The average heights of students of different grades are given. If the mean and median are same, find the value of x.

120

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113

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122

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126

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Solution

The correct option is B 113
The given data set is

102, 108, x, 118, 124

Here, x is the median of the given data.

It is given that mean and median of the data set are same.
Mean = $\frac{s u m o f a l l d a t a}{n u m b e r o f d a t a}$

Mean = $\frac{102 + 108 + 118 + 124 + x}{5}$

$⟹$ x= $\frac{452 + x}{5}$

$⟹$ x $\times$ 5 = 452 + x

$⟹$ 5x - x = 452

$⟹$ 4x = 452

$⟹$ x = $\frac{452}{4}$

=113

Hence, the value of x is 113.

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