measures of Position Quartile, Decile, Percentile

MEASURES OF POSITION
-are techniques that divide a set into equal
groups
-a method by which the position that a particular
data set can be identified.

MEASURES OF POSITION
1. Quartiles
2. Deciles
3. Percentiles

MEASURES OF POSITION FOR
UNGROUPED DATA

QUARTILES
 are the score points which divide a distribution
into four equal parts.

QUARTILE FOR UNGROUPED DATA
MENDENHALL AND SINCICH METHOD
-a method of finding the quartile value
-this method is developed by William Mendenhall
and Terry Sincich to find the positionof the
quartile position

To find Q1, Q2 and Q3, use the formula below:
Qk = (n + 1)
where
n = number of data/score
K = position of the quartile

Example:
1. The score of 7 students obtained in Statistics
quiz are: 7, 4, 3, 6, 7, 4, 8
Find:
a. Q1- Lower quartile
b. Q2 – Middle quartile
c. Q3 – Upper Quartile

Given: 3, 4, 4, 6, 7, 7, 8
Note: Scores must be arranged in ascending order
Qk = (n + 1) Qk = (n + 1) Qk = (n + 1)
Q1 = ( 7+ 1) Q2 = ( 7+ 1) Q3 = ( 7+ 1)
Q1 = 2nd
Q2 = 4th
Q3 = 6th
Q1 is 4 Q2 is 6 Q3 is 7

LINEAR INTERPOLATION
-a method of finding the quartile value.
-is a method of constructing new data points
within the range of an discrete set of known data
points.
-We need to use the interpolation if the value of
the position is in the decimal form.

Steps in using the interpolation method
1. Arrange the scores in ascending order
2. Locate the position of the score in the distribution
3. Since the result is in decimal number, proceed to linear
interpolation.
4. Find the difference between the two values wherein Q1 is
situated
5. Multiply the result in step 2 by the decimal part obtained in
step 4
6. Add the result in step 5 to the second smaller number in step 4

Example 2.
Find the first quartile (Q1) and third quartile (Q3),
given the scores of 9 students in their
mathematics activity using linear interpolation
1, 27, 16, 7, 31, 7, 30, 3, 21

Step 1: Arrange the scores in ascending order
1, 3, 7, 7, 16, 21, 27, 30, 31
Step 2: Locate the position of the score in the
distribution
Q1 = (n + 1)
= (9 + 1)
Q1 = 2.5 th

Step 3:Since the result is in decimal number, proceed to
linear interpolation.
Step 4: Find the difference between the two values
wherein Q1 is situated
1, 3, 7, 7, 16, 21, 27, 30, 31
Q1 is between the values 3 and 7, therefore
= 7 – 3
= 4

Step 5: Multiply the result in step 2 by the decimal part
obtained in step 4
= 4( 0.5)
= 2
Step 6: Add the result in step 5 to the second smaller
number in step 4
= 3 + 2
= 5
Therefore the value of Q1 is equal to 5

Find the 3rd
Quartile (Q3) = ?

Step1: 1, 3, 7, 7, 16, 21, 27, 30, 31
Step 2: Q3 = (n + 1)
= (9 + 1)
Q1 = 7.5 th
Step 3:
Step 4: Q3 is between 27 and 30
30 – 27 = 4
Step 5: 4(0.5) = 2
Step 6: 27 + 2 = 29

Activity 1
1. Find the Q1, Q2 and Q3 given the scores of 11
students in their Mathematics activity using
Mendenhall and Sincich Method
4, 9, 7, 14, 10, 8, 12, 15, 6, 11, 9
2. Find the Q1, Q2 and Q3 given the scores of 11 students
in their Mathematics activity using linear interpolation: 4,
9, 7, 14, 10, 8, 12, 15, 6, 11

DECILES
 Deciles are the nine score points which divide a
distribution into ten equal parts.

DECILES FOR UNGROUPED DATA
Example 3
Find the 3rd
decile or D3 of the following scores of
a random sample of ten students:
35, 42, 40, 28, 15, 23, 33, 20, 18 and 28.

Solution:
Arrange in ascending order.
15, 18, 20, 23, 28, 28, 33, 35, 40, 42
To find its D3 position, use the Dk = (n + 1) and round off
to the nearest integer.
D3 = (n + 1) = (10 + 1) = (11) = 3.3 3
D3 is the 3rd
element
Therefore, D3 = 20

Example 4
a. Mrs Labonate gave a test to her students in
statistics. The students finished their test in 35
minutes. This time is the 2.5th
decile of the allotted
time. What does this mean?
b. Anthony is a secretary in one big company in Metro
Manila. His salary is in the 7th
decile. Should Anthony
be glad about his salary or not? Explain your answer.

Explanation
a. This means that 25% of the learners finished the
test. A low quartile considered good, because it
means the students finished the test in a short
period of time.
b. 70% of the employees receive a salary that is less
than or equal to his salary and 30% of the
employees receive a salary that is greater than his
salary. Anthony should be pleased with his salary.

Activity 2
Mrs. Marasigan is a veterinarian. One morning,
she asked her secretary to record the service
time for 15 customers. The following are service
times in minutes: 20, 35, 55, 28, 46, 32, 25, 56,
55, 28, 37, 60, 47, 52, 17. Find the value of 2nd
decile, 6th
decile and 8th
decile.

PERCENTILES
 are ninety-nine score points which divide the
distribution into one hundred equal parts, so
that each part represent the data set.

PERCENTILES FOR UNGROUPED DATA
Example 5
Find the 60th
percentile or P60 of the following test
scores of a random sample of ten students:
35, 42, 40, 28, 15, 23, 33, 20, 18 and 28.

PERCENTILES FOR UNGROUPED DATA
Solution:
Arrange in ascending order.
15, 18, 20, 23, 28, 28, 33, 35, 40, 42
To find its P60 position, use the Dk = (n + 1) and
round off to the nearest integer.
P60 = (n + 1) = (10 + 1) = (11) = 6.6 7
P60 is the 7th
element
Therefore, P60 = 33

PERCENTILES
Activity 3
The scores of Miss World candidates from seven
judges were recorded as follows:
8.45, 9.20, 8.56, 9.13, 8.67, 8.85 and 9.17.
What is the P35 of the judges’ scores?

MEASURES OF POSITION FOR
GROUPED DATA

measures of Position Quartile, Decile, Percentile

measures of Position Quartile, Decile, Percentile

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measures of Position Quartile, Decile, Percentile