# Find the Mean Deviation from the Mean for the Data:Xi1030507090fi42428168 - Mathematics

Find the mean deviation from the mean for the data:

 xi 10 30 50 70 90 fi 4 24 28 16 8

#### Solution

 xi fi fi​xi $\left| x_i - \bar{x} \right|$ $f_i \left| x_i - 50 \right|$ 10 4 40 40 160 30 24 720 20 480 50 28 1400 0 0 70 16 1120 20 320 90 8 720 40 320 $N = 80$ $\sum^n_{i = 1} f_i x_i = 4000$ $\sum^n_{i = 1} f_i \left| x_i - 50 \right| = 1280$
$\bar{ x } = \frac{\sum ^n _{i = 1} f_ix_i}{N} = \frac{4000}{80} = 50$
$MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i -\bar{ x } \right| = \frac{1}{80} \times 1280 = 16$
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.2 | Q 4.3 | Page 11