Question

The observation 29, 32, 48, 50, x, x+2, 72, 78, 84, 95 are arranged in ascending order. What is the value of x if the median of the data is 63?

Answer 1

If number of observations is even, then the median will be the average of `(n/2)th and the (n/2+1)`th observations.
In the given case, 𝑛=10⟹`(n/2)`𝑡ℎ=5 𝑡ℎ 𝑎𝑛𝑑 `(n/2+1)`𝑡ℎ=6𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛.
Thus, 63=`(x+(x+2))/2`
⟹126=2𝑥+2
⟹ 124=2𝑥
⟹ 𝑥=62
Thus, the value of x is 62.