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Question
Following 10 observations are arranged in ascending order as follows.
2, 3, 5, 9, x + 1, x + 3, 14, 16, 19, 20
If the median of the data is 11, find the value of x.
Solution
Observations are arranged in ascending order as follows:
2, 3, 5, 9, x + 1, x + 3, 14, 16, 19, 20
As, the number of observations = 10, which is an even number.
∴ The numbers in the five and six observations will come to the middle.
Median = 11
∴ मध्यक = `((x + 1) + (x + 3))/2`
∴ 11 = `(2x + 4)/2`
∴ 11 × 2 = 2x + 4
∴ 22 = 2x + 4
∴ 22 − 4 = 2x
∴ 2x = 18
∴ x = `18/2`
∴ x = 9
So, the value of x is 9.
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