Question

The bar graph shows the frequency of wickets taken by a bowler in her career. The median number of wickets taken in a match is __________ (rounded off to one decimal place).

Hint:

In grouped or frequency data, find the interval in which the median observation lies using cumulative frequency.

Answer 1

Correct Answer: 4

From the bar graph, the frequencies are: \[ \begin{aligned} 0 &: 5
1 &: 7
2 &: 8
3 &: 25
4 &: 20
5 &: 17
6 &: 8
7 &: 4
8 &: 3
9 &: 2
10 &: 1 \end{aligned} \] Total matches: \[ N = 5 + 7 + 8 + 25 + 20 + 17 + 8 + 4 + 3 + 2 + 1 = 100 \] For an even number of observations, the median is the average of the 50th and 51st observations in the cumulative distribution. Compute cumulative frequencies: \[ \begin{aligned} 0 &: 5
1 &: 12
2 &: 20
3 &: 45
4 &: 65
\end{aligned} \] The 50th and 51st observations both fall in the interval corresponding to 4 wickets. Thus the median number of wickets is: \[ \boxed{4.0} \]