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Finding Mean for Grouped Data When Class Intervals Are Not Given

In the freque...

Question

In the frequency distribution of discrete data given below the frequency $y$ against value $0$ is missing
Variable $(x)$ $0$ $1$ $2$ $3$ $4$ $5$
Frequency $(f)$ $y$ $20$ $40$ $40$ $20$ $4$
If the mean is $2.5$ then the missing frequency $y$ will be __________

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Solution

The correct option is D $4$
Mean $= \frac{\sum f_{i} x_{i}}{\sum f_{i}}$
$\Rightarrow \frac{0 \times y + 1 \times 20 + 2 \times 40 + 3 \times 40 + 4 \times 20 + 5 \times 4}{y + 20 + 40 + 40 + 20 + 4} = 2.5$
$\Rightarrow \frac{20 + 80 + 120 + 80 + 20}{124 + y} = 2.5$
$\Rightarrow 320 = 2.5 (124 + y)$
$\Rightarrow 320 = 310 + 2.5 y \Rightarrow 2.5 y = 10 \Rightarrow y = 4$

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Variable $(x)$	$0$	$1$	$2$	$3$	$4$	$5$
Frequency $(f)$	$y$	$20$	$40$	$40$	$20$	$4$