Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# In 22, 24, 30, 27, 29, 31, 25, 28, 41, 42 find the number of observations lying between ¯ X − M.D. and ¯ X + M.D, where M.D. is the mean deviation from the mean. - Mathematics

In  22, 24, 30, 27, 29, 31, 25, 28, 41, 42 find the number of observations lying between

$\bar { X }$  − M.D. and

$\bar { X }$   + M.D, where M.D. is the mean deviation from the mean.

#### Solution

Let $\bar{x}$   be the mean of the data set.

$\bar{ x } = \frac{22 + 24 + 30 + 27 + 29 + 31 + 25 + 28 + 41 + 42}{10} = 29 . 9$

 $x_i$ $\left| d_i \right| = \left| x_i - 29 . 9 \right|$ 22 7.9 24 5.9 30 0.1 27 2.9 29 0.9 31 1.1 25 4.9 28 1.9 41 11.9 42 12.1 Total 48.8

$MD = \frac{1}{10} \times 48 . 8 = 4 . 88$

$\bar{ x } - M . D . = 29 . 9 - 4 . 88 = 25 . 02,$

$\text{ and } \bar { x } + M . D . = 29 . 9 + 4 . 88 = 34 . 78$

There are 5 observations between 25.02 and 34.78.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.1 | Q 5.2 | Page 6