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Mathematics
Quarter 4 – Module 1:
Measures of Position for
Ungrouped Data
Mathematics – Grade 10
Quarter 4 – Module 1: Measures of Position for Ungrouped Data
First Edition, 2020

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Mathematics
Quarter 4 – Module 1:
Measures of Position for
Ungrouped Data
Introductory Message
For the facilitator:
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 at home. Furthermore, you are
expected to encourage and assist the learners as they do the tasks included
in the module.

For the learner:

As a learner, you must learn to become responsible of your own
learning. Take time to read, understand, and perform the different activities
in the module.
As you go through the different activities of this module be reminded of
the following:
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 Let Us Try before moving on to the other
activities.
3. Read the instructions carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your
answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are done.
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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 Let Us Learn

After going through this module, you are expected to:

Ø Illustrates the following measures of position: quartiles, deciles, and
percentiles. (M10SP-IVa-1)

Specifically, you will;

1. define measures of position
2. locate the specified measures of position of the ungrouped data.
3. find the specified measures of position of the ungrouped data.

Let Us Try

Encircle the letter of your chosen answer.

1. When the distribution is divided into ten equal parts, how do you call each
score point that describes the distribution?
A. decile B. interquartile C. percentile D. quartile

2. Which of the following is equivalent to the upper quartile?

A. 1st quartile C. 75th percentile
B. 5 decile
th D. 85th percentile

3. Which of the following measures of position divides the distribution into 100
equal parts?
A. decile B. quartile C. quantile D. percentile
4. Which of the following is the difference between the third quartile and the
first quartile?
A. Interquartile range C. middle quartile
B. lower quartile D. upper quartile
5. Which of the following is equivalent to the 5th decile?
A. 75th percentile B. 50th percentile C. 25th percentile D. 5th percentile

6. In the given data 16, 14, 17, 19, 15, 18, 13, what is the middle score?
A. 15 B. 16 C. 17 D. 18
7. If Mariel is top in a group of 10, how many percent of the students are below
on her rank?
A. 10 B. 50 C. 70 D. 90
8. Which of the following does NOT belong to the group?
I. Q1 II. D2 III. D5 IV. P25
A. I and II B. II and III C. III and IV D. I and IV

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 9. How many percent of the distribution is higher than the first quartile?
A. 75% B. 50% C. 25% D. 15%

10. When the distribution is divided into four equal parts, how do you call each
score point that describes the distribution?
A. decile B. interquartile C. percentile D. quartile

Let Us Study

Can you still remember the measure of central tendency? If so, let us try to identify
the mean, mode, and median in the given data set:

A group of students obtained the following scores in their statistics quiz:

8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9
Let’s arrange the given score. We have,
1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9

Questions:
1. What is the sum of the scores?
2. What is the average score?
3. What is the middle score?
4. What scores appeared most of the time?

The sum of the scores is 58, therefore, the mean is 5.27, which is obtained by
adding the scores and divided by the number of students.
The mode is 5 and 8, those are obtained by identifying the number/s which
frequently appear.
The median is 5, which is obtained by arranging all the numbers in ascending
order and identify the middle number.

The mean, median, and mode are called measures of central tendency.

In our pre-assessment you have noticed, the word quartile, decile, and percentile
have been repeatedly mentioned. These are the three different types of measures of
position. Measures of position give us a way to see where a certain data point of
value falls in a sample or distribution. A measure can tell us whether a value is
about average, or whether it is unusually high or low. Measures of position are used
for quantitative data that falls on some numerical scale.

The Quartile for Ungrouped Data

The quartiles are the score points which divide a distribution into 4 equal
parts so that each part represents ¼ of the data set. Twenty-five percent (25%) of the

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distribution is below the first quartile, fifty-percent (50%) are below the second
quartile, and seventy-five percent (75%) are below the third quartile.

Lower Quartile Median or Upper Quartile

𝑄! Second Quartile 𝑄#
𝑄"

a. 25% of the data has a value ≤ 𝑄!

b. 50% of the data has a value ≤ 𝑥̅ 𝑜𝑟 𝑄"
c. 75% of the data has a value ≤ 𝑄#

Using the Mendenhall and Sincich Method:

!
Lower Quartile(L) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = " (𝑛 + 1) round to the nearest integer

𝑄! = 𝐿𝑡ℎ 𝑒𝑙𝑒𝑚𝑒𝑛𝑡. If L falls halfway between two integers round up.

#
Upper Quartile(U) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = " (𝑛 + 1) round to the nearest integer

𝑄# = 𝑈𝑡ℎ 𝑒𝑙𝑒𝑚𝑒𝑛𝑡. If U falls halfway between two integers round down.

Interquartile Range is the difference between the Upper quartile and the
Lower quartile

Examples:
1. A group of students obtained the following scores in their statistics
quiz: 8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9.

First, arrange the scores in ascending order:

1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9

𝑄! 𝑄" 𝑄#
Lower Middle quartile Upper
quartile (MEDIAN) quartile

Observe how the lower quartile (𝑄! ), middle quartile (𝑄" ), and upper quartile (𝑄# ) of
the scores were obtained.

Complete the statement below:

The first quartile(lower) 3 is obtained by _______________________________________.

(observe the position of 3 from 1 to 5)

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The second quartile(middle) 5 is obtained by ___________________________________.
(observe the position of 5 from 1 to 9)
The third quartile(upper) 8 is obtained by _______________________________________.
(observe the position of 8 from 6 to 9)

2. Given are the scholastic grades in Mathematics of the randomly selected

grade 10 students

82, 85, 90, 81, 79, 89, 94, 95, 97, 85, 83, 90

Step 1. Arrange the data in ascending order

79, 81, 82, 83, 85, 85, 89, 90, 90, 94, 95, 97
1 2 3 4 5 6 7 8 9 10 11 12

Step 2. Find its position using the formula below

𝒌
𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒐𝒇 𝑸𝒌 = (𝒏 + 𝟏)
𝟒
Where: k = 1,2,3
n = is the number of elements in a given data

First Quartile Second Quartile

1 2
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = (𝑛 + 1) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄% = (𝑛 + 1)
4 4
1 1
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = (12 + 1) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄% = (12 + 1)
4 2
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = (0.25)(13) 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄" = (0.5)(13)
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = 3.25 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄% = 6.5
𝑄! = 3$% 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑄" is the average of the 6th and the
7th element.
𝑄! = 82
85 + 89
25% of the students have a grade 𝑄" =
2
in Mathematics of less than or
equal to 82. 𝑄" = 87
50% of the students have a grade in
Mathematics of less than or equal
to 87.

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Third Quartile

3
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = (𝑛 + 1)
4
3 𝐼𝑛𝑡𝑒𝑟𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝑅𝑎𝑛𝑔𝑒 = 𝑄# − 𝑄!
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = (12 + 1)
4 𝐼𝑛𝑡𝑒𝑟𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝑅𝑎𝑛𝑔𝑒 = 90 − 82
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = (0.75)(13)
𝐼𝑛𝑡𝑒𝑟𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝑅𝑎𝑛𝑔𝑒 = 8
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = 9.75

𝑄# = 9'( 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 (round down)

𝑄# = 90
75% of the students have a grade in
Mathematics of less than or equal
to 90
79, 81, 82, 83, 85, 85, 89, 90, 90, 94, 95, 97

𝑄! 𝑄" 𝑄#
The first, second, and third quartile can be obtained also using Interpolation.

Step 1: Arrange the given data in ascending order.

Step 2: Find the position of each quartile.

Using the example above:

Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄! = 3.25, therefore, 𝑄! is between the 2nd and 3rd elements.

Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄" = 6.5, therefore, 𝑄" is between the 6th and 7th elements.

Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄# = 9.75, therefore, 𝑄# is between the 9th and 10th

elements.

Step 3. Interpolate to obtain the value of 𝑄! , 𝑄" , and 𝑄#

79, 81, 82, 83, 85, 85, 89, 90, 90, 94, 95, 97
1 2 3 4 5 6 7 8 9 10 11 12

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 For the First Quartile For the Second Quartile
Position of 𝑄! = 3.25 Position of 𝑄" = 6.5

Steps: Steps:
1. Subtract the 2nd element 82 − 81 1. Subtract the 6th element 89 − 85
to the 3rd element =1 to the 7th element =4

2. The decimal part 0.25 2. The decimal part 0.5

(position) (position)
3. Multiply the decimal (1)(0.25) 3. Multiply the decimal part (4)(0.5)
part and the result in = 0.25 and the result in =2
number 1. number 1.
4. Add the result to the 81 + 0.25 4. Add the result to the 85 + 2
smaller value = 81.25 smaller value = 87

Therefore, 𝑸𝟏 = 𝟖𝟏. 𝟐𝟓 Therefore, 𝑸𝟐 = 𝟖𝟕

For the Third Quartile

Position of 𝑄# = 9.75

Steps:
1. Subtract the 10th 94 − 90
element to the 9th =4
element
2. The decimal part 0.75
(position)
3. Multiply the decimal (4)(0.75)
part and the result in =3
number 1.
4. Add the result to the 90 + 3
smaller value = 93

Therefore, 𝑸𝟑 = 𝟗𝟑

The Decile for Ungrouped Data

The deciles are the nine score points which divide a distribution into ten equal
parts. Deciles are denoted as 𝐷! , 𝐷" , 𝐷# , 𝐷) , 𝐷* , 𝐷+ , 𝐷, , 𝐷- , 𝐷. . They are computed in the
same way that the quartiles are calculated.

𝐷! 𝐷" 𝐷# 𝐷) 𝐷* 𝐷+ 𝐷, 𝐷- 𝐷.

The 1st decile (𝐷! ) is the 10th percentile (𝑃!/ ). It means 10% of the data is less
than or equal to the value of 𝑃!/ 𝑜𝑟 𝐷! , and so on.

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3. Ages of a COVID 19 Patient of a certain district of Davao City.

47 74 19 23 38 36 14 62 62 9
17 34 53 14 23 26 45 45 77 43
7 27 67 23 33 31 40 48 46 15
5 42 `15 34 36
Find the value of the 2nd decile, 6th decile, and 8th decile.
SOLUTION:
Step 1: Arrange the given data
5 7 9 14 14 15 15 17 19 23
23 23 26 27 31 33 34 34 36 36
38 40 42 43 45 45 46 47 48 53
62 62 67 74 77

Note: In solving the decile, the same process in the quartile should be done.

Finding the 2nd decile:

𝑘 Using Linear Interpolation
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷3 = (𝑛 + 1)
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Since the 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" = 7.2, therefore,
2
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" = (35 + 1) 𝐷" is between the 7th element and the
10
8th element.
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" = (0.2)(36)
1. 8th element – 17 − 15 = 2
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" = 7.2 7th element
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷" ≈ 7th element 2. decimal part 0.2
of 7.2
𝐷" = 15 3. Multiply the (2)(0.2) = 0.4
result in 1
20% of the COVID 19 Patient and 2
is younger or equal to 15 4. Add it to the 15 + 0.4 = 15.4
years old. smaller value

Therefore, 𝐷" = 15.4,

20% of the COVID 19 Patient is

younger or equal to 15.4 years old.

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Finding the 6th Decile

𝑘 Using Linear Interpolation

𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷3 = (𝑛 + 1)
10
Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷+ = 21.6, therefore,
6
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷+ = (35 + 1) 𝐷+ is between the 21st element and the
10
22nd element.
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷+ = (0.6)(36)
1. 22nd element – 21st 40 − 38 = 2
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷+ = 21.6 element
𝐷+ ≈ 224% 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 2. decimal part of 21.6 0.6

𝐷+ ≈ 40 3. Multiply the result (2)(0.6) = 1.2

in 1 and 2
60% of the COVID 19 Patient 4. Add it to the 38 + 1.2 = 39.2
is younger or equal to 40 smaller value
years old. Therefore, 𝐷+ = 39.2,

60% of the COVID 19 Patient is

younger or equal to 39.2 years old.

Finding 𝑫𝟖

𝑘 Using Linear Interpolation

𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷3 = (𝑛 + 1)
10
Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷- = 28.8, therefore,
8
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷- = (35 + 1) 𝐷- is between the 28th element and the
10
29th element.
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷- = (0.8)(36)
1. 29th element – 28th 48 − 47 = 1
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐷- = 28.8 element
𝐷- ≈ 29'( 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 2. decimal part of 28.8 0.8

𝐷- ≈ 48 3. Multiply the result (1)(0.8) = 0.8

in 1 and 2
80% of the COVID 19 Patient 4. Add it to the 47 + 0.8 = 47.8
is younger or equal to 48 smaller value
years old Therefore, 𝐷- = 47.8,

80% of the COVID 19 Patient is

younger or equal to 47.8 years old.

The Percentile for Ungrouped Data

The percentiles are the ninety-nine score points which divide a

distribution into one hundred equal parts so that each part represents the
data set. Percentiles indicate the percentage of scores that a given value is
higher or greater than.

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 For example, the first percentile (P1) separates the lowest 1% from the
other 99%.

𝑄! 𝑄" 𝑄#
𝑃"* 𝑃*/ 𝑃,*

𝐷! 𝐷" 𝐷# 𝐷) 𝐷* 𝐷+ 𝐷, 𝐷- 𝐷.
𝑃!/ 𝑃"/ 𝑃#/ 𝑃)/ 𝑃*/ 𝑃+/ 𝑃,/ 𝑃-/ 𝑃./

4. Using the above data on Ages of Covid 19 Patient of a certain District

in Davao City, find the 40th Percentile and the 75th Percentile.
5 7 9 14 14 15 15 17 19 23
23 23 26 27 31 33 34 34 36 36
38 40 42 43 45 45 46 47 48 53
62 62 67 74 77
Finding the 40th Percentile

𝑘 Using Linear Interpolation

𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃3 = (𝑛 + 1)
100
Since 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃)/ = 14.4, therefore,
40
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃)/ = (35 + 1)
100 𝑃)/ is between the 14th element and the
15th element.
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃)/ = (0.4)(36)
1. 15th element – 14th 31 − 27 = 4
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃)/ = 14.4
element
𝑃)/ ≈ 14'( 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 2. decimal part of 14.4 0.4

𝑃)/ ≈ 27 3. Multiply the result (4)(0.4) = 1.6

in 1 and 2
40% of the COVID 19 Patient
4. Add it to the 27 + 1.6 = 28.6
is younger or equal to 27 smaller value
years old Therefore, 𝑃)/ = 28.6,

40% of the COVID 19 Patient is

younger or equal to 28.6 years old.

9
Finding the 75th Percentile

𝑘
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃3 = (𝑛 + 1)
100
75
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃,* = (35 + 1)
100
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃,* = (0.75)(36)

𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑃,* = 27

𝑃,* = 27'( 𝑒𝑙𝑒𝑚𝑒𝑛𝑡

𝑃,* = 46

75% of the COVID 19 Patient

is younger or equal to 46
years old

Let Us Practice

Study the given data and answer the questions that follow. Show your
solution.

1. Ages of the SSG Officers of Dacudao NHS: 14, 15, 17, 16, 18, 15, 15, 16,
17, 16, 15, 17, 14, 17, 15, 15, 16, 14, 15, 18. Find the following using
Mendenhall and Sincich Method.
a. First Quartile
b. 4th Decile
c. 80 Percentile

2. The new cases of COVID 19 in the Philippines as of February 21, 2021,

are as follows:
REGION NEW CASES
NCR NATIONAL CAPITAL REGION 618
CAR CORDILLERA ADMINISTRATIVE REGION 176
I ILOCOS REGION 49
II CAGAYAN VALLEY 45
III CENTRAL LUZON 101
IV A CALABARZON 160
IV B MIMAROPA 4
V BICOL REGION 11
VIII EASTERN VISAYAS 30
VI WESTERN VISAYAS 93
VII CENTRAL VISAYAS 404

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 IX ZAMBOANGA PENINSULA 24
X NORTHERN MINDANAO 31
XI DAVAO REGION 60
XII SOCCKSARGEN 45
XIII CARAGA REGION 34
BARMM BANGSAMORO AUTONOMOUS REGION IN 8
MUSLIM MINDANAO

a. Arrange the data from the lowest number of cases to the highest
number of cases, indicating the region and the number of cases.
b. What region belongs to the first quartile?
c. What are the regions below the first quartile?
d. How many cases belong to the 75th percentile?
e. Is Davao Region belong to the 5th Decile?
f. What region/s belong to the upper 10% of having most of the new
cases?
g. How many new cases that belong to 30% percentile and below?
h. What are the Regions or areas that are higher or equal to the 60th
percentile?
i. What will be your contribution to minimize the number of new cases
in your area?

Let Us Practice More

Complete the Cross Quantile puzzle by finding the specified measures of

position using linear interpolation. (In filling the boxes, disregard the decimal point.
Show your solution.)

Given: Ages of selected teachers:

23, 25, 27, 30, 33, 38, 40, 41, 43, 43, 45, 48, 53
1 2 3
Across
1. 𝐷! 4
4. 𝑃,-
5. 𝑃-* 5
8. 𝑃)- Down
10. 𝐷- 6
2. 𝑃#*
3. 𝑃)*
7 8 9
5. 𝑄#
6. 𝑃--
7. 𝑃!* 10
9. 𝐷+

SOLUTION:

11
 FINAL
Find POSITION SUBTRACT MULTIPLY ADD
VALUE
𝐷" 2
(14) = 2.8 27 − 25 = 2 (2)(0.8) = 1.6 25 + 1.6 = 26.6 𝐷" = 26.6
10
1. 𝐷!

2. 𝑃#*

3. 𝑃)*
4. 𝑃,-

5. 𝑃-*

5. 𝑄#

6. 𝑃--

7. 𝑃!*

8. 𝑃)-

9. 𝐷+

10. 𝐷-

Let Us Remember

Measures of Positions

Quartiles – divides the distribution into 4 equal parts.

𝒌
𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒐𝒇 𝑸𝒌 = 𝟒 (𝒏 + 𝟏), where 𝑘 = 1,2,3 and
n is the number of elements in a given data

Deciles – divides the distribution into 10 equal parts.

𝒌
𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒐𝒇 𝑫𝒌 = 𝟏𝟎 (𝒏 + 𝟏), where 𝑘 = 1,2,3,4,5,6,7,8,9

Percentiles – divides the distribution into 100 equal parts.

𝒌
𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒐𝒇 𝑷𝒌 = 𝟏𝟎𝟎 (𝒏 + 𝟏), where 𝑘 = 1, 2, 3, 4, … , 99

12
 Let Us Assess

1. When the distribution is divided into four equal parts, how do you call each
score point that describes the distribution?
A. decile B. interquartile C. percentile D. quartile

2. When the distribution is divided into ten equal parts, how do you call each
score point that describes the distribution?
A. decile B. interquartile C. percentile D. quartile

3. Which of the following measures of position divides the distribution into 100
equal parts?
A. decile B. quartile C. quantile D. percentile

4. Which of the following is equivalent to the upper quartile?

A. 1st quartile C. 75th percentile
B. 5th decile D. 85th percentile

5. Which of the following is equivalent to the 5th decile?

A. 75th percentile B. 50th percentile C. 25th percentile D. 5th percentile

6. How many percent of the distribution is higher than the first quartile?
A. 75% B. 50% C. 25% D. 15%

For numbers 7 to 10, please refer to the data below:

The Number of released modules per section of grade 10 level.
40, 37. 40, 41, 40, 35, 32, 26, 37, 40, 35, 38, 38, 37, 35, 38

7. What is the first quartile?

A. 32 B. 35 C. 37 D. 38

8. What is the 75th percentile?

A. 37 B. 38 C. 40 D. 41

9. What is the interquartile range?

A. 3 B. 4 C. 5 D. 6

10. What is the 6th Decile?

A. 37 B. 38 C. 40 D. 41

13
 Let Us Enhance

Take a survey of 15 of your classmates.

1. Choose one of the following categories:

a. Weight in kilogram
b. Height in centimeters
c. Number of Facebook friends
Write the name of your classmates and their corresponding value of
the chosen category.

2. Arrange the given data from lowest to highest.

3. Find two values of each quantile. One lower and one upper. Show
your solution.

Example: 𝑄! 𝑎𝑛𝑑 𝑄# , 𝐷% 𝑎𝑛𝑑 𝐷' , 𝑃#( 𝑎𝑛𝑑 𝑃'(

RUBRICS: TOTAL POINTS 70

OUSTANDING SATISFACTORY DEVELOPING BEGINNING
CRITERIA RATING
10 8 4 2
DATA The Data is The data The values are Values not
GATHERI complete, with gathered has arranged from arranged.
NG name of the name but no lowest to
correspondents values. highest.
and values. The values are
The values are arranged from
arranged from lowest to highest.
lowest to
highest.
Accuracy The The The The
(Per computations computations are computations computation
measures are accurate. accurate. Use of are erroneous s are
of Position A wise use of key concepts of and show erroneous
solved) key concepts of measures of some use of and do not
measures of position is key concepts show some
position is evident. of measures of use of key
evident. position. concepts of
measures of
position.

OVERALL RATING

14
 Let Us Reflect

We encountered so many difficulties and challenges in our different lives

especially this time of the pandemic. We have to stand our position, whether we
have to protect ourselves and our loved ones by staying at home or enjoy life
as long as we live by going outside. Don’t lose hope.
We have to remember that for every problem there will always be a solution
and an answer so we have to be patient in solving the problem or might be a part of
the solution and not be part of the problem.

Understanding Level:
A. Color your level of understanding about Measures of Position, whether it is
10%, 20%, 30% … or 100%

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

B. Write the things you’ve learned about measures of position depending on your
level of understanding. 10% equivalent to 1 sentence.

15
 16
Let Us Assess Let Us Practice More
1. D 1 2 3 1. 𝐷! = 23.8
2. A 2 3 8 3 2. 𝑃%& = 32.7
3. D 4 3. 𝑃'& = 38.6
4. C 2 4 4 8 4 4. 𝑃(# = 44.84
5. B 5 5. 𝑃#& = 47.7
6. A 4 7 7 6 5. 𝑄% = 44
7. B 6. 𝑃## = 49.6
8. C 6
7. 𝑃!& = 25.2
9. C 4 4 8. 𝑃'# = 39.44
10. B 7 8 9 9. 𝐷" = 41.8
2 3 9 4 4 10. 𝐷# = 45.6
10
4 5 6 6 1
2 8
Let Us Practice: b. Eastern Visayas
c. Mimaropa,
1. a. 𝑄! = 15 b. 𝐷" = 16 c. 𝑃#$ = 17 Bangsamoro, Bicol
2. a. Region, and
REGION NEW Zamboanga
CASES Peninsula
IVB MIMAROPA 4 d. 101
BARMM BANGSAMORO AUTONOMOUS 8 e. No, Davao Region is
REGION IN MUSLIM MINDANAO above the 5th Decile.
V BICOL REGION 11 f. National Capital
IX ZAMBOANGA PENINSULA 24 Region
VIII EASTERN VISAYAS 30 g. 77
X NORTHERN MINDANAO 31 h. Davao Region,
XIII CARAGA REGION 34 Western Visayas,
XII SOCCKSARGEN 45 Central Luzon,
Calabarzon,
II CAGAYAN VALLEY 45
Cordillera
I ILOCOS REGION 49
Autonomous Region,
XI DAVAO REGION 60 Central Visayas and
VI WESTERN VISAYAS 93 National Capital
III CENTRAL LUZON 101 Region.
IVA CALABARZON 160 i. Answer may vary
CAR CORDILLERA ADMINISTRATIVE 176
REGION
VII CENTRAL VISAYAS 404
NCR NATIONAL CAPITAL REGION 618
Let Us Try:
1. A 6. B
2. C 7. D
3. D 8. B
4. A 9. A
5. B 10. D
Answer Key
 References

Callanta, Melvin M., et.al, Mathematics Learner’s Module, Department of

Education, 2015, pp 355 – 378.
“Updates on Covid on Davao Region”, Department of Health Davao Region
Facebook Page, February 21, 2021.

“New Cases by Region: COVID-19 Philippines in Numbers”, covid19stats.ph,

February 22, 2021.
For inquiries or feedback, please write or call:
Department of Education – Davao City Division
Elpidio Quirino Ave., Poblacion District, Davao City, 8000 Davao del Sur

Telefax: (082) 224-3274, (082) 222-1672

E-mail Address: davao.city@deped.gov.ph