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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
Solution
Given data in ascending order: 6, 8, 10, 12, 13, x
Total number of observation = N = 6 (even)
:. Median = `((N/2)^"th" term + (N/2 +1)^"th" term)/2`
`= ((6/2)^"th" term + (6/2 + 1)^"th" term)/2`
`= ("3 rd term + 4th term")/2`
`= (10 + 12)/2`
`= 22/2`
= 11
Now, Mean = `(6 + 8 + 10 + 12 + 13 + x)/6 = (49 + x)/6`
It is given that
Mean = Median
`=> (49 + x)/6 = 11`
`=> 49 + x = 66`
`=> x = 17`
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