Question

here are the scores of 17 students on a geography test. 57, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 76, 76, 81, 83, 87. 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 (smallest score) is 57, and the maximum value (largest score) is 87.

Step2: Find the median (Q2)

There are 17 data points. The median is the middle value, which is the 9th value (since \(\frac{17 + 1}{2}=9\)). The 9th value is 67. So, \(Q2 = 67\).

Step3: Find the lower quartile (Q1)

The lower half of the data is the first 8 values: 57, 59, 60, 61, 62, 63, 64, 65. The median of this lower half is the average of the 4th and 5th values. The 4th value is 61, and the 5th value is 62. So, \(Q1=\frac{61 + 62}{2}=\frac{123}{2} = 61.5\).

Step4: Find the upper quartile (Q3)

The upper half of the data is the last 8 values: 68, 69, 70, 76, 76, 81, 83, 87. The median of this upper half is the average of the 4th and 5th values. The 4th value is 76, and the 5th value is 76. So, \(Q3=\frac{76+76}{2}=76\).

Step5: Draw the box - and - whisker plot

• The left whisker extends from the minimum (57) to \(Q1\) (61.5).
• The box extends from \(Q1\) (61.5) to \(Q3\) (76), with a line inside the box at the median (67).
• The right whisker extends from \(Q3\) (76) to the maximum (87).

Answer:

To draw the box - and - whisker plot:

• Mark the minimum value (57) on the left end of the whisker.
• Mark \(Q1 = 61.5\) as the left end of the box.
• Mark the median \(Q2=67\) with a line inside the box.
• Mark \(Q3 = 76\) as the right end of the box.
• Mark the maximum value (87) on the right end of the whisker.

(On the given number line from 55 to 90, we place the points as follows: left whisker dot at 57, left box dot at 61.5, median dot at 67, right box dot at 76, right whisker dot at 87, and draw the box between 61.5 and 76 with the median line at 67, and whiskers from 57 to 61.5 and 76 to 87.)