Find the mean and variance for the following frequency distribution- Class 0-10 10-20 20-30 30-40 40-50 Frequencies 5 8 15 16 6

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Standard XI

Statistics

Mean Deviation from Mean for Continuous Series

Find the mean...

Question

Find the mean and variance for the following frequency distribution.

$\begin{matrix} Class & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 Frequencies & 5 & 8 & 15 & 16 & 6 \end{matrix}$

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Solution

$\begin{matrix} Mid values Classes & x_{i} & f_{i} & u = \frac{x - 105}{30} & f u & f u^{2} 0 - 10 & 5 & 5 & - 2 & - 6 & 18 10 - 20 & 15 & 8 & - 1 & - 6 & 12 20 - 30 & 25 & 15 & 0 & - 5 & 5 30 - 40 & 35 & 16 & 1 & 0 & 0 40 - 50 & 45 & 6 & 2 & 3 & 3 50 & 10 & 68 \end{matrix}$

$M e a n (¯ ¯ ¯ x) = A + \frac{\sum f u}{N} \times h = 25 + \frac{10}{50} \times 10 = 25 + 2 = 27$

$V a r i a n c e (σ^{2}) = \frac{h^{2}}{N^{2}} [N \sum f u^{2} - (\sum f u)^{2}]$ $= \frac{(10)^{2}}{(50)^{2}} [50 \times 68 - (10)^{2}] = \frac{100}{2500} [3400 - 100] = \frac{1}{25} \times 3300 = 132$ .

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Find the mean and variance for the following frequency distribution. Class 0−10 10−20 20−30 30−40 40−50 Frequencies 5 8 15 16 6

Mid valuesClasses xi fiu=x−10530fufu20−10 5 5 −2−61810−20 15 8 −1−61220−30 25 15 0−5 530−40 35 16 1 0 040−50 45 6 2 3 350 1068 Mean(¯¯¯x)=A+∑fuN×h=25+1050×10=25+2=27 Variance(σ2)=h2N2[N∑fu2−(∑fu)2] =(10)2(50)2[50×68−(10)2]=1002500[3400−100]=125×3300=132.

Find the mean and variance for the following frequency distribution.

$\begin{matrix} Class & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 Frequencies & 5 & 8 & 15 & 16 & 6 \end{matrix}$