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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.
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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