Introduction to statistics

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Question

If the arithmetic mean of the following data is 7, then
$a + b =$
$x_{i}$ 4 6 7 9
$f_{i}$ a 4 b 5

Easy

Solution

We have,
$\begin{array}{l} 7 = \frac{4 a + 24 + 7 b + 45}{a + 4 + b + 5} \\ \Rightarrow 4 a + 7 b + 69 = 7 a + 7 b + 63 \Rightarrow a = 2 \end{array}$

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