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प्रश्न
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.
उत्तर
11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47
n = 9, odd
∴ Median = `((9 + 1)/(2))^(th)`
24 = 5th observation = (x + 4)
24 = x + 4 ...(As median = 24)
24 – 4 = x
`=>` x = 20
∴ Observation are 11, 12, 14, (20 – 2), (20 + 4), (20 + 9), 32, 38, 47
or
11, 12, 14, 18, 24, 29, 32, 38, 47
Mean = `barX`
= `(11 + 12 + 14 + 18 + 24 + 29 + 32 + 38 + 47)/(9)`
= `(225)/(9)`
= 25
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