Find the mean deviation about mean for the following continuous distribution. | Height (in cms) | 95-105 | 105-115 | 115-125 | 125-135 | 135-145 | 145-155 | |---|---|---|---|---|---|---| | No. of Boys | 9 | 13 | 26 | 30 | 12 | 10 |

> > [!TLDR] > Find the mean using class midpoints, then take the frequency-weighted average of the absolute deviations of each midpoint from the mean. > > Class midpoints $x_i$ and frequencies $f_i$: > > | Class | 95-105 | 105-115 | 115-125 | 125-135 | 135-145 | 145-155 | > |---|---|---|---|---|---|---| > | $x_i$ | 100 | 110 | 120 | 130 | 140 | 150 | > | $f_i$ | 9 | 13 | 26 | 30 | 12 | 10 | > > $N=\sum f_i = 9+13+26+30+12+10=100$. > > **Mean:** $\sum f_ix_i = 900+1430+3120+3900+1680+1500=12530$. > > $$\bar x = \frac{12530}{100} = 125.3.$$ > > **Absolute deviations $|x_i-\bar x|$ and their weighted sum:** > > | $x_i$ | $|x_i-125.3|$ | $f_i$ | $f_i|x_i-125.3|$ | > |---|---|---|---| > | 100 | 25.3 | 9 | 227.7 | > | 110 | 15.3 | 13 | 198.9 | …

Find the mean deviation about mean for the followi – Class 12 Mathematics

Question of 165

Find the mean deviation about mean for the following continuous distribution.

Height (in cms)	95-105	105-115	115-125	125-135	135-145	145-155
No. of Boys	9	13	26	30	12	10

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Find the mean using class midpoints, then take the frequency-weighted average of the absolute deviations of each midpoint from the mean.

Class midpoints $x_i$ and frequencies $f_i$ :

Class	95-105	105-115	115-125	125-135	135-145	145-155
$x_i$	100	110	120	130	140	150
$f_i$	9	13	26	30	12	10

$N=\sum f_i = 9+13+26+30+12+10=100$ .

Mean: $\sum f_ix_i = 900+1430+3120+3900+1680+1500=12530$ .

$\bar x = \frac{12530}{100} = 125.3.$

Absolute deviations $|x_i-\bar x|$ and their weighted sum:

| $x_i$ | $|x_i-125.3|$ | $f_i$ | $f_i|x_i-125.3|$ |

|---|---|---|---|

| 100 | 25.3 | 9 | 227.7 |

| 110 | 15.3 | 13 | 198.9 | …

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