The observations 56, 58, 63, x-5, x+1, 75, 81 | vedclass

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(B) The given observations are $56, 58, 63, x-5, x+1, 75, 81, 85$. Total number of observations $n = 8$,which is an even number. For an even number of

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$69$

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(B) The given observations are $56, 58, 63, x-5, x+1, 75, 81, 85$. Total number of observations $n = 8$,which is an even number. For an even number of observations,the median is the average of the $(\frac{n}{2})^{th}$ and $(\frac{n}{2} + 1)^{th}$ terms. Here,$n = 8$,so the median is the average of the $4^{th}$ and $5^{th}$ terms. $4^{th}$ term $= x-5$ $5^{th}$ term $= x+1$ Median $= \frac{(x-5) + (x+1)}{2} = 67$ $\frac{2x - 4}{2} = 67$ $x - 2 = 67$ $x = 69$.

The observations $56, 58, 63, x-5, x+1, 75, 81, 85$ have been arranged in ascending order. If the median of the data is $67$,find the value of $x$.

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