Question

A scientist was studying the monthly rainfall pattern in regions A and B. The two sets of data shown below has the monthly rainfall recorded in cm for 8 months.

A: 16, 10, 10, 12, 0, 7, 12, 17

B: 8, 4, 3, 2, 10, 8, 3, 14

Compare the variability in monthly rainfall for regions A and B using the coefficient of mean deviation about the median.

• A. Region A shows more variability in monthly rainfall
• B. Region B shows more variability in monthly rainfall
• C. Both regions show equal variability in monthly rainfall
• D. Nothing can be concluded

Answer 1

The correct option is B

Region B shows more variability in monthly rainfall

Arranging in ascending order,

A: 0, 7, 10, 10, 12, 12, 16, 17
$Median=\frac{10+12}{2}=11$

B: 2, 3, 3, 4, 8, 8, 10,14
$Median=\frac{4+8}{2}=6$

Deviations of data A about median: 11, 4, 1, 1, 1, 1, 5, 6
Deviations of data B about median: 4, 3, 3, 2, 2, 2, 4, 8

$M.D_A\left(M\right)=\frac{11+4+1+1+1+1+5+6}{8}=\frac{30}{8}=3.75$

$M.D_B\left(M\right)=\frac{4+3+3+2+2+2+4+8}{8}=\frac{28}{8}=3.5$

$CoefficientofM.D_A\left(M\right)=\frac{3.75}{11}=0.34$
$CoefficientofM.D_B\left(M\right)=\frac{3.5}{6}=0.58$

Hence, region B has higher variability in monthly rainfall.