Let the observations are x₁, x₂, x₃, x₄, …, x₁₅

and Let mean =

Given: Variance = 6 and n = 15

We know that,

Putting the given values, we get

or …(i)

It is given that each observation is increased by 8, we get new observations

Let the new observation be y₁, y₂, y₃, …, y₁₅

where y_i = x_i + 8 …(ii)

or x_i = y_i – 8 …(iii)

Now, we find the variance of new observations

Now, we calculate the value of

We know that,

[from eq. (ii)]

…(iv)

Putting the value of eq. (iii) and (iv) in eq. (i), we get

So,

= 6