Chapter 12.5, Problem 11MCQ

To determine

To Find: The values of minimum, first quartile, median, third quartile, and maximum of each data set.

Answer to Problem 11MCQ

The value of the minimum of the data set (2) is $6$ . and the maximum of the data set (2) is $42$ . And the value of Median: $28$ , and the value of first quartile $Q_1=8.$ ,And value of Third quartile is $Q_3=37.$

Explanation of Solution

Given information:

The value of Commute $(mi):8$ $33$ $28$ $7$ $42$ $9$ $30$ $38$ $22$ $6$ $37$

Calculation:

Let us consider the data for the commute $(mi);$

$8$

$33$

$28$

$7$

$42$

$9$

$30$

$38$

$22$

$6$

$37$

Identify the minimum, first quartile, median, third quartile, and maximum of each data set (1). Then make a box and whisker plot.

Use two parts to given the answer: in first part identify the minimum, first quartile, median, third quartile, and maximum of each data set, and in the second part make a box and whisker plot.

Part I: use the following steps to identify minimum, first quartile, median, third quartile, and maximum of each data set given in (1).

Step 1: arrange the data in increasing order that is order from least to greatest.

$6$

$7$

$8$

$9$

$22$

$28$

$30$

$33$

$37$

$38$

$42$

Step 2: Find the minimum and maximum:

Minimum: The least number is data set is called the minimum. Therefore the minimum of the data set (2) is $6$ .

Maximum: The greatest number in data set is called maximum. Therefore the maximum of the data set (2) is $42$ .

Step 3: Find the median.

Median: The median is the middle value in the data set, when data values are arranged in order and it is represented by $Q$ . If the numbers of data values are even in the data set, then the median of an even number of data values is the mean of the two middle data values and if the numbers of data values are odd in the data set, then the median is the muddle value in the data set. The numbers of data values given in equation(2) are odd. Hence its median is the middle data value is $28$ .

Median: $28$ .

Step 4: Find the first quartile and third quartile.

First Quartile: If the data set is divided into four equal parts, then the first quartile is the median of the lower half of the data and it is represented by $Q_1.$

The median of the lower half of the data is $8.$

Therefore first quartile $Q_1=8.$

Third Quartile: If the data set is divided in to four equal parts, then the third quartile is the median of the upper half of the data and it is represented by $Q_3.$

The median of the upper half of the data is $37.$

Therefore, the value of Third quartile is $Q_3=37.$

Part II: Make a box-and whisker plot for the data $set\left(2\right).$

A box-and −whisker plot is a graph that represented a set of data along a horizontal line. It consist three parts: a box, extended from first quartile to third quartile and has vertical line through median and two whiskers, the left whisker extended from minimum to first quartile and the right whisker extended from third quartile to the minimum.

Therefore, the box is;

  

Therefore, value of the minimum of the data set (2) is $6$ . and the maximum of the data set (2) is $42$ . And the value of Median: $28$ , and the value of first quartile $Q_1=8.$ ,And value of Third quartile is $Q_3=37.$