# Find the Mean, Mode, S.D. and Coefficient of Skewness for the Following Data: Year Render:102030405060no. of Persons (Cumulative):1532517897109 - Mathematics

Find the mean, mode, S.D. and coefficient of skewness for the following data:

 Year render: 10 20 30 40 50 60 No. of persons (cumulative): 15 32 51 78 97 109

#### Solution

 Year render No. of persons (cumulative) $f_i$ $u_i = \frac{x_i - 35}{10}$ $f_i u_i$ ${u_i}^2$ $f_i {u_i}^2$ 10 15 15 - 2.5 - 37.5 6.25 93.75 20 32 17 - 1.5 - 25.5 2.25 38.25 30 51 19 - 0.5 - 9.5 0.25 4.75 40 78 27 0.5 13.5 0.25 6.75 50 97 19 1.5 28.5 2.25 42.75 60 109 12 2.5 30 6.25 75 $\sum f_i = N = 109$ $\sum f_i u_i = - 0 . 5$ $\sum f_i {u_i}^2 = 261 . 25$

$\bar{X} = A + h\left( \frac{\sum f_i u_i}{N} \right)$

$= 35 + 10\left( \frac{- 0 . 5}{109} \right)$

$= 34 . 96 \text{ years }$

$\sigma^2 = h^2 \left[ \frac{\sum f_i {u_i}^2}{N} - \left( \frac{\sum f_i u_i}{N} \right)^2 \right]$

$= 100\left[ \frac{261 . 25}{109} - \frac{0 . 25}{11881} \right]$

$= 100 \times 2 . 396$

$= 239 . 6$

$\sigma = \sqrt{239 . 6}$

$= 15 . 47 \text{ years }$

Coefficient of skewness = Mean - Mode

= 34.96 - 40

= -5.04

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.5 | Q 3 | Page 38