Question

here are the scores of 16 students on a geography test. 61, 63, 64, 66, 66, 70, 73, 74, 75, 81, 81, 84, 87, 88, 89, 90. notice that the scores are ordered from least to greatest. make a box-and-whisker plot for the data.

Explanation:

Step1: Find the minimum and maximum

The minimum value (min) is the first data point, and the maximum value (max) is the last data point.
Min = 61, Max = 90

Step2: Find the median (Q2)

Since there are 16 data points (even number), the median is the average of the 8th and 9th values.
8th value: 74, 9th value: 75
Median ($Q_2$) = $\frac{74 + 75}{2} = 74.5$

Step3: Find the first quartile (Q1)

The first quartile is the median of the lower half (first 8 data points: 61, 63, 64, 66, 66, 70, 73, 74).
There are 8 data points (even), so Q1 is the average of the 4th and 5th values.
4th value: 66, 5th value: 66
$Q_1 = \frac{66 + 66}{2} = 66$

Step4: Find the third quartile (Q3)

The third quartile is the median of the upper half (last 8 data points: 75, 81, 81, 84, 87, 88, 89, 90).
There are 8 data points (even), so Q3 is the average of the 4th and 5th values.
4th value: 84, 5th value: 87
$Q_3 = \frac{84 + 87}{2} = 85.5$

Step5: Plot the values

• Min: 61 (left whisker end)
• Q1: 66 (left box end)
• Median (Q2): 74.5 (middle line in box)
• Q3: 85.5 (right box end)
• Max: 90 (right whisker end)

On the number line, mark these points:

• Draw a dot at 61 (min)
• Draw a dot at 66 (Q1)
• Draw a dot at 74.5 (median)
• Draw a dot at 85.5 (Q3)
• Draw a dot at 90 (max)
• Draw the box from 66 to 85.5, with a vertical line at 74.5.
• Draw the whiskers from 61 to 66 and from 85.5 to 90.

Answer:

The box - and - whisker plot has:

• Minimum: 61
• First Quartile ($Q_1$): 66
• Median ($Q_2$): 74.5
• Third Quartile ($Q_3$): 85.5
• Maximum: 90

When plotted on the given number line (from 60 to 90 with appropriate intervals), the box is between 66 and 85.5, the median line is at 74.5, the left whisker goes from 61 to 66, and the right whisker goes from 85.5 to 90.