Chapter 11.6, Problem 19PPSE

Solution

Toidentify:The quartiles by graphing a box and whisker plot of the data.

  

Quartiles for June: $Q_1=83,Q_3=84$

Quartiles for July: $Q_1=85,Q_3=86$

Quartiles for August: $Q_1=85,Q_3=86$

Given information:

The given graph is shown below:

  

Explanation:

Consider the given information.

Make the table by using the graph.

June	84	84	85	82	83
July	85	86	87	84	85
August	86	86	87	84	85

Since the total number of data set is 5 which is odd number so median is the exactly middle value.

Find Quartiles for June:

Sorted the data as shown:

82, 83, 84, 84, 85

Thus, median is 84.

First quartile $Q_1$ of the data set is the data value at the middle position of the first half of the ordered data set. Since there are 5 values so the first half of the data set has 3 data values including mean. So $Q_1$ will be the 2^nd value which is 83.

The third $Q_3$ of the data set is the data value at the middle position of the second half of the ordered data set. Since there are 5 values so the second half of the data set has 3 data values. So $Q_3$ will be the 4^th value which is 84.

Find Quartiles for July:

Sorted the data as shown:

84, 85, 85, 86, 87

Thus, median is 85.

First quartile $Q_1$ of the data set is the data value at the middle position of the first half of the ordered data set. Since there are 5 values so the first half of the data set has 3 data values including mean. So $Q_1$ will be the 2^nd value which is 85.

The third $Q_3$ of the data set is the data value at the middle position of the second half of the ordered data set. Since there are 5 values so the second half of the data set has 3 data values. So $Q_3$ will be the 4^th value which is 86.

Find Quartiles for August:

Sorted the data as shown:

84, 85, 86, 86, 87

Thus, median is 86.

First quartile $Q_1$ of the data set is the data value at the middle position of the first half of the ordered data set. Since there are 5 values so the first half of the data set has 3 data values including mean. So $Q_1$ will be the 2^nd value which is 85.

The third $Q_3$ of the data set is the data value at the middle position of the second half of the ordered data set. Since there are 5 values so the second half of the data set has 3 data values. So $Q_3$ will be the 4^th value which is 86.

The required graph is shown below: