If the variance of the following frequency distribution is 50, then x is equal to Class10-2020-3030-40Frequency2x2

Solution:

Computation of Variance

Class	MId- Values x_i	Frequencies $f_{i}$	$u_{i} = \frac{x_{i} - 25}{10}$	$f_{i} u_{i}$	$f_{i} u_{i}^{2}$
10-20	15	2	-1	-2	2
20-30	25	x	0	0	0
30-40	35	2	1	2	2
		N=4+ x		$Σ f_{i} u_{i} = 0$	$Σ f_{i} u_{i}^{2} = 4$

$\bar{X} = 25 + 10 (\frac{1}{4 + x} \times 0) = 25 [Using \bar{X} = a + h (\frac{1}{N} Σ f_{i} u_{i})]$

Now,

Variance = 50

$\begin{array}{l} \Rightarrow h^{2} \{\frac{1}{N} Σ f_{i} u_{i}^{2} - {(\frac{1}{N} Σ f_{i} u_{i})}^{2}\} = 50 \\ \Rightarrow 100 (\frac{4}{4 + x} - 0) = 50 \Rightarrow 8 = 4 + x \Rightarrow x = 4 \end{array}$

If the variance of the following frequency distribution is 50, then x is equal to
Class 10-20 20-30 30-40
Frequency 2 x 2

Solution:

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