Question

Let the data \(4, 10, x, y, 27\) be in the increasing order. If the median of the data is 18 and its mean deviation about mean is 7.6, then the mean of this data is :

• A. 16.5
• B. 17
• C. 16
• D. 15.5

Hint:

The median of five ordered values is the middle one, so \(x=18\); express \(y\) through the mean and use the mean deviation condition.

Answer 1

The Correct Option is A

For five values in increasing order the median is the third value, so \(x=18\) and \(y\ge 18\).
Let the mean be \(m\). Then \(4+10+18+y+27=5m\), so \(y=5m-59\).
Since \(18\le y\le 27\), we get \(15.4\le m\le 17.2\). In this range \(m>10\), \(m<18\) and \(y-m=4m-59>0\), so the absolute deviations are \(m-4,\ m-10,\ 18-m,\ 4m-59,\ 27-m\).
Their sum is \((m-4)+(m-10)+(18-m)+(4m-59)+(27-m)=4m-28\).
Mean deviation \(=\frac{4m-28}{5}=7.6\) gives \(4m=66\), so \(m=16.5\) (then \(y=23.5\), consistent with the ordering).
Answer: (1) 16.5