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Question
The mean of 35 observations is 20, out of which mean of first 18 observations is 15 and mean of last 18 observation is 25. Find the 18th observation.
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Solution
Mean = `("sum of observations")/("Total number of observations")`
∴ sum of observations = Mean × Total number of observations
∴ sum of 35 observations = 20 × 35
= 700
Sum of first 18th observations = 15 × 18
= 270
Sum of last 18th observations = 25 × 18
= 450
18th observation = Sum of first 18 observations + Sum of last 18 observations - 35th observations
= 270 + 450 − 700
= 720 − 700
= 20
∴ The 18th observation is 20.
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