Advertisements
Advertisements
Question
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.
Sum
Advertisements
Solution
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
shaalaa.com
Is there an error in this question or solution?
