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Median

Find the medi...

Question

Question 58
Find the median of the given data, if the mean is 4.5.
5, 7, 7, 8, x, 5, 4, 3, 1, 2

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Solution

Given, mean = 4.5
We know that, $M e a n = \frac{S u m o f a l l o b s e r v a t i o n s}{T o t a l n u m b e r o f o b s e r v a t i o n s} \Rightarrow 4.5 = \frac{5 + 7 + 7 + 8 + x + 5 + 4 + 3 + 1 + 2}{10} \Rightarrow 4.5 \times 10 = 42 + x \Rightarrow 45 - 42 = x ∴ x = 3$
Now, arrange the data in ascending order
1, 2, 3, 3, 4, 5, 5, 7, 7, 8.
Here, n = 10 (even)
Median $= \frac{V a l u e o f \frac{n}{2} t h o b s e r v a t i o n + V a l u e o f (\frac{n}{2} + 1) t h o b s e r v a t i o n}{2} = \frac{V a l u e o f 5 t h o b s e r v a t i o n + V a l u e o f 6 t h o b s e r v a t i o n}{2} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5$

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