Calculate the mean deviation (about the mean) and the standard deviation for the following distribution. | Classes | 20–40 | 40–80 | 80–100 | 100–120 | 120–140 | | --- | --- | --- | --- | --- | --- | | Frequencies | 3 | 6 | 20 | 12 | 9 |

Calculate the mean deviation (about the mean) and – Class 11 Economics

Exercises · Q11

Calculate the mean deviation (about the mean) and the standard deviation for the following distribution.

Classes	20–40	40–80	80–100	100–120	120–140
Frequencies	3	6	20	12	9

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Mean = 94.8; M.D.(mean) = 19.97; S.D. = 26.17.

Step 1 — Mean. Class mid-points are 30, 60, 90, 110, 130. $\sum fm = (3)(30) + (6)(60) + (20)(90) + (12)(110) + (9)(130) = 90 + 360 + 1800 + 1320 + 1170 = 4740$ , and $\sum f = 50$ , so $\bar{X} = \dfrac{4740}{50} = 94.8$ .

Step 2 — Working table (with $d = m - 94.8$ ).

Class	f	m	\|d\|	f\|d\|	fd²
20–40	3	30	64.8	194.4	12597.12
40–80	6	60	34.8	208.8	7266.24
80–100	20	90	4.8	96.0	460.80
100–120	12	110	15.2	182.4	2772.48
120–140	9	130	35.2	316.8	11151.36

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