Question

the data shows a sample of states percentage of public high school graduation rates for a recent year.
75 87 76 85 81 88 66 75 89 90 85 87 73
send data to excel
part: 0 / 2
part 1 of 2
draw the boxplot for the given data.
(there is a boxplot drawing area with a number line labeled high school graduation rates from 60 to 100, and some interactive buttons on the right.)

Explanation:

Step1: Order the data

First, we order the data set: \( 66, 73, 75, 75, 76, 81, 85, 85, 87, 87, 88, 89, 90 \)

Step2: Find the median (Q2)

The number of data points \( n = 13 \), which is odd. The median is the middle value, at position \( \frac{n + 1}{2}=\frac{13+1}{2}=7 \). So the median (Q2) is the 7th value, which is \( 85 \).

Step3: Find Q1 (median of lower half)

The lower half of the data (excluding the median) is \( 66, 73, 75, 75, 76, 81 \) (6 values). The median of this set is the average of the 3rd and 4th values. The 3rd value is \( 75 \), the 4th value is \( 75 \). So \( Q1=\frac{75 + 75}{2}=75 \).

Step4: Find Q3 (median of upper half)

The upper half of the data (excluding the median) is \( 85, 87, 87, 88, 89, 90 \) (6 values). The median of this set is the average of the 3rd and 4th values. The 3rd value is \( 87 \), the 4th value is \( 88 \). So \( Q3=\frac{87+88}{2}=87.5 \).

Step5: Find the minimum and maximum

The minimum value is \( 66 \), and the maximum value is \( 90 \).

Step6: Draw the boxplot

• The box spans from Q1 (\( 75 \)) to Q3 (\( 87.5 \)), with a line at the median (Q2, \( 85 \)) inside the box.
• The whiskers extend from the minimum (\( 66 \)) to Q1 and from Q3 to the maximum (\( 90 \)).

Answer:

To draw the boxplot:

• Minimum: \( 66 \)
• Q1: \( 75 \)
• Median (Q2): \( 85 \)
• Q3: \( 87.5 \)
• Maximum: \( 90 \)

The box is between \( 75 \) and \( 87.5 \), with a line at \( 85 \). The left whisker goes from \( 66 \) to \( 75 \), and the right whisker goes from \( 87.5 \) to \( 90 \).