Question

The runs scored by RCB in the first 6 matches of IPL-17 are respectively 172, 157, 148, 142, 161, 213. Find the mean deviation about median of the scores using the assumed mean method.

• A. 13.5
• B. 14.5
• C. 15.5
• D. 16.5

Answer 1

The correct option is D

16.5

Arrange the scores in ascending order
142, 148, 157, 161, 172, 213

$Median=\frac{157+161}{2}=159$

Calculate deviations about an assumed mean (A) of 160.

Deviations from the assumed mean are tabulated below

$\begin{array}{cc}X& D=|X-A|\\ 142& 18\\ 148& 12\\ 157& 3\\ 161& 1\\ 172& 12\\ 213& 53\\ & \sum D=99\end{array}$

$M.D\left(M\right)=\frac{\sum D+(M-A)(\sum f_B-\sum f_A)}{n}=\frac{99+(159-160)(3-3)}{6}=\frac{99}{6}=16.5$