Statistics and

Probability
Quarter 4 – Module 18:
Calculating the Pearson’s
Sample Correlation Coefficient
Statistics and Probability – Grade 11
Alternative Delivery Mode
Quarter 4 – Module 18: Calculating the Pearson’s Sample Correlation Coefficient
First Edition, 2020
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 Statistics and
Probability
Quarter 4 – Module 18:
Calculating the Pearson’s
Sample Correlation Coefficient
Introductory Message
For the facilitator:

Welcome to the Statistics and Probability for Senior High School Alternative
Delivery Mode (ADM) Module on Calculating the Pearson’s Sample Correlation
Coefficient!

This module was collaboratively designed, developed, and reviewed by educators

both from public and private institutions to assist you, the teacher or the
facilitator, in helping the learners meet the standards set by the K to 12
Curriculum while overcoming their personal, social, and economic constraints in
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This learning resource hopes to engage the learners into guided and independent
learning activities at their own pace and time. Furthermore, this also aims to help
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In addition to the material in the main text, you will also see this box in the body of
the module:

Notes to the Teacher

This contains helpful tips or strategies
that will help you in guiding the learners.

As a facilitator, you are expected to orient the learners on how to use this module.
You also need to keep track of the learners' progress while allowing them to
manage their own learning. Furthermore, you are expected to encourage and assist
the learners as they do the tasks included in the module.

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For the learner:

Welcome to the Statistics and Probability for Senior High School Alternative
Delivery Mode (ADM) Module on Calculating the Pearson’s Sample Correlation
Coefficient!

The hand is one of the most symbolical parts of the human body. It is often used to
depict skill, action, and purpose. Through our hands we may learn, create, and
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This module was designed to provide you with fun and meaningful opportunities
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This module has the following parts and corresponding icons:

What I Need to Know This will give you an idea of the skills or
competencies you are expected to learn in
the module.

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check what you already know about the
lesson to take. If you get all the answers
correct (100%), you may decide to skip this
module.

What’s In This is a brief drill or review to help you link

the current lesson with the previous one.

What’s New In this portion, the new lesson will be

introduced to you in various ways such as a
story, a song, a poem, a problem opener, an
activity, or a situation.

What Is It This section provides a brief discussion of

the lesson. This aims to help you discover
and understand new concepts and skills.

What’s More This comprises activities for independent

practice to solidify your understanding and
skills of the topic. You may check the
answers to the exercises using the Answer
Key at the end of the module.

What I Have Learned This includes questions or blank

sentences/paragraphs to be filled in to
process what you learned from the lesson.

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 What I Can Do This section provides an activity which will
help you transfer your new knowledge or
skill into real life situations or concerns.

Assessment This is a task which aims to evaluate your

level of mastery in achieving the learning
competency.

Additional Activities In this portion, another activity will be given

to you to enrich your knowledge or skill of
the lesson learned. This also aims for
retention of learned concepts.

Answer Key This contains answers to all activities in the

module.

At the end of this module, you will also find:

References This is a list of all sources used in

developing this module.

The following are some reminders in using this module:

1. Use the module with care. Do not put unnecessary mark/s on any part of
the module. Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities
included in the module.
3. Read the instruction carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your
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5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not
hesitate to consult your teacher or facilitator. Always bear in mind that you are
not alone.

We hope that through this material, you will experience meaningful learning
and gain deep understanding of the relevant competencies. You can do it!

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 What I Need to Know

This module was designed and written with you in mind. It is here to help
you master computing Pearson’s sample correlation coefficient r. The scope of this
module permits its use in many different learning situations. The language used
recognizes the diverse vocabulary level of students. The concepts are arranged to
follow the standard sequence of the learning area.

After going through this module, you are expected to:

1. define Pearson’s sample correlation coefficient r;
2. state the formula for Pearson’s sample correlation coefficient r;
3. compute the Pearson’s sample correlation coefficient r; and
4. apply and solve real-life problems using Pearson’s sample correlation
coefficient.

Are you ready now to study about the calculation of Pearson’s sample correlation
coefficient using your ADM module? Good luck and may you find it helpful.

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 What I Know

Directions: Choose the best answer to the given questions or statements. Write the
letter of your choice on a separate sheet of paper.

1. Which of the following is a statistical method that measures the strength of

the linear relationship between two variables?
A. z - value
B. scatterplot
C. testing hypothesis
D. Pearson’s sample correlation coefficient

2. Which of the following is the formula for Pearson’s sample correlation

coefficient r?
A. r =n ¿ ¿
B. r =¿ ¿
C. r =n ¿ ¿
D. r =¿ ¿

3. In the Pearson r, what does n represent?

A. sum of x-values
B. sum of square x-values
C. number of paired values
D. sum of the products of paired values x and y

4. Which of the following is the first step in computing Pearson’s sample

correlation coefficient r ?
A. Complete the table.
B. Construct the table.
C. Get the sum of all entries in all columns.
D. Substitute all the values obtained by all summations.

5. Which of the following values CANNOT represent a correlation coefficient r ?

A. -1
B. 0
C. 0.25
D. 1.001

6. Based on the bivariate data below, which among the choices is the correctly
constructed table?
X 2 8 11 9
Y 13 20 22 5

A. X Y XY X2 Y2 C.
X Y XY X2 Y2
1 2 2 13
3 8 20
2 8 1 22
0 1
2 11 PAGE \* MERGEFORMAT
9 14
5
2
5 9
B. D.
X Y X2 Y2 X Y XY X3 Y3
2 1 2 13
3 8 20
8 2
0 1 22
11 2 1
2 9 5
9 5
7. In the bivariate data on X 1 2 3
the right, which among the choices is the correct Y 18 13 7
completed table?

A. C.
X Y XY X2 Y2 X Y XY X2 Y2
1 18 18 1 324 1 1 1 324 18
2 13 26 4 169 8
2 1 4 169 26
3 7 21 9 64 3
6 39 68 14 557 3 7 9 64 21
6 3 14 557 68
B. D.
2 2 X 9Y XY X 2
Y2
X Y XY X Y
1 1 18 324 1 1 18 1 18 324
8 2 13 4 26 169
2 1 26 169 4
3 7 9 21 64
3
3 7 21 64 9 6 39 14 68 557
6 3 68 557 14
8. Using 9 the following summation values below,
what is the value of Pearson r ?
n=4 ∑ X = ∑ Y = 15 ∑ XY = 39 ∑ X 2= 30 ∑ Y 2= 65
10
A. -0.02
B. 0
C. 0.23
D. 1

9. Using the following summation values below, what is the value of Pearson
r?
n=3 ∑ X = 6 ∑ Y = 39 ∑ XY = 68 ∑ X 2= 14 ∑ Y 2= 557
A. -1
B. -0. 74
C. 0
D. 0.39

For numbers 10-12, refer to the following bivariate data:

X 1 2 3
Y 5 9 8

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 10. Which of the following is the CORRECT completed table for the bivariate
data?
A. C.
X Y XY X2 Y2 X Y XY X2 Y2
1 5 1 25 5 1 5 5 1 25
2 9 4 81 18 2 9 18 4 81
3 8 9 64 24 3 8 24 9 64
6 22 14 170 47 6 22 47 14 170

B. D.
X Y XY X2 Y2 X Y XY X2 Y2
1 5 1 5 25 1 5 5 25 1
2 9 4 18 81 2 9 18 81 4
3 8 9 24 64 3 8 24 64 9
6 22 14 47 170 6 22 47 170 14

11. When you substitute all the summation ( ∑ ❑¿ values in the formula for
Pearson r, which among the choices is its best representation?
4 ( 47 )−(6)(22)
A. r =
√ [ 3 ( 14 )−22 ][ 3 ( 170 )−6 ]
2 2

4 (47)−(6)(22)
B. r =
√ [ 3 ( 14 )−6 ] [ 3 ( 170 )−22 ]
2 2

3 ( 47 )−(6)(22)
C. r =
√ [ 3 ( 14 )−22 ][ 3 ( 170 )−6 ]
2 2

3( 47)−(6)(22)
D. r =
√ [ 3 ( 14 )−6 ] [ 3 ( 170 )−22 ]
2 2

12. What is the value of r ?

A. 0.93
B. 0.72
C. 0.16
D. -0.16

For numbers 13-15, refer to the bivariate data below:

X 3 2 0 1 3
Y 10 24 21 15 28

13. Which of the following is the CORRECT completed table for the bivariate
data?
A. C. X Y XY X2 Y2
X Y XY X2 Y2 10 3 30 100 9
10 3 30 9 100 24 2 48 576 4
24 2 48 4 576 21 0 0 441 0
21 0 0 0 441 15 1 15 225 1
15 1 15 PAGE
1 \*225 28 3 84 784 9
MERGEFORMAT 14
28 3 84 9 784 98 9 177 2126 23
98 9 177 23 2126
 B. X Y X2 Y2 XY2 X Y XY X2 Y2
D. 3 10 30 9 100 3 10 30 9 100
2 24 48 4 576 2 24 48 4 576
0 21 0 0 441 0 21 0 0 441
1 15 15 1 225 1 15 15 1 225
3 28 84 9 784 3 28 84 9 784
9 98 177 23 2126 9 98 177 23 2126

14. When you substitute all the summation ( ∑ ) values in the formula for
Pearson r, which among the choices is its best representation?
5 (177 )−(9)(98)
A. r =
√ [ 5 ( 23 )−9 ][ 5 ( 2126 )−98 ]
2 2

5 ( 177 ) +( 9)(98)
B. r =
√ [ 5 ( 23 )−9 ][ 5 ( 2126 )−98 ]
2 2

5 (2126 )−(9)(98)
C. r =
√ [ 5 ( 23 )−9 ][ 5 ( 2126 )−98 ]
2 2

5 ( 2126 )+(9)(98)
D. r =
√ [ 5 ( 23 ) +9 ][ 5 ( 2126 ) +98 ]
2 2

15. What is the value of r?

A. 0
B. 0.02
C. 0.16
D. 0.61

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 Lesson
Calculating the Pearson’s
1 Sample Correlation Coefficient

In the previous lesson, we learned about bivariate data and pairs of variables
that are related to each other. We also learned how to construct the scatter plots of
these bivariate data and determine the strength and direction of their association
or relationship based on how the points are scattered. In this module, you will
focus on the correlation of bivariate data. Check your readiness for this lesson by
answering the following exercises.

What’s In

Directions: Identify the trend and strength of correlation of the scatter plots below.
Choose your answer from the choices inside the box.

perfect positive correlation perfect negative correlation

strong positive correlation strong negative correlation
weak positive correlation weak negative correlation
no or negligible correlation

1. 3.

2. 4.

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 5.

How can we determine if there is a correlation between two variables: X and

Y? By observing the scatter plot, you can tell if the correlation is positive, negative,
or non-existent. If the points on the scatter plot closely resemble a straight line,
then the correlation may be positive or negative depending on the trend of the line.
It has a positive correlation if the line is increasing or rising from left to right. It has
a negative correlation if the line is decreasing or it is trending downward from left
to right. Meanwhile, the variables have no or negligible correlation if the points are
scattered randomly on the scatter plot.
We can only estimate the direction and strength of the relationship between
variables using a scatter plot. Is there a way to get the exact direction and strength
of the relationship between variables? Just like any other measurement, correlation
between two variables can be represented by a single number. This number can
determine exactly whether the relationship is negative or positive. It can also tell
exactly the degree or strength of the relationship. Let’s try the next activity.

What’s New

The following tables show the bivariate data x and y. Without constructing a
scatter plot, tell whether they have positive, negative, or no/negligible correlation.
Then, briefly explain your answer.
1. ____________________________
x 1 2 3 4 5 6 ____________________________
y 5 10 10 15 25 30 ____________________________

2. ____________________________
x 1 3 11 10 6 9 ____________________________
y 14 6 12 11 10 9 ____________________________

3. ____________________________
x 10 8 6 4 2 1 ____________________________
y 16 19 26 24 29 36 ____________________________

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Guide Questions:
1. How do you assess the bivariate data do determine the trend of its
correlation?
___________________________________________________________________________
___________________________________________________________________________

2. Do you think it is easy to determine the trend of its correlation? Why and
why not?
___________________________________________________________________________
___________________________________________________________________________

3. Is there a way to get the exact number that will represent its correlation?
___________________________________________________________________________
___________________________________________________________________________

The scatter plot helps us visualize the relationship of the variables in a

bivariate data. However, only the trend of the correlation can be exactly
determined. We can only estimate the degree of the association whether the
variables have weak, moderate, or high degree of relationship. Meanwhile, there is
a statistical method that can be used to evaluate the strength of relationship
between two quantitative variables.

What Is It

The Pearson’s sample correlation coefficient (also known as Pearson r ),

denoted by r, is a test statistic that measures the strength of the linear relationship
between two variables. To find r, the following formula is used:

r =n ¿ ¿

The correlation coefficient (r) is a number between -1 and 1 that describes

both the strength and the direction of correlation. In symbol, we write -1 ≤ r ≤ 1.
Illustrative Example:
Teachers of Pag-asa National High School instilled among their students the
value of time management and excellence in everything they do. The table below
shows the time in hours spent in studying (X) by six Grade 11 students and their
scores in a test (Y). Solve for the Pearson’s sample correlation coefficient r.

X 1 2 3 4 5 6
Y 5 10 10 15 25 30

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 The next section will guide you on how to compute the Pearson product
moment correlation r.

STEPS SOLUTION
1. Construct a table as shown on
the right side. X Y XY X2 Y2
1 5
2 10
3 10
4 15
5 25
6 30

2. Complete the table.

a. Multiply entries in the X and Y X Y XY X2 Y2
columns. Put them under the
XY column. 1 5 5 1 25
2 10 20 4 100
b. Square all the entries in the X 3 10 30 9 100
column. Put them under X2
4 15 60 16 225
column.
12
5 25 5 25 625
c. Square all the entries in the Y
18
column. Put them under Y2
6 30 0 36 900
column.

3.
a. Get the sum of all entries in the X Y XY X2 Y2
X column. This is ∑ X .
1 5 5 1 25
b. Get the sum of all entries in the 2 10 20 4 100
Y column. This is ∑ Y . 3 10 30 9 100
4 15 60 16 225
c. Get the sum of all entries in the
XY column. This is ∑ XY . 5 25 125 25 625
6 30 180 36 900
d. Get the sum of all entries in the
X2 column. This is ∑ X 2.
∑Y2
∑ X ∑ Y ∑ XY =
= = = ∑X 2
1,97
e. Get the sum of all entries in the 21 95 420 = 91 5
Y2 column. This is ∑ Y 2.

4. Substitute the values obtained Here n = 6 because there are six (6)
from Step 3 in the formula: pairs of values.

r =n ¿ ¿ r =n ¿ ¿

6(420)−(21)(95)
¿
√[ 6 ( 91 )−(21) ] [ 6 ( 1,975 )−(95) ]
2 2

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 2,520−1,995
¿
√ [ 546−441 ][ 11,850−9,025 ]
You may use your
calculator here! 525
¿
√ [ 105 ][ 2,825 ]
525
¿
√296,625
r ≈ 0.96395 or 0.96

The value of r is a positive

number. Therefore, we can say
accurately that there is a positive
correlation between hours spent in
studying and their scores in a test.

Note: For consistency of our answer,

round your final answer into two
decimal places.

In the next module, we will interpret the strength of value of computed r and
we will involve more real-life problems to solve using Pearson r. In the
meantime, let’s focus on computing the Pearson’s sample correlation coefficient
r.

Let’s try to answer all the activities that follow.

Notes to the Teacher

In the next part, the value of r will be
interpreted given a scale. The numbers in the scale are
expressed in two decimal places. Tell students that for
consistency of answers, they should round the value of
r into two decimal places except for a very small
number which is nearly zero. During computation,
rounding of partial answer may be done in three to
four decimal places. Also, the symbol ≈ will be used for
r to indicate that the numbers were rounded off.

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 What’s More

Activity 1.1 Let Me Guide You!

In this activity, you will be guided on how to compute the Pearson’s sample
correlation coefficient r. First, fill in the blank parts of the table with the correct
values of each cell. After completing the table, get the sum of each column. Then,
substitute the values obtained in the given formula. Finally, perform the indicated
operations to calculate the value of r.

X 1 3 4 5 7
Y 35 20 15 10 15

X Y XY X2 Y2
1 35 35
3 20 9 400
4 15 60 225
5 10 25
7 15 105 225
∑ X= ∑Y= ∑ XY = ∑X = 2
∑ Y 2=
20 ______ 310 ______ 2,175

n = 5 (since there are 5 pairs of values)

r =n ¿ ¿
¿ 5(310)−(20)¿ ¿

¿ 1,550−¿ ¿ ¿
√[ ¿] ¿¿¿
¿ Be careful in
substituting the
¿−¿ ¿ √ [ ¿ ¿ ] [ ¿¿ ] ¿ values, make sure
they are correct.
¿−¿ ¿ √ ¿¿ ¿ Always double check.

¿−¿ ¿ ¿¿ ¿
r ≈−0.81

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Activity 1.2 Complete Me!
Directions: Complete the table below. Then, fill in the blanks in the formula to
arrive at the computed Pearson r.

X Y XY X2 Y2
15 5 225
23 3
11 8 64
9 10 100
15 8 64
20 20 400
∑ X= ∑Y= ∑ XY = ∑ X 2= ∑ Y 2=
_____ _____ 842 1,581 _____

r =n ¿ ¿ n = ____

r =¿¿ (842)−¿ ¿

r ≈ 0.03
Activity 1.3 Let Me Guide You Because…
Directions: The title of the activity is incomplete and to reveal the real message,
follow the given directions. Using the given sum, substitute each to the
formula of Pearson’s sample correlation coefficient. Then, compute the
value of r. Choose your answer from the LETTER BOX below. Write the
letter that corresponds to your answer on the DECODING AREA.
(Show your solution.)

1.
n=5 ∑ X= ∑ Y = 85 ∑ XY = ∑ X 2= 75 ∑ Y 2= 1,875
17 375

2.
n=8 ∑ X= ∑Y= ∑ XY =1,02 ∑ X 2= 816 ∑ Y 2= 1,725
72 105 0

3.
n=6 ∑ X= ∑ Y = 34 ∑ XY = 79 ∑ X 2= 734 ∑ Y 2= 364
22

Letter Box
Y T I L R
1 0.73 -0.14 0.31 0

DECODE…
Let me guide you because…
3 2 1

Activity 1.4 You Can Do It!

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 In Mapalad Integrated High School, a guidance counselor believes that
aptitude score is related to performance. The following sample data obtained from
six students show their aptitude and performance score. Compute the Pearson r.
Show your solution. Aptitude Quarterly Assessment
Score (X) Score (Y)
8 14
15 5
11 8
7 12
5 2
10 11

What I Have Learned

Answer the following questions below:

1. What do you call a statistical method that measures the strength of
correlation between two variables?
2. To find Pearson r, what is the formula to be used?
3. Briefly discuss the steps in computing the Pearson’s sample correlation
coefficient r.

What I Can Do

Ask your 10 classmates about their previous grade in Mathematics and

Science subjects. Create a table for the data obtained from the survey and solve for
Pearson’s sample correlation coefficient r between the grades in Mathematics and
Science.
Previous Grade
Names
Mathematics Science
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.

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 Assessment

Directions: Choose the best answer to the given questions or statements. Write the
letter of your choice on a separate sheet of paper.

1. Which of the following is used to measure the strength of the association

between bivariate data?
A. z – value
B. diagram
C. Pearson - b
D. Pearson’s sample correlation coefficient

2. Which of the following is the Pearson r formula?

A. r =¿ ¿
B. r =n ¿ ¿
C. r =n ¿ ¿
D. r =¿ ¿
3. In the formula of Pearson r, what is the meaning of ∑ xy ?
A. sum of x-values
B. sum of square x-values
C. sum of the square of paired values x and y
D. sum of the products of paired values x and y
4. In computing Pearson r, which of the following is the next step after obtaining
the sum of all entries in all columns in the table?
A. Construct a table.
B. Complete the table.
C. Simplify and compute for the value of r.
D. Substitute all the sum and n in the formula.
5. Which of the following is the range of the correlation coefficient (r)?
A. 0 ≤ r ≤ 1
B. 1 ≤ r ≤ -1
C. -1 < r < 1
D. -1 ≤ r ≤ 1

6. In the given bivariate data, which among X -1 0 1 2

the choices is the correctly constructed
Y 10 13 9 15
table?
A. X Y XY X2 Y2 C. X Y XY X2 Y2
-1 10 10 -1
0 13 13 0
1 9 9 1
2 15 15 2

B. X Y XY X2 Y2 D. X Y XY X3 Y3
-1 15 -1 15
0 9 PAGE \* MERGEFORMAT 14 9
0
1 13 1 13
2 10 2 10
7. In the bivariate data on the right, which X 2 4 6
among the choices is the correct completed Y 1 3 5
table?

A. C.
X Y XY X2 Y2 X Y XY X2 Y2
2 1 2 4 1 2 1 2 4 1
4 3 12 16 9 4 3 12 16 9
6 5 30 36 25 6 5 30 36 25
B. 12 9 35 56 44 12 9 44 56 35 D.
X Y XY X2 Y2 X Y X2 Y2 XY
2 1 2 1 4 2 1 2 4 1
4 3 12 9 16 4 3 12 16 9
6 5 30 25 36 6 5 30 36 25
12 9 44 35 56 12 9 44 56 35

8. Using the given summation values below, what is the value of Pearson r?
n = 3 ∑ X = 6 ∑ Y = 30 ∑ XY = 60 ∑ X 2= 14 ∑ Y 2= 450
A. -0.06
B. 0
C. 0.11
D. 1

9. Using the given summation values below, what is the value of Pearson r?
n=5 ∑ X = ∑ Y = 15 ∑ XY = 90 ∑ X 2= 60 ∑ Y 2= 135
10
A. – 1
B. 0
C. 0.99
D. 1
For numbers 10-12, refer to the following X 1 2 3
bivariate data: Y 10 8 9
10.Which of the following is the CORRECT completed table for the bivariate data?
A. X Y XY X2 Y2 C. X Y XY X2 Y2
1 10 100 1 1 1 1 100 1 1
0 0 0
2 8 64 1 4 2 8 64 1 4
6 6
3 9 81 2 9 3 9 81 2 9
7 7
6 27 245 5 14 6 2 245 5 14
3 7 3

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 B. D.
X Y XY X2 Y2 X Y XY X2 Y2
1 10 10 1 100 1 10 10 1 100
2 8 16 4 64 2 8 16 4 64
3 9 27 9 81 3 9 27 9 81
6 27 53 14 245 6 27 53 245 14

11.When you substitute all the summation (∑ ❑¿ values in the formula for
Pearson r, which among the choices is its best representation?
3 ( 53 )−(6)(27)
A. r =
√ [ 3 ( 14 )−6 ] [ 3 ( 245 )−27 ]
2 2

3 ( 53 )−(6)(27)
B. r =
√ [ 3 ( 14 )+6 ][ 3 ( 245 )+ 27 ]
2 2

3 ( 27 )−(6)(27)
C. r =
√ [ 3 ( 14 )−6 ] [ 3 ( 245 )−27 ]
2 2

3 ( 53 )−(6)(27)
D. r =
√ [ 3 ( 6 ) −14 ] [ 3 ( 27 )−245 ]
2 2

12.What is the value of r ?

A. 0.95 C. -0.25
B. 0.75 D. -0.5

For numbers 13-15, refer to the X -2 0 3 4 1

following bivariate data: Y 8 5 8 13 20
13.Which of the following is the CORRECT completed table for the bivariate data?
A. X Y XY X2 Y2 C. X Y XY X2 Y2
-2 8 -16 4 64 -2 8 -16 4 64
0 5 0 0 25 0 5 0 0 25
3 8 24 9 64 3 8 24 9 64
4 13 52 16 169 4 13 52 16 169
B. 1
X
20
X Y YXY
20 1
XYX2
400
X 2 Y2 Y2 D. 1 20 20 1 400
6 54 80 722 30 6 54 80 30 722
-2 -28 864 -164 64-16 4
0 0 5 525 00 25 0 0
3 3 8 864 249 6424 9
4 413 13
169 5216 16952 16
1 120 20
400 201 40020 1
14. When you substitute all the
6 654 54
722 8030 72280 30
summation ( ∑ ) values in the
formula for Pearson r, which among the choices is its best representation?
5 ( 80 )−(6)(54)
A. r =
√ [ 5 ( 30 )−6 ][ 5 ( 722 )−54 ]
2 2

5 ( 80 )−(6)(54)
B. r =
√ [ 5 ( 30 ) +6 ][ 5 ( 722 ) +54 ]
2 2

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 5 ( 80 )−(6)(54)
C. r =
√ [ 5 ( 6 ) −30 ][ 5 ( 54 )−722 ]
2 2

( 6 ) ( 54 )−5 ( 80 )
D. r =
√ [ 5 ( 30 )−6 ][ 5 ( 722 )−54 ]
2 2

15.What is the value of r?

A. – 0.27
B. 0.27
C. 0.48
D. 0.84

Additional Activities

An ice cream vendor records the maximum daily temperature and the
number of ice creams he sells each day. An eight-day result is shown in the
table below.

Maximum
Temperatur 26 28 24 28 23 24 27 32
e (OC)
Number of
Ice Creams 21 38 42 47 29 19 52 56
Sold

Follow the directions below:

1. Display the data in a scatter plot and identify the trend of correlation.
2. Compute the Pearson’s sample correlation coefficient r.
3. Interpret the result of the data.

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Answer Key

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What I Know What’s In
1. D 6. C 11. D 1. strong negative correlation
2. A 7. A 12. B 2. no/negligible correlation
3. B 8. C 13. D 3. strong positive correlation
4. C 9. A 14. A
4. perfect positive correlation
5. perfect negative correlation
5. D 10. C 15. B

What’s New
1. Positive Correlation
As X values increase, the Y values also increase and vice versa.
2. No/Negligible Correlation
High values of one variable correspond to either high or low values of
another variable.
3. Negative Correlation
As X values increase, the Y values decrease and vice versa.

What’s More
Activity 1.1

X Y XY X2 Y2
1 35 35 1 1225
3 20 60 9 400
4 15 60 16 225
5 10 50 25 100
7 15 105 49 225
∑X ∑ XY ∑ X 2
= ∑Y= = = ∑ Y 2=
20 95 310 100 2,175
¿ 5310 ¿−20¿ 95¿ ¿
√[ 5 ( 100 ) −20 ¿¿¿ 2 ][ 5 ( 2,175 )−95 ¿ ¿¿ 2 ]
1,550−1,900
¿
√ [ 500−400 ][ 10,875−9,025 ]
−350
¿
√ [ 100 ][ 1,850 ]
−350
r=
√ 185,000

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What’s More
Activity 1.2

X Y XY X2 Y2
15 5 75 225 25
23 3 69 529 9
11 8 88 121 64
9 10 90 81 100
15 8 120 225 64
20 20 400 400 400
∑ X= ∑Y= ∑ XY = ∑ X 2= ∑ Y 2=
93 54 842 1,581 662

6 (842)−(93)(54)
r=
√ [ 6 ( 1,581 )−(93) ] [ 6 ( 662 )−(54) ]
2 2

Activity 1.3 Activity 1.4

1. r ≈ 1
2. r ≈ 0.31 r ≈ -0.08
3. r ≈ -0.14
Let me Guide You because… ILY

What I Have Learned What I

1. Pearson’s sample correlation coefficient/ Pearson r / Can Do
Pearson
Computed
2. r =n ¿ ¿ Pearson r
may vary.
3. Complete the table by getting all the sum for x, y, xy, x2,
and y2. Substitute all the sum in the formula and the
value of n. Then, simplify and solve for the Pearson r.

Additional Activities Assessment

1. Positive Correlation 1. D 11. A
2. C 12. D
3. D 13. C
4. D 14. A
5. D 15. B
6. A
7. C
8. B
9. D
10. B
2. r ≈ 0.69
3. As the temperature rises, the number of ice
creams sold also increases.

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References
Books

Albacea, Zita VJ., Mark John V. Ayaay, Isidoro P. David, and Imelda E. De Mesa.
Teaching Guide for Senior High School: Statistics and Probability. Quezon City:
Commision on Higher Education, 2016.

Caraan, Avelino Jr S. Introduction to Statistics & Probability: Modular Approach.

Mandaluyong City: Jose Rizal University Press, 2011.
De Guzman, Danilo. Statistics and Probability. Quezon City: C & E Publishing Inc,
2017.
Punzalan, Joyce Raymond B. Senior High School Statistics and Probability.
Malaysia: Oxford Publishing, 2018.
Sirug, Winston S. Statistics and Probability for Senior High School CORE Subject A
Comprehensive Approach K to 12 Curriculum Compliant. Manila: Mindshapers
Co., Inc., 2017.
Ubarro, Arvie D., Josephine Lorenzo S. Tan, Renato Guerrero, Simon L. Chua, and
Roderick V. Baluca. Soaring 21st Century Mathematics Precalculus. Quezon
City, Philippines: Phoenix Publishing House Inc., 2016.

Online Resources
Project Maths Development Team. “Teaching & Learning Plans: The Correlation
Coefficient.” Accessed May 23, 2020.
https://www.projectmaths.ie/documents/T&L/CorrelationCoefficient.pdf
Study.com. “Pearson Correlation Coefficient: Formula, Example & Significance.”
Accessed May 23, 2020. https://study.com/academy/practice/quiz-
worksheet-pearson-correlation-coefficient.html

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For inquiries or feedback, please write or call:

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