Question

1. the test scores from mrs. grays math class are shown below.

72, 73, 66, 71, 82, 85, 95, 85, 86, 89, 91, 92
construct a box - and - whisker plot to display these data.

Explanation:

Step1: Order the data

First, we need to order the data from least to greatest.
The data is: 66, 71, 72, 73, 82, 85, 85, 86, 89, 91, 92, 95

Step2: Find the minimum and maximum

The minimum value (the smallest number) is 66.
The maximum value (the largest number) is 95.

Step3: Find the median (Q2)

Since there are 12 data points (an even number), the median is the average of the 6th and 7th values.
The 6th value is 85 and the 7th value is 85.
Median $Q2=\frac{85 + 85}{2}=85$

Step4: Find the lower quartile (Q1)

The lower half of the data is: 66, 71, 72, 73, 82, 85 (the first 6 values).
The median of the lower half (Q1) is the average of the 3rd and 4th values in this lower half.
The 3rd value is 72 and the 4th value is 73.
$Q1=\frac{72+73}{2}=\frac{145}{2} = 72.5$

Step5: Find the upper quartile (Q3)

The upper half of the data is: 85, 86, 89, 91, 92, 95 (the last 6 values).
The median of the upper half (Q3) is the average of the 3rd and 4th values in this upper half.
The 3rd value is 89 and the 4th value is 91.
$Q3=\frac{89 + 91}{2}=\frac{180}{2}=90$

Now, to construct the box - and - whisker plot:

• The minimum value (66) is the left end of the left whisker.
• The lower quartile (Q1 = 72.5) is the left end of the box.
• The median (Q2 = 85) is the line inside the box.
• The upper quartile (Q3 = 90) is the right end of the box.
• The maximum value (95) is the right end of the right whisker.

Answer:

To construct the box - and - whisker plot, we use the values: minimum = 66, Q1 = 72.5, median = 85, Q3 = 90, maximum = 95. The box - and - whisker plot will have a left whisker from 66 to 72.5, a box from 72.5 to 90 with a line at 85 (the median), and a right whisker from 90 to 95. (Note: Since this is a description of the box - and - whisker plot construction, the final answer in terms of the key values for the plot are min = 66, Q1 = 72.5, median = 85, Q3 = 90, max = 95)