Q3 of 14 Page 269

The mean of first 8 observation is 18; last 8 observation is 20. If the mean of all 15 observation is 19 find the 8th observation

Let 8th observation be x


Mean of first 8 observations = 18


where K is sum of first 7 terms


x = 144 – k ..(i)


Mean of last 8 observations = 20


Where L is sum of last 7 terms


x = 160 – L ..(ii)


Equating both the equations


160 – L = 144 – K


16 + K = L ..(iii)


Mean of all 15 terms = 19



K + X + L = 285


From equation (i), (ii), (iii)


K + (144-K) + (16 + K) = 285


⇒ K = 125


Replacing value in equation (i)


We get x = 19


So, 8th term is 19


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