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Question
The median of the following observations
11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24.
Find the value of x and hence find the mean.
Solution
The observations in ascending order are:
11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47
Number of observations = n = 9 (odd)
Median = `((n+1)/2)^"th"`observation = 5th observation
∴ x + 4 = 24
`=> x = 20`
Thus, the observations are 11, 12, 14, 18, 24, 29, 32, 38, 47
`:. "Mean" = (11 + 12 + 14 + 18 + 24 + 29 + 32 + 38 + 47)/9 = 225/9 = 25`
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