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प्रश्न
The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of x.
उत्तर
The numbers are 6, 8, 10, 12, 13 and x
Mean = `(6 + 8 + 10 + 12 + 13 + x)/(6)`
Mean = `(49 + x)/(6)` ...(1)
For Median
n = 6 ...(Even)
Median = `((n/2)^(th) term + (n/2 + 1)^(th) term)/(2)`
∴ Median = `(3^(rd) term + 4^(th) term)/(2)`
= `(10 + 12)/(2)`
= `(22)/(2)`
= 11 ...(2)
From (1) and (2) (From question)
Median = Mean
∴ `11 = (49 + x)/(6)`
`=>` x = 66 – 49
`=>` x = 17
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