Introduction to statistics

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Question

If the mean of the following data is $5.5,$ then $x =$
$\begin{aligned} x_{i} \end{aligned}$ 2 4 6 8
$f_{i}$ 3 5 6 $x$

Moderate

Solution

We have,
Mean= $5.5$
$\begin{array}{l} \Rightarrow \frac{6 + 20 + 36 + 8 x}{3 + 5 + 6 + x} = 55 \\ \Rightarrow 62 + 8 x = (14 + x) \times 5.5 \Rightarrow 2.5 x = 15 \Rightarrow x = 6 \end{array}$

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Variate x	1	2	3	4	5
Frequency f of x	4	5	y	1	2