The document discusses cumulative frequency distributions and how to convert them to simple frequency distributions. It provides examples of converting cumulative frequency tables with class intervals of varying sizes to simple frequency tables by taking the differences between cumulative frequency counts. This allows one to find the simple frequency for each class interval.

1. Session 12

2. Measures of Central
Tendency
Arithmetic Mean

3. Cumulative Frequency
Cumulative frequency distribution has a running total of the values.
It is constructed by adding the frequency of the first class interval to the
frequency of the second class interval, and so on…
x f
15-20 3
20-25 7
25-30 15
30-35 21
35-40 12
40-45 6
Less than
Cumulative
Frequency

4. Cumulative Frequency
Cumulative frequency distribution has a running total of the values. It is
constructed by adding the frequency of the first class interval to the frequency of
the second class interval, and so on…
Less than
x f
15-20 3
20-25 7
25-30 15
30-35 21
35-40 12
40-45 6
Less than
Cumulative
Frequency
3
10
25
46
58
64

5. Cumulative Frequency
Cumulative frequency distribution has a running total of the values. It is
constructed by adding the frequency of the first class interval to the frequency of
the second class interval, and so on…
x f
15-20 3
20-25 7
25-30 15
30-35 21
35-40 12
40-45 6
More than
Cumulative
Frequency

6. Cumulative Frequency
Cumulative frequency distribution has a running total of the values. It is
constructed by adding the frequency of the first class interval to the frequency of
the second class interval, and so on…
More than
x f
15-20 3
20-25 7
25-30 15
30-35 21
35-40 12
40-45 6
More than
Cumulative
Frequency
64
61
54
39
18
6

7. Conversion of cumulative frequency - Less than
x c f
Less than 20 3
Less than 25 10
Less than 30 25
Less than 35 46
Less than 40 58
Less than 45 64
In x values end values upper limit
How to Convert cf into f
Find the differences b/w x values
Find the lower limit
20-5 = 15
25-5 = 20
30-5 = 25
35-5 = 30
40-5 = 35
45-5 = 40
Here difference is 5
Now find the lower limit by deducting
difference form upper limit
Lower limit

8. How to Convert cf into f
Find the lower limit
x c f
15-20 3
20-25 10
25-30 25
30-35 46
35-40 58
40-45 64
f
3
Find the simple frequency (f)
10-3 =7
25-10=15
46-25=21
58-46=12
64-58=6
Conversion of cumulative frequency - Less than

9. x c f
15-20 3
20-25 10
25-30 25
30-35 46
35-40 58
40-45 64
f
3
7
15
21
12
6
Conversion of cumulative frequency - Less than

10. Problem- Less than
x c f
Less than 5 3
Less than 10 12
Less than 15 18
Less than 20 30
Less than 25 55
Less than 30 78
Less than 35 92
Less than 40 100
5-5 = 0
10-5 = 5
15-5 = 10
20-5 = 15
25-5 = 20
30-5 = 25
35-5 = 30
40-5 = 40
Lower limit
difference is 5

11. Problem- Less than
x c f
0-5 3
5-10 12
10-15 18
15-20 30
20-25 55
25-30 78
30-35 92
35-40 100
f
3
12-3 = 9
18-12= 6
30-18 = 12
78-55= 23
55-30= 25
92-78= 14
100-92= 8
f
3
9
6
12
25
23
14
8

12. Problem- Less than
x c f
Less than 20 4
Less than 30 9
Less than 40 15
Less than 50 32
Less than 60 45
Less than 70 52
Less than 80 60
Less than 90 67
Less than 100 75
difference is 10

13. Problem- Less than
x c f
10-20 4
20-30 9
30-40 15
40-50 32
50-60 45
60-70 52
70-80 60
80-90 67
90-100 75
difference is 10
f
4
5
6
17
13
7
8
7
8

14. Problem- Less than
x c f
Less than 110 4
Less than 120 14
Less than 130 26
Less than 140 42
Less than 150 62
Less than 160 75
Less than 170 90
Less than 180 100
difference is 10

15. Problem- Less than
x c f
100-110 4
110-120 14
120-130 26
130-140 42
140-150 62
150-160 75
160-170 90
170-180 100
f
4
10
12
16
20
13
15
10

16. Problem- Less than
x c f
Less than 20 4
Less than 22 10
Less than 24 24
Less than 26 33
Less than 28 50
Less than 30 70
Less than 32 85
Less than 34 95
Less than 36 100
difference is 2

17. Problem- Less than
x c f
18-20 4
20-22 10
22-24 18
24-26 33
26-28 50
28-30 70
30-32 85
32-34 95
34-36 100
f
4
6
8
15
17
20
15
10
5

18. Problem- Less than
x c f
Less than 100 4
Less than 200 9
Less than 300 22
Less than 400 30
Less than 500 47
Less than 600 52
Less than 700 64
Less than 800 70
Less than 900 75
Home Work 1

19. Problem- Less than
x c f
Less than 50 3
Less than 150 12
Less than 200 25
Less than 250 37
Less than 300 55
Less than 350 73
Less than 400 84
Less than 450 92
Less than 500 100
Home Work 2

20. Problem- Less than
x c f
Less than 9.5 5
Less than 19.5 13
Less than 29.5 27
Less than 39.5 40
Less than 49.5 62
Less than 59.5 76
Less than 69.5 84
Less than 79.5 90
Less than 89.5 97
Less than 99.5 100
Home Work 3