Question

The mean of x, x + 2, x + 4, x + 6 and x + 8 is 11, find the mean of the first three observations.

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

= `[ x + x + 2 + x + 4 + x + 6 + x + 8 ]/5` 

= `[ 5x + 20 ]/5`
= x + 4 

Also, it's given that mean of the given data is 11.
⇒ x + 4 = 11
⇒ x = 7

Hence the mean of the first three observation = `[ x + x + 2 + x + 4 ]/3`

= `[3x + 6]/3`
= x + 2
= 7 + 2
= 9.