Q5 of 69 Page 6

The mean of 23 observations is 34. If the mean of the first 12 observations is 32 and that of the last 12 observations is 38, find the 12th observation.

Let the 12th observation be x


Given that mean of 23 observations = 34


∴ sum of 23 observations = 23 × 34 = 782


Mean of the first 12 observations = 32


Sum of first 12 observations = 12 × 32 = 384


Mean of the last 12 observations = 38


Sum of the last 12 observations = 12 × 38 = 456


Therefore,


Sum of first 12 observations + sum of last 12 observations – 12th observation = sum of 23 observations


384 + 456 - x = 782


⇒ 840 – x = 782


⇒ x = 58


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