Find the mean and median of the data :

35, 48, 92, 76, 64, 52, 51, 63 and 71.

If 51 is replaced by 66, what will be the new median ?

Mean = $\dfrac{\text{Sum of all observations}}{\text{Number of all observations}}$

= $\dfrac{35 + 48 + 92 + 76 + 64 + 52 + 51 + 63 + 71}{9}$

= $\dfrac{552}{9}$

= 61.33

Hence, the mean is 61.33.

On arranging the given set of data in ascending order, we get :

35, 48, 51, 52, 63, 64, 71, 76, 92

Number of observations, n = 9 (odd)

Median = $\Big[\dfrac{n+1}{2}\Big]^{th}$ term

= $\Big[\dfrac{9+1}{2}\Big]^{th}$ term

= $\Big[\dfrac{10}{2}\Big]^{th}$ term

= $5^{th}$ term

= 63

Hence, the median is 63.

When 51 is replaced by 66, and the given set of data is arranged in ascending order, we get :

35, 48, 52, 63, 64, 66, 71, 76, 92

Number of observations, n = 9 (odd)

Median = $\Big[\dfrac{n+1}{2}\Big]^{th}$ term

= $\Big[\dfrac{9+1}{2}\Big]^{th}$ term

= $\Big[\dfrac{10}{2}\Big]^{th}$ term

= $5^{th}$ term

= 64

Hence, the new median is 64.