# Find the Mean Deviation from the Mean for the Data:Classes0-100100-200200-300300-400400-500500-600600-700700-800frequencies489107543 - Mathematics

Find the mean deviation from the mean for the data:

 Classes 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 Frequencies 4 8 9 10 7 5 4 3

#### Solution

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

 Classes $f_i$ Midpoints   $x_i$ $f_i x_i$ $\left| x_i - X \right|$ =   $\left| x_i - 358 \right|$ $f_i \left| x_i - X \right|$ 0−100 4 50 200 308 1232 100−200 8 150 1200 208 1664 200−300 9 250 2250 108 972 300−400 10 350 3500 8 80 400−500 7 450 3150 92 644 500−600 5 550 2750 192 960 600−700 4 650 2600 292 1168 700−800 3 750 2250 392 1176 $\sum^8_{i = 1} f_i = 50$ $\sum^8_{i = 1} f_ix_i= 17900$ $\sum^8_{i = 1} f_i \left| x_i - X \right| = 7896$

$N = \sum^6_{i = 1} f_i = 50$ and

$\sum^6_{i = 1} f_i x_i = 17900$

$\bar{ X } = \frac{\sum^{8} _{i = 1} f_i x_i}{\sum ^8_{i = 1} f_i} = \frac{17900}{50} = 358$

$\therefore \text{ Mean deviation } = \frac{1}{N} \sum^8_{i = 1} f_i \left| x_i - X \right|$
$= \frac{7896}{50}$
$= 157 . 92$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.3 | Q 2.1 | Page 16

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