (on
weekdays)
Rating
on
Feeling
Today (1
very
unhappy,
10
happiest)
Actual
Weight
(in
kg)*
Actual
Height
(in
m)*
* to be obtained in next lesson

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ASSESSMENT
1. Name at least one difference between a statistical question and a non statistical question.
ANSWER: Statistical questions are answered by collecting data with variation (and consequently
summaries for the data will be required), while non-statistical questions are questions where answer
require specific facts (and not data with variation), so summary statistics and graphs will not be needed
for non-statistical questions.
2. Ten persons were randomly selected and asked how many letters were in their middle names,
and we received the following data: 6, 6, 7, 12, 15, 7, 8, 7, 6, 7
 Ask students to make a bar graph with this data
Answer:
01234
Frequency
5 10 15
letters

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3. Martin collected data over the last 10 days on the amount of hours of sleep he had every night,
and made a line plot of these data.
 What was the most sleep he got in one night? __________________ Answer: 12 hrs
 What was the least amount of sleep he got in one night? ________________ Answer: 7 hrs
 What is the most common amount of sleep I get? _________________ Answer:8 hrs
 How many nights did he sleep less than 9 hours? _________________ Answer: 6 nights
 How many nights did he sleep more than 9 hours? _____________ Answer: 2 nights
4. Ronald collected information about favorite sports among his friends
 What is the most popular type of dog from the data? Answer: Basketball
 How many of Ronald’s friends that were questioned do not consider Basketball or Football
as their favorite sport? Answer: 5
 How many friends did Ronald question? Answer : 12
Explanatory Note: Teachers have the option to just ask this assessment orally to the entire class, or
to group students and ask them to identify answers, or to give this as homework, or to use some
questions/items here for a chapter examination.
0
1
2
3
4
5
6
Favorite Sport
Frequency
Sport
Chess Basketball Football Volleyball
Hours of Sleep per Night:
x
x
x x x
x x x x x
6 7 8 9 10 11 12
x – one night