This document provides information on calculating percentiles for grouped data. There are two key steps: 1) Locate the class where the percentile falls. For example, to find the 30th percentile, locate the class containing the 15th data point. 2) Use the formula: Percentile = Lower Boundary of class + (Cumulative Frequency of class - Actual Frequency below percentile) / Total Frequency * (Number of data points - Cumulative Frequency at class). This calculates what value corresponds to the percentile based on the class boundaries and frequencies. The document then works through an example calculating the 30th, 54th, and 86th percentiles using a table of workers' daily wages grouped into classes. It concludes by summar

1. MATHEMATICS 10
WELCOME TO

2. What are the two measures of
position for grouped data?

3. What is the formula for finding the
quartile for grouped data?

4. QUARTILE (𝑄𝑘) FOR
GROUPED DATA

5. DECILE (𝐷𝑘) FOR
GROUPED DATA

6. What is the third measure of position
for grouped data?

7. PERCENTILE FOR
GROUPED DATA

8. The following table shows the daily wages of 50 workers
in a private company.
How much does the bottom 30% of the employees
earn?

9. QUARTILE (𝑄𝑘) FOR
GROUPED DATA
DECILE (𝐷𝑘) FOR
GROUPED DATA

10. PERCENTILE FOR
GROUPED DATA

11. 30TH PERCENTILE (𝑃30)
FOR GROUPED DATA
Find 30th percentile
Example:
The following table shows the daily wages of 50
workers in a private company.
How much does the bottom 30% of the
employees earn?

12. EXAMPLE:
The following table shows the daily wages of
50 workers in a private company.
(Complete the Frequency Distribution Table
below)
Daily Wages
(Php)
Frequency
(f)
Lower
Boundary
(LB)
<cf
701 – 750 12 700.5 50
651 – 700 9 650.5 38
601 – 650 5 600.5 29
551 – 600 6 550.5 24
501 – 550 14 500.5 18
451 - 500 4 450.5 4
30TH PERCENTILE (𝑃30)
FOR GROUPED DATA

13. Daily Wages
(Php)
Frequency
(f)
Lower
Boundary
(LB)
<cf
701 – 750 12 700.5 50
651 – 700 9 650.5 38
601 – 650 5 600.5 29
551 – 600 6 550.5 24
501 – 550 14 500.5 18
451 - 500 4 450.5 4
Find 𝑃30
i. Locate the 𝑃30class:
𝑷𝟑𝟎
ii. 𝐿𝐵 =
𝑁 = 50
𝑐𝑓𝑏 =
𝑓𝑃30
=
𝑖 =
𝑘𝑁
100
30 × 50
100
=
1500
100
= 𝟏𝟓
500.5
4
14
50
30TH PERCENTILE (𝑃30)
FOR GROUPED DATA
i. Locate the 𝑃𝑘 class
ii. State the given

14. 𝑃30 = 500.5 +
1500
100
− 4
14
50
𝑃30 = 500.5 + 39.2857
𝑃30 = 539.7857 𝑜𝑟 539.79
iv. Therefore, 30% of the workers are earning less
than or equal to Php 539.79 daily.
30TH PERCENTILE (𝑃30)
FOR GROUPED DATA
𝑃30 = 500.5 +
15 − 4
14
50
𝑃30 = 500.5 +
11
14
50
Find 𝑃30
𝐿𝐵 = 500.5 𝑁 = 50
𝑐𝑓𝑏 = 4
𝑓𝑃30
= 14
𝑖 = 50 𝑘 = 30
𝑃30 = 500.5 +
30 × 50
100
− 4
14
50
iii.
i. Locate the 𝑃𝑘 class
ii. State the given
iii. Solve using the
formula
iv. Interpret

15. Using the same data, find 𝑃54 and 𝑃86
Daily Wages
(Php)
Frequency
(f)
Lower
Boundary
(LB)
<cf
701 – 750 12 700.5 50
651 – 700 9 650.5 38
601 – 650 5 600.5 29
551 – 600 6 550.5 24
501 – 550 14 500.5 18
451 - 500 4 450.5 4
PERCENTILE FOR
GROUPED DATA

16. GENERALIZATION
1. What is the process in finding the
percentile for grouped data
i. Locate the 𝑃𝑘 class
ii. State the given
iii. Solve using the formula
iv. Interpret
2. What is the formula finding the
percentile for ungrouped data?

17. Scores Frequency
(f)
LB <cf
46-50 4 45.5 50
41-45 8 40.5 46
36-40 11 35.5 38
31-35 9 30.5 27
26-30 12 25.5 18
21-25 6 20.5 6
Calculate the 32nd percentile of the Mathematics
test scores of 50 students.
PERCENTILE FOR
GROUPED DATA

18. THANK YOU!!!