Chapter SH, Problem 13.4.1EP

To determine

To construct: a box and whisker plot for the given data

Answer to Problem 13.4.1EP

The box and whiskers:

  

Explanation of Solution

Given:

  $42,23,31,27,32,48,37,25,19,26,30,41,32,29$

Calculation:

Step 1:

Arrange the data in increasing order.

  $19,23,25,26,27,29,30,31,32,32,37,41,42,48$

Draw the number line that contains the minimum and maximum values of the data.

  

Step 2:

Mark the minimum and maximum values, median, upper and lower quartiles above the number line. Identify the outliers. Denote it with asterisk. It is not connected with the plot.

Here median is $\frac{30+31}{2}=30.5$

Divide the data into two halves.

  $\stackrel{\text{Lower half}}{\overbrace{19,23,25,26,27,29,30}},\stackrel{\text{ median }}{30.5}\stackrel{\text{Upper hall }}{\overbrace{31,32,32,37,41,42,48}}$

Median of lower half is

  $LQ=26$

Median of upper half is

  $\text{UQ}=37$

  

Step 3:

Draw the box and whiskers.

  

Conclusion:

Therefore, the box and whiskers plot is drawn.