Q.
The frequency distribution table is given here.
Class
30 - 40
40 - 50
50 - 60
60 - 70
70 - 80
80 - 90
90 - 100
Frequency
3
7
12
15
8
3
2
Find the mean
| Class | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| Frequency | 3 | 7 | 12 | 15 | 8 | 3 | 2 |
Statistics
Solution:
From the given data, we construct the following table:
Class
Frequency$f_i$
Mid point$( x_i)$
$ f_i x_i $
$(x_i - \bar x)^2$
$f_i(x_i - \bar x)^2$
30 - 40
3
35
105
729
2187
40 - 50
7
45
315
289
2023
50 - 60
12
55
660
49
588
60 - 70
15
65
975
9
135
70 - 80
8
75
600
169
1352
80 - 90
3
85
255
529
1587
90 - 100
2
95
190
1089
2178
Total
50
3100
10050
Thus Mean $ \bar x = \frac{1}{N} \sum\limits_{i=1}^{7} f_{i}x_{i}$
$ = \frac{3100}{50} = 62$,
| Class | Frequency$f_i$ | Mid point$( x_i)$ | $ f_i x_i $ | $(x_i - \bar x)^2$ | $f_i(x_i - \bar x)^2$ |
|---|---|---|---|---|---|
| 30 - 40 | 3 | 35 | 105 | 729 | 2187 |
| 40 - 50 | 7 | 45 | 315 | 289 | 2023 |
| 50 - 60 | 12 | 55 | 660 | 49 | 588 |
| 60 - 70 | 15 | 65 | 975 | 9 | 135 |
| 70 - 80 | 8 | 75 | 600 | 169 | 1352 |
| 80 - 90 | 3 | 85 | 255 | 529 | 1587 |
| 90 - 100 | 2 | 95 | 190 | 1089 | 2178 |
| Total | 50 | 3100 | 10050 |