This document provides examples of calculating relative frequency distributions and percentage frequency distributions from raw data. It defines relative frequency as the frequency divided by the total frequency, and percentage frequency as the relative frequency multiplied by 100. The first example uses data on student weights to calculate these distributions and answer questions about percentages of students within certain weight ranges. The second example calculates distributions from data on children's birthdays and estimates births on a particular day if the total births were 10,000.

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
https://www.slideshare.net/NadeemUddin17
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2. Relative Frequency Distribution:
A relative frequency distribution is made by dividing
each frequency of a distribution by the total frequency
and expressing the result either as a decimal or as a
percent(Percentage frequency distribution).
1-The total of relative frequencies always equal to one.
2- The total of Percentage frequency distribution
always equal to 100.

3. Example-1
The following data show the weights (in pounds) of 30 students of a
school.
(a) Find relative frequency distribution.
(b) Find percentage frequency distribution.
(c) What percentage of the student‘s weight is less 117 pounds.
(d) What percentage of the student‘s weight is over 117 pounds.
(e) What percentage of the student‘s weight is in between 100 and 126
pounds.
Class Interval Frequency
91 - 99 3
100 – 108 7
109 – 117 11
118 – 126 7
127 – 135 2
30

4. Class
Interval
Frequency Relative Frequency=
𝒇
𝒇
Percentage Frequency=
𝒇
𝒇
× 𝟏𝟎𝟎
91 - 99 3
100 – 108 7
109 – 117 11
118 – 126 7
127 – 135 2
30 1 100
1.0
30
3
 10100
30
3

23.0
30
7

33.23100
30
7

37.0
30
11
 67.36100
30
11

23.0
30
7

33.23100
30
7

07.0
30
2
 67.6100
30
2

Solution:
(a) And (b)

5. (c) From column four
Percentage of the student's weight is less 117 pounds = 10% + 23.33% + 36.67%
Percentage of the student's weight is less 117 pounds = 70%
(d) From column four
Percentage of the student's weight is over 117 pounds = 23.33% + 6.67%
Percentage of the student's weight is over 117 pounds = 30%

6. (e) From column four
Percentage of the student's weight is in between 100 and 126 pounds =
23.33% + 36.67% + 23.33%
Percentage of the student's weight is in between 100 and 126 pounds = 83.33%

7. We can also classify information according to qualitative
characteristics, such as blood group, color of cars, race,
religion and gender, which do not fall into numerical
categories.
Example – 2
The following data show the birthdays of 25 children.
Days f
Mon
Tue
Wed
Thu
Fri
Sat
Sun
4
2
5
2
2
7
3
25

8. (a) Find relative frequency distribution and percentage frequency distribution.
(b) Estimate the number of birth on Saturday if the total birth is 10,000 in a city.
Solution:
(a) Days F Relative
frequency
Percentage
frequency
Mon
Tue
Wed
Thu
Fri
Sat
Sun
4
2
5
2
2
7
3
0.16
0.08
0.2
0.08
0.08
0.28
0.12
16
8
20
8
8
28
12
25 1 100
(b) Number of birth on Saturday = 10,000 × 28% = 1200 births