Question

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?

Answer 1

Let `barx` be the mean of n number of observation x₁, x₂, x₃, ......, x_n.
Mean = `[ x_1 + x_2 + x_3 + ....... + x_n ]/n`

Therefore,
Mean of given data = `[ 35 + 48 + 92 + 76 + 64 + 52 + 51 + 63 + 71 ]/9`

= `552/9`
= 61.33

Let us rewrite the given data in ascending order:
Thus, we have
35, 48, 51, 52, 63, 64, 71, 76, 92
There are 9 observations, which is odd.

Therefore, median = `(( n +1 )/2)^"th"` Observation

⇒ Median = `(( 9 + 1)/2)^"th"` Observation

⇒ Median = `( 10/2 )^"th"` Observation 

⇒ Median = 5^th Observation 

⇒ Median = 63.

If 51 is replaced by 66, the new set of data in ascending order is: 35, 48, 52, 63, 64, 66, 71, 76, 92
Since median = 5^th observation,
We have a new median = 64.