This presentation is all about finding the percentile, decile and quartile of a grouped data. an example is provided in each type of measure of positions.

1. Quarter 4
Week 2
MATH10
OBJECTIVE
S
1. Identify the specific
measures of position.
(e.g. Percentile,
Decile, Quartile)
2. Calculate the specific
measures of position.
(e.g. Percentile, Decile,
Quartile).
LYN ON ME

3. Frequency Distribution Table (FDT)

4. Frequency Distribution Table (FDT)
• Class Limits
• Class Frequency
• Class Boundaries
• Class Width
• Class Mark

5. Frequency Distribution Table (FDT)
• Class Limits
• – the smallest (lower
class limit) and largest
(upper class limit)
values that can fall in a
given class interval

6. Frequency Distribution Table (FDT)
• Class Frequency
– the number of
observations falling
in a particular class.

7. Frequency Distribution Table (FDT)
• Class Boundaries
– are values halfway
between the upper class
limit of one class and
the lower class limit of
the next class.

8. Frequency Distribution Table (FDT)
• Class Width
– are numerical
difference between the
upper and lower
boundaries of any class.

9. Frequency Distribution Table (FDT)
• Class Mark
– midpoint between the
given class interval.
- The average of the
upper limit and the
lower limit of a class.

10. Computing the Percentile of
Grouped Data
𝑃𝑘= 𝐿𝑝 +
𝑐(
𝑛𝑘
100
−𝐹𝑏)
𝑓𝑝

11. Computing the Percentile of Grouped Data
𝑃𝑘= 𝐿𝑝 +
𝑐(
𝑛𝑘
100
−𝐹𝑏)
𝑓𝑝

12. Score frequency
1 - 10 4
11 - 20 18
21 - 30 21
31 - 40 49
41 - 50 21
51 - 60 7
EXAMPLE 1: Consider the scores of 120 grade 10 students in
the 3rd quarter math examination, find the 30th percentile of
the distribution.

13. Score frequency Lower class bound Cumulative
frequency
1 - 10 4
11 - 20 18
21 - 30 21
31 - 40 49
41 - 50 21
51 - 60 7
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 30th percentile of the distribution.
n = 120

14. Score frequency Lower class bound Cumulative
frequency
1 - 10 4
11 - 20 18
21 - 30 21
31 - 40 49
41 - 50 21
51 - 60 7
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 30th percentile of the distribution.
1- 0.5
11- 0.5
21- 0.5
0.5
10.5
20.5
Minus 0.5

15. Score frequency Lower class bound Cumulative
frequency
1 - 10 4 0.5
11 - 20 18 10.5
21 - 30 21 20.5
31 - 40 49 30.5
41 - 50 21 40.5
51 - 60 7 50.5
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 30th percentile of the distribution.

16. Score frequency Lower class bound Cumulative
frequency
1 - 10 4
11 - 20 18
21 - 30 21
31 - 40 49
41 - 50 21
51 - 60 7
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 30th percentile of the distribution.
92
113
120
4
22
43

17. Score frequency Lower class
bound
Cumulative
frequency
1 - 10 4 0.5 4
11 - 20 18 10.5 22
21 - 30 21 20.5 43
31 - 40 49 30.5 92
41 - 50 21 40.5 113
51 - 60 7 50.5 120
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 30th percentile of the distribution.
Compute
𝑛𝑘
100
n = 120
n = 120 k = 30
𝑛𝑘
100
=
120(30)
100
= 36

18. Score frequen
cy
Lower class
bound
Cumulative
frequency
1 - 10 4 0.5 4
11 - 20 18 10.5 22
21 - 30 21 20.5 43
31 - 40 49 30.5 92
41 - 50 21 40.5 113
51 - 60 7 50.5 120
Lp = 20.5
fp = 21
Fb = 22
c = 10
𝑛𝑘
100
= 36
𝑃𝑘= 𝐿𝑝 +
𝑐(
𝑛𝑘
100
−𝐹𝑏)
𝑓𝑝
𝑃30 = 20.5 + 10(36 − 22)
21

19. Computing the Percentile of Grouped Data
𝑃30 = 20.5 +
10(36 − 22)
21
𝑃30 = 20.5 + 6.67 = 27.17
Therefore, the 30th percentile of this set of data is 27.17.
Interpretation: 30% of all data points are below (or less than) 27.17
𝑃𝑘= 𝐿𝑝 +
𝑐(
𝑛𝑘
100
−𝐹𝑏)
𝑓𝑝

20. Computing the Decile of Grouped Data
𝐷𝑘= 𝐿𝐷 +
𝑐(
𝑛𝑘
10
−𝐹𝑏)
𝑓𝐷

21. Computing the Decile of Grouped Data
𝐷𝑘= 𝐿𝐷 +
𝑐(
𝑛𝑘
10
−𝐹𝑏)
𝑓𝐷

22. Score frequency Lower class bound Cumulative
frequency
1 - 10 4 0.5 4
11 - 20 18 10.5 22
21 - 30 21 20.5 43
31 - 40 49 30.5 92
41 - 50 21 40.5 113
51 - 60 7 50.5 120
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 7th decile of the distribution.

23. Score frequency Lower class
bound
Cumulative
frequency
1 - 10 4 0.5 4
11 - 20 18 10.5 22
21 - 30 21 20.5 43
31 - 40 49 30.5 92
41 - 50 21 40.5 113
51 - 60 7 50.5 120
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 7th decile of the distribution.
Compute
𝑛𝑘
10
n = 120
n = 120 k = 7
𝑛𝑘
10
=
120(7)
10
= 84

24. Score frequency Lower class
boundary
Cumulative
frequency
1 - 10 4 0.5 4
11 - 20 18 10.5 22
21 - 30 21 20.5 43
31 - 40 49 30.5 92
41 - 50 21 40.5 113
51 - 60 7 50.5 120
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 7h decile of the distribution.
LD = 30.5
fD = 49
Fb = 43
c = 10
𝑛𝑘
100
= 84
𝐷𝑘= 𝐿𝐷 +
𝑐(
𝑛𝑘
10
−𝐹𝑏)
𝑓𝐷

25. Computing the Decile of Grouped Data
𝐷7 = 20.5 + 8.37 = 38.87
Therefore, the 7th decile of this set of data is 38.87.
Interpretation: 70% of all data points are below (or less than) 38.87
𝐷𝑘= 𝐿𝐷 +
𝑐(
𝑛𝑘
10
−𝐹𝑏)
𝑓𝐷
𝐷7= 30.5 +
10(84−43)
49
LD = 30.5
fD = 49
Fb = 43
c = 10
𝑛𝑘
100
= 84

26. Computing the Quartile of Grouped Data
𝑄𝑘= 𝐿𝑄 +
𝑐(
𝑛𝑘
4
−𝐹𝑏)
𝑓𝑄

27. Score frequency Lower class bound Cumulative
frequency
1 - 10 4 0.5 4
11 - 20 18 10.5 22
21 - 30 21 20.5 43
31 - 40 49 30.5 92
41 - 50 21 40.5 113
51 - 60 7 50.5 120
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 1st quartile of the distribution.

28. Score frequency Lower class
bound
Cumulative
frequency
1 - 10 4 0.5 4
11 - 20 18 10.5 22
21 - 30 21 20.5 43
31 - 40 49 30.5 92
41 - 50 21 40.5 113
51 - 60 7 50.5 120
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 1st quartile of the distribution.
Compute
𝑛𝑘
4
n = 120
n = 120 k = 1
𝑛𝑘
4
=
120(1)
4
= 30

29. Score frequency Lower class
bound
Cumulative
frequency
1 - 10 4 0.5 4
11 - 20 18 10.5 22
21 - 30 21 20.5 43
31 - 40 49 30.5 92
41 - 50 21 40.5 113
51 - 60 7 50.5 120
EXAMPLE 1: Consider the scores of 120 grade 10 students in the 3rd quarter
math examination, find the 1st quartile of the distribution.
LQ = 20.5
fQ = 21
Fb = 22
c = 10
𝑛𝑘
4
= 30
𝑄𝑘= 𝐿𝑄 +
𝑐(
𝑛𝑘
4
−𝐹𝑏)
𝑓𝑄

30. Computing the Quartile of Grouped Data
𝑄1 = 20.5 + 10(30 − 22)
21
𝑄1 = 20.5 + 3.81 = 24.31
Therefore, the 1st quartile of this set of data is 24.31.
Interpretation: 25% of all data points are below (or less than) 24.31.
𝑄𝑘= 𝐿𝑄 +
𝑐(
𝑛𝑘
4
−𝐹𝑏)
𝑓𝑄
LQ = 20.5
c = 10
𝑛𝑘
4
= 30
Fb = 22
fQ = 21

32. Activity 1
The following measurements are weights of dogs in a city
veterinary clinic (in pounds): 65, 63, 68, 59, 74, 59, 68, 61, 64, 60,
69, 72, 55, 64, 56, 67, 55, 73, 59, 60, 65
a. Complete the table including the
lower boundaries and
cumulative frequencies.
b. Which interval contains the median?
c. Which interval contains the upper
quartile?
d. What is the 75th percentile of
this distribution?