The following is the cumulative frequency distribution (of less than type) of 1000 persons each of age 20 years and above. Determine the mean age
Age below (in years) 30 40 50 60 70 80
Number of persons 100 220 350 750 950 1000
Solution:
Given, the data represents the less than type cumulative frequency distribution of 1000 persons each of age 20 years and above.
We have to determine the mean age.
|
Age below (in years) |
Number of persons (cf) |
Class |
frequency |
|
Below 30 |
100 |
20 - 30 |
100 |
|
Below 40 |
220 |
30 - 40 |
220 - 100 = 120 |
|
Below 50 |
350 |
40 - 50 |
350 - 220 = 130 |
|
Below 60 |
750 |
50 - 60 |
750 - 350 = 400 |
|
Below 70 |
950 |
60 - 70 |
950 - 750 = 200 |
|
Below 80 |
1000 |
70 - 80 |
1000 - 950 = 50 |
To find mean,
|
Class |
Frequency (fi) |
Class mark (xi) |
ui = (xi - 45)/10 |
fiui |
|
20 - 30 |
100 |
25 |
-2 |
-200 |
|
30 - 40 |
120 |
35 |
-1 |
-120 |
|
40 - 50 |
130 |
45 |
0 |
0 |
|
50 - 60 |
400 |
55 |
1 |
400 |
|
60 - 70 |
200 |
65 |
2 |
400 |
|
70 - 80 |
50 |
75 |
3 |
150 |
|
Total |
∑fi = 1000 |
∑fiui = 630 |
We know that
A = 45, h = 10, ∑fi = 1000 and ∑fiui = 630
Mean = A + (h × ∑fiui / ∑fi)
Substituting the values
Mean = 45 + (10 × 630/1000)
= 45 + 6.3
= 51.3
Therefore, the mean is 51.3 years
✦ Try This: The following is the cumulative frequency distribution (of less than type) of some persons each of age 20 years and above. Determine the mean age.
| Age below (in years) | Number of persons |
| 10 | 120 |
| 20 | 230 |
| 30 | 340 |
| 40 | 760 |
| 50 | 850 |
| 60 | 990 |
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14
NCERT Exemplar Class 10 Maths Exercise 13.4 Sample Problem 1
The following is the cumulative frequency distribution (of less than type) of 1000 persons each of age 20 years and above. Determine the mean age. Age below (in years)30 40 50 60 70 80 Number of persons 100 220 350 750 950 1000
Summary:
The mean age of 100 persons each of age 20 years and above is 51.3 years
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