Question

Age of pandas in a zoo is plotted in the box and whisker plot. Find which of the following data set is represented by the given plot.


\( \begin{array}{llllllllllll}8 & 10 & 12 & 14 & 16 & 18 & 20 & 22 & 24 & 26 & 28 & 30\end{array} \)

• A. 12, 14, 16, 18, 18, 24, 28
• B. 12, 14, 16, 20, 20, 26, 28
• C. 10, 12, 14, 16, 18, 20, 24
• D. 12, 14, 16, 18, 20, 24, 28

Answer 1

The correct option is D 12, 14, 16, 18, 20, 24, 28

Let us find the lower quartile, median and upper quartile of the given plot.


The first data set is

12, 14, 16, 18, 20, 24, 28

For a set with an odd number of values, the median is the middle value of the data set when it is arranged in an ascending or descending order.

In a box and whisker plot, the box is drawn from the first quartile (lower quartile) to the third quartile (upper quartile).

Hence, median of the data set = 18.
Lower half data = 12, 14, 16
Lower quartile = 14
Upper half data = 20, 24, 28
Upper quartile = 24
Hence, Q1, Q2, Q3 of the data are 14, 18, 24. Hence, this satisfies the given box plot.



The next data set is

12, 14, 16, 20, 20, 26, 28

Median of the data set = 20.
Lower half data = 12, 14, 16
Lower quartile = 14
Upper half data = 20, 26, 28
Upper quartile = 26
Hence, Q1, Q2, Q3 of the data are 14, 20, 26. Hence, this does not satisfy the given box plot.



The next data set is

10, 12, 14, 16, 18, 20, 24

Median of the data set = 16.
Lower half data = 10, 12, 14
Lower quartile = 12
Upper half data = 18, 20, 24
Upper quartile = 20
Hence, Q1, Q2, Q3 of the data are 12, 16, 20. Hence, this does not satisfy the given box plot.


The next data set is
12, 14, 16, 18, 18, 24, 28

Median of the data set = 18.
Lower half data = 12, 14, 16
Lower quartile = 14
Upper half data = 18, 24, 28
Upper quartile = 24
Hence, Q1, Q2, Q3 of the data are 14, 18, 24. Hence, this does not satisfy the given box plot


Hence, the data set 12, 14, 16, 18, 20, 24, 28 is plotted in the given box plot.