The mean of 13 observation is 14. If the mean of the first 7 observation is 12 and that of last 7 observation is 16, find the 7th observation.
The mean of 13 observation is 14. If the mean of the first 7 observation is 12 and that of last 7 observation is 16, find the 7th observation.
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Let the 7th observation be p. Now,
Sum of 13 observation = 13 × 14 = 182.
Sum of first 7 observation = 12 × 7 = 84.
Sum of last 7 observation = 16 × 7 = 112.
Sum of last 6 observation = 112 - p.
Sum of 13 observation = Sum of first 7 observation + Sum of last 6 observation
= 84 + 112 - p = 196 - p
So, 196 - p = 182
=>p = 196 - 182 = 14.
Thus, the 7th observation is 14.
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