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 8^th 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, 8^th term is 19