Answer :

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 yi = xi + 8 …(ii)


or xi = yi – 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


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