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Question
If the median of the scores 1, 2, x, 4, 5 (where 1 < 2 < x < 4 < 5) is 3, then find the mean of the scores.
Solution
The given data is 1, 2, x, 4 and 5. Since 1<2<x<4<5, the given data is already in ascending order.
Here, the number of observation n = 5 , which is an odd number.
Hence, the median is
`((n+1)/2)^(th) ` observation
`= ((5+1)/2)^(th) `observation
=3rd observation
= x
Here, it is given that the median is 3. Hence, we have x = 3.
The mean is `(1+2+3+4+5)/5`
`=15/5`
= 3
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Is it the correct answer and why?
