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Find the mean deviation about the mean for the data Height

Question

Find the mean deviation about the mean for the data
Height of cms Number of boys
95-105 9
105-115 13
115-125 26
125-135 30
135-145 12
145-155 10

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Find the mean deviation about the mean for the data

Height of cms	Number of boys
95-105	9
105-115	13
115-125	26
125-135	30
135-145	12
145-155	10

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Text solutionVerified

The following table is formed

Height of cms	Number of boys $f_{i}$	mid-point $X_{i}$	$f_{i} \times X_{i}$	$∣ x_{i} - \overset{x}{ˉ} ∣$	$f_{i} ∣ x_{i} - \overset{x}{ˉ} ∣$
95-105	9	100	900	25.3	227.7
105-115	13	110	1430	14.3	198.9
115-125	26	120	3120	5.3	137.8
125-135	30	130	3900	4.7	141
135-145	12	140	1680	14.7	176.4
145-155	10	150	1500	24.7	247

Here

N = i = 1 \sum 6 f_{i} = 100, i = 1 \sum 6 f_{1} x_{i} = 12530

∴ \overset{ˉ}{X} = \frac{1}{N} i = 1 \sum 6 f_{i} x_{i} = \frac{1}{100} \times 12530 = 125.3

∴ M . D . (\overset{x}{ˉ}) = \frac{1}{N} i = 1 \sum 6 f_{i} ∣ x_{1} - \overset{x}{ˉ} ∣= \frac{1}{100} \times 1128.8 = 11.28

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Question Text	Find the mean deviation about the mean for the data
Answer Type	Text solution:1
Upvotes	150