Question

the data shows a sample of states percentage of public high school graduation rates for a recent year.
76 84 76 80 85 78 74 78 91 95 79 88
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part: 0 / 2
part 1 of 2
draw the boxplot for the given data.
(boxplot drawing area with axis labeled high school graduation rates from 60 to 100)

Explanation:

Step1: Order the data

First, we order the data set: \( 74, 76, 76, 78, 78, 79, 80, 84, 85, 88, 91, 95 \)

Step2: Find the median (Q2)

Since there are 12 data points, the median is the average of the 6th and 7th values. The 6th value is \( 79 \) and the 7th is \( 80 \), so \( \text{Median} = \frac{79 + 80}{2} = 79.5 \)

Step3: Find Q1 (median of lower half)

The lower half of the data (first 6 values: \( 74, 76, 76, 78, 78, 79 \)) has a median (Q1) as the average of the 3rd and 4th values. The 3rd value is \( 76 \) and the 4th is \( 78 \), so \( Q1 = \frac{76 + 78}{2} = 77 \)

Step4: Find Q3 (median of upper half)

The upper half of the data (last 6 values: \( 80, 84, 85, 88, 91, 95 \)) has a median (Q3) as the average of the 3rd and 4th values. The 3rd value is \( 85 \) and the 4th is \( 88 \), so \( Q3 = \frac{85 + 88}{2} = 86.5 \)

Step5: Find the minimum and maximum

The minimum value is \( 74 \) and the maximum is \( 95 \)

Step6: Draw the boxplot

• The box goes from Q1 (\( 77 \)) to Q3 (\( 86.5 \)), with a line at the median (\( 79.5 \)) inside the box.
• The whiskers extend from the minimum (\( 74 \)) to Q1 and from Q3 to the maximum (\( 95 \)).

Answer:

To draw the boxplot, we use the values: Minimum = 74, Q1 = 77, Median = 79.5, Q3 = 86.5, Maximum = 95. The box is between 77 and 86.5, the median line is at 79.5, and the whiskers go from 74 to 77 and from 86.5 to 95. (Note: Since this is a drawing instruction, the key is to identify the five - number summary as above to construct the boxplot.)