Question

independent practice
using the line provided, construct a box - and - whisker plot for the 12 scores below.
26, 32, 19, 65, 57, 16, 28, 42, 40, 21, 38, 10

Explanation:

Step1: Order the data

First, we need to order the given scores from least to greatest. The scores are 26, 32, 19, 65, 57, 16, 28, 42, 40, 21, 38, 10. When we order them, we get: 10, 16, 19, 21, 26, 28, 32, 38, 40, 42, 57, 65.

Step2: Find the minimum and maximum

The minimum value (the smallest number) in the ordered data is 10, and the maximum value (the largest number) is 65.

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 28 and the 7th value is 32. So the median \( Q2=\frac{28 + 32}{2}=\frac{60}{2} = 30\).

Step4: Find the lower quartile (Q1)

The lower half of the data is the first 6 values: 10, 16, 19, 21, 26, 28. The median of this lower half (Q1) is the average of the 3rd and 4th values. The 3rd value is 19 and the 4th value is 21. So \( Q1=\frac{19+21}{2}=\frac{40}{2}=20\).

Step5: Find the upper quartile (Q3)

The upper half of the data is the last 6 values: 32, 38, 40, 42, 57, 65. The median of this upper half (Q3) is the average of the 3rd and 4th values. The 3rd value is 40 and the 4th value is 42. So \( Q3=\frac{40 + 42}{2}=\frac{82}{2}=41\).

Step6: Construct the box - and - whisker plot

• The minimum value (10) is the left - most point of the whisker.
• The lower quartile (Q1 = 20) is the left - hand side of the box.
• The median (Q2 = 30) is the line inside the box.
• The upper quartile (Q3 = 41) is the right - hand side of the box.
• The maximum value (65) is the right - most point of the whisker.

To draw the plot on the number line:

1. Mark the minimum (10) and maximum (65) on the number line.
2. Draw a box from Q1 (20) to Q3 (41).
3. Draw a vertical line inside the box at the median (30).
4. Draw whiskers from the box to the minimum (10) and maximum (65).

Answer:

To construct the box - and - whisker plot:

• Minimum: 10
• Q1: 20
• Median (Q2): 30
• Q3: 41
• Maximum: 65

On the given number line, mark 10 (left whisker end), draw a box from 20 to 41 with a vertical line at 30 inside the box, and draw the right whisker to 65.