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

# Calculate the A.M. and S.D. for the following distribution: Class: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Frequency: 18 16 15 12 10 5 2 1 - Mathematics

Calculate the A.M. and S.D. for the following distribution:

 Class: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Frequency: 18 16 15 12 10 5 2 1

#### Solution

 Class $f_i$ Midpoint $\left( x_i \right)$ $u_i = \frac{x_i - 35}{10}$ $f_i u_i$ $f_i {u_i}^2$ 0−10 18 5 -3 - 54 162 10−20 16 15 -2 - 32 64 20−30 15 25 -1 - 15 15 30−40 12 35 0 0 0 40−50 10 45 1 10 10 50−60 5 55 2 10 20 60−70 2 65 3 6 18 70−80 1 75 4 4 16 $\sum f_i = 79$ $\sum f_i u_i = - 71$ $\sum f_i {u_i}^2 = 305$
$\bar{X} = a + h\left( \frac{\sum f_i u_i}{N} \right) = 35 + 10\left( \frac{- 71}{79} \right) = 26 . 01$

AM = 26.01

$\sigma^2 = h^2 \left[ \frac{\sum f_i {u_i}^2}{N} - \left( \frac{\sum f_i u_i}{N} \right)^2 \right] = 100\left[ \frac{305}{79} - \frac{5041}{6241} \right] = 305 . 20$

$\sigma = \sqrt{305 . 20} = 17 . 47$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.6 | Q 3 | Page 42