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The mean of first 8 observations is 18 and last 8 observations is 20 . If the mean of all 15 observations is 19 , find the 8 th observation?

The mean of first 8 observation = 18

So, Sum of first 8 observation = 818 = 144

And, the mean of last 8 observation = 20

So, sum of last 8 observation = 820 =160

Sum of 16 observation = 144 +160 = 304

Sum of 15 observation = (1519) =285

Eighth observation = (sum of 16 observation) – (sum of 15 observation)

   = (304) – (285) = 19

Hence, 8th observation is 19.

 

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 Sum of observations/ No. of observations = Mean

so Mean * No. of observations = Sum of observations

Mean of first 8 observations = 18

Sum of observations (S1) = 18 * 8 =144

Mean of last 8 observations = 20

Sum of observations (S2) = 20*8 = 160

Mean of all 15 observations = 19

Sum of observations (S3) = 19*15 = 285

8th observation = S3 - (S1 + S2)

 = 285 - 204

  = 81.

HOPE THIS HELPS!!!

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