# Find the Mean Deviation from the Mean for the Data:Classes95-105105-115115-125125-135135-145145-155frequencies91316263012 - Mathematics

Find the mean deviation from the mean for the data:

 Classes 95-105 105-115 115-125 125-135 135-145 145-155 Frequencies 9 13 16 26 30 12

#### Solution

We will compute the mean deviation from the mean in the following way:

 Classes Frequency  $f_i$ Midpoints $x_i$ $f_i x_i$ $\left| x_i - X \right|$ = $\left| x_i - 128 . 58 \right|$ $f_i \left| x_i - X \right|$ 95−105 9 100 900 28.58 257.22 105−115 13 110 1430 18.58 241.54 115−125 16 120 1920 8.58 137.28 125−135 26 130 3380 1.42 36.92 135−145 30 140 4200 11.42 342.6 145−155 12 150 1800 21.42 257.04 $\sum^6_{i = 1} f_i = 106$ $\sum^6_{i = 1} f_i x_i = 13630$ $\sum^8_{i = 1}| f_i x_i |- \bar{x}= 1272.6$

$N = \sum^6_{i = 1} f_i = 106$ and

$\sum^6_{i = 1} f_i x_i = 13630$

$\therefore X = \frac{\sum^6_{i = 1} f_i x_i}{\sum^6_{i = 1} f_i}$

$= \frac{13630}{106}$

$= 128 . 58$

$\therefore \text{ Mean deviation } = \frac{1}{N} \sum^8_{i = 1} f_i \left| x_i - X \right|$

$= \frac{1272 . 6}{106}$

$= 12 . 005$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.3 | Q 2.2 | Page 16