Question

The following dot plots show the number of baskets scored by two players in 31 basketball matches. Each dot represents a match played.

What is the difference between the median of the lower half of the data set (Q1) of Player A and the upper half of the data set (Q3) of Player B?

• A. $41$
• B. $40$
• C. $42$
• D. $43$

Answer 1

The correct option is C $42$

As the number of matches played is odd, to find the median basket count, we will have to use the following formula: ${\left(\frac{n+1}{2}\right)}^{th}$ term
Here $n=31$, where $n$ is the number of matches played.

Median basket count $={\left(\frac{31+1}{2}\right)}^{th}$ term $={\frac{32}{2}}^{th}$ term $={16}^{th}$ term

Player A:

Number of elements in the lower half of the data set $=16-1=15$
Median of the lower half of the data set $={\left(\frac{15+1}{2}\right)}^{th}$ term from the start
$=8^{th}$ term from the start
$=105$ baskets

Player B:

Similarly, the number of elements in the upper half of the data set $=16-1=15.$
Median of the upper half of the data set $={\left(\frac{15+1}{2}\right)}^{th}$ term from the last
$=8^{th}$ term from the last
$=63$ baskets

Difference between the medians = |105-63|=42