Grade

10

MATHEMATICS
QUARTER 4 – MODULE 1
MELC 1

MY POSITION
PART I.
MELC 1: Illustrates the following measures of position: quartiles, deciles, and
percentiles

A. Introduction and Discussion

In this module, you will be able to learn about the measures of position.
Measures of position are used to describe the position of a data value in relation to
the other data. The most frequent measures of positions are quartiles, deciles, and
percentiles.

1. QUARTILES are the score points which divide a distribution into four equal parts. Each
set of data has three quartiles.

a. First Quartile ( is a number such that at most one-fourth or 25% of the data
are smaller in value than 1 , and at most three-fourths or 75% are larger. It is sometimes
called the lower quartile.
b. Second Quartile ( is a number such that one-half or 50% of the data are
below and above in value than 2 . 2 is obviously the median.
c. Third Quartile ( is a number such that at most three-fourths or 75% of the data
are smaller in value than 3 , and at most one-fourth or 25% are larger. It is sometimes called
the upper quartile.

The difference between 1 and 3 is called the interquartile range.

Quartiles can be represented by the diagram below when the data is arranged in increasing
order.

L H

a. 25% of the data has a value ≤ 𝑄1

b. 50% of the data has a value ≤ 𝑄2
c. 75% of the data has a value ≤ 𝑄3

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2. DECILES are the nine score points that divide a distribution into ten equal parts.

3. PERCENTILES are the ninety-nine score points which divide a distribution into one
hundred equal parts, so that each part represents the data set. It is used to characterize
values according to the percentage below them.

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 𝑃1 separates the lowest 1% from the other 99%.
2
𝑃2 separates the lowest 2% from the other 98%.

𝑃3 separates the lowest 3% from the other 97%.

𝑃99 separates the lowest 99% from the other 1%.

B. Illustrative Examples
1. How many percent corresponds to 3 if you will interpret it?

Answer: 75% of the data have a value less than or equal to 3.

2. George is an IT expert in one big company. His salary is in the 8th decile. Should George
be glad about his salary or not?

Answer: 80% of the employees receive a salary that is less than or equal to his salary and
20% of the employees receive a salary that is greater than his salary. George should be
pleased with his salary.

3. There are 11 data items. 2, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11.

th
The median or 2 is the 6 item. So 2 = 7
The lower quartile is the 3rd item. So 1 = 5
The upper quartile is the 9th item. So 3 = 9
What do the information above mean?

Answer:
2, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11

1 2 3
 25% of the data have a value that is less than or equal to 5.
 50% of the data have a value that is less than or equal to 7.
 75% of the data have a value that is less than or equal to 9.

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4. Below is the table showing the ages of 15 students in Eastern Pangasinan Agricultural
College.

Name Age Name Age Name Age

Joseph 13 Anne 14 Jaimie 14
Lea 12 Chito 16 Maye 12
Tina 15 Dave 15 Ruben 17
Marc 14 Paul 14 Donna 17
Vince 13 Zeny 17 Ruby 15

a. If the value of 1 is 13, describe the ages of the students.

b. If 7 = 15, how many students have age 15 and below?
c. If 16 years old is the 75th percentile of the ages of the 15 students, what does it
mean?

Answer:
a. Since 1 is 13, then there are 4 students whose age is less than or equal to 13.
b. Since 7 is 15, then there are 11 students whose age is less than or equal to 15.
c. It means that 75% of the students are 16 years old and below or 25% of the students are
16 years old and above.

Part II. Activities

Activity I: Check it Out!

Directions: Study each problem and answer what is/are being asked.

1. You are the third tallest student in a group of 10. If you are the third tallest student,
therefore 7 students are shorter than you. It also means that 70% of the students are
shorter than you. On the other hand, if you are the 7th tallest student in a group of 10,
what percent of the students are shorter than you?

Answer: ______________________

2. Given a test in Statistics, the 75th percentile score is 20. What does it mean? What
is its measure of position in relation to the other data?

Answer: ______________________

3. The 78th percentile means 78% are smaller than the given value. Does making the
80th percentile mean that you made an 80% on test? Justify.

Answer: ______________________

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 5
Activity I: Check it Out!
1. 30% of the students are shorter than you.
2.Interpretation: It means 75% of all the scores obtained are less than or equal to
the score of 20.
th
3. No. the 80 percentile would mean that a person did better than 80% of the students who took
the same test.
Key Answer
2 J. 6 10.
1 I. 7 9.
6 H. 4 8.
7 G. 2 7.
4 F. 1 6.
5 E. 3 5.
3 D. 5 4.
C. Median of the upper half 3 3.
B. Median of the lower half 2 2.
A. Median 1 1.
B A
Directions: Match Column A with Column B.
Activity II: Match Me!
 5. D 10. H
4. E 9. G
3. C 8. F
2. A 7. J
1. B 6. I
Activity II: MATCH ME!

Part III. Assessment

Directions: Choose the letter of the correct answer. Write your answer on a separate sheet
of paper.

1. What measures of position divides the distribution into 100 equal parts?
A. Quartiles C. Percentiles
B. Deciles D. Range

2. What is the equivalent of lower quartile in terms of percentile?

A. 50th Percentile C. 10th Percentile
B. 25th Percentile D. 2nd Percentile

3. It tells where a specific data value falls within the data set or its relative position in
comparison with other data values.
A. Measures of central tendency C. Measures of position
B. Measures of variability D. Median

4. The second quartile is also the ____________.

A. 7th percentile C. 3rd decile
B. 5th decile D. 2nd decile

5. The difference between Upper quartile and Lower quartile is called _____________.
A. Range C. Mean
B. Interquartile Range D. Median

6. Lilian got a score of 55, which is equivalent to the 70th percentile in

a mathematics test. Which of the following is NOT true?
A. 70% of the students got a score less than or equal to Lilian’s score.
B. Thirty percent of the class got scores of 55 and above.
C. If the passing mark is the first quartile, she passed the test.
D. Her score is below the 5th decile.

7. In a 50-item test, Angela got a score of 35 which is the third quartile.

This means that:
A. She got the highest score.
B. Her score is higher than 25% of her classmates.
C. She surpassed 75% of her classmates.
D. Seventy-five percent of the class did not pass the test.

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8. In the set of scores 14, 17, 10, 22, 19, 24, 8, 12, and 19, the median score
is _______.
A. 17 C. 16
B. 15 D. 13

For items 9 to 10, refer to the given table below.

Mathematics Quiz Scores of 15 Grade-10 Aphrodite Students

Name Score Name Score Name Score
Amy 17 Michelle 17 Aila 17
Evan 11 Albert 11 D-anne 16
Sarah 15 Isaac 18 Aidan 19
Carl 12 Cherry 17 Jethro 14
Angelo 16 Nica 18 Noah 15

9. If 1 is 12, how many students belong to the lowest 25%?

A. 2 B. 3 C. 4 D. 5

10. If 5 is 16, how many students belong to the lower 50%?

A. 3 B. 5 C. 6 D. 8

References:

1. Department of Education. Mathematics – Grade 10 Learner’s Module. Rex Bookstore,

Inc., Pasig City, Philippines, 2015.

2. Orlando A. Oronce and Marilyn O. Mendoza. 2019. E-Math Worktext in Mathematics 10.
Rex Book Store