Find out the missing value of the variate for the following distr… - Vidyadip

Question

Find out the missing value of the variate for the following distribution whose mean is 31.87.

Value (X)	12	20	27	33	?	54
Frequency (f)	8	16	48	90	30	8

✓

Answer

The missing value of the variate is taken as Y.

Value (X)	Frequency (f)	fX
12	8	96
20	16	320
27	48	1296
33	90	2970
Y	30	30Y
54	8	432
	$\Sigma f=200$	$\Sigma f X=5114+30 Y$

Here,
$\begin{array}{l}
\bar{X}=31.87 \text { (Given) } \\
\Sigma f=200 \\
\Sigma f X=5114+30 Y
\end{array}$
Now,
$\bar{X}=\frac{\Sigma f X}{\Sigma f}$
Now substituting the values in above formula, we get
$\begin{array}{l}
\Rightarrow \quad 31.87=\frac{5114+30 Y}{200} \\
\Rightarrow 31.87 \times 200=5114+30 Y \\
\Rightarrow 6374=5114+30 Y \\
\Rightarrow 1260=30 Y \\
\Rightarrow Y=\frac{1260}{30}=42
\end{array}$
Hence, the missing value of the variate for the given distribution is $4 2$.

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