Question

1. the students in ms. glenns math class earned the grades shown below.

65, 70, 70, 80, 80, 82, 88, 88, 90, 90, 95
which box - and - whisker plot represents these data?

Explanation:

Step1: Find the minimum, Q1, median, Q3, maximum

The data set is: 65, 70, 70, 80, 80, 82, 88, 88, 90, 90, 95 (n = 11, odd number of data points)

• Minimum: The smallest value is 65.
• Q1 (First Quartile): The median of the lower half. The lower half is 65, 70, 70, 80, 80 (n = 5, median is the 3rd value). So Q1 = 70.
• Median: The middle value (6th value since n = 11). The 6th value is 82.
• Q3 (Third Quartile): The median of the upper half. The upper half is 88, 88, 90, 90, 95 (n = 5, median is the 3rd value). So Q3 = 90.
• Maximum: The largest value is 95.

Step2: Analyze the box - and - whisker plots

A box - and - whisker plot has a box from Q1 to Q3, a line inside the box at the median, and whiskers from the minimum to Q1 and from Q3 to the maximum.

Now let's check the plots:

• The minimum is 65, so the left whisker should start at 65.
• Q1 = 70, Q3 = 90, median = 82.

Looking at the options (we can infer from the axes):

• The first plot (option 1) should have: left whisker from 65 to 70, box from 70 to 90, median at 82, right whisker from 90 to 95. We need to match this with the given plots. After calculating the five - number summary (min = 65, Q1 = 70, median = 82, Q3 = 90, max = 95), we can identify the correct plot.

Answer:

To determine the correct box - and - whisker plot, we first find the five - number summary:

• Minimum: 65
• Q1: 70
• Median: 82
• Q3: 90
• Maximum: 95

A box - and - whisker plot has a whisker from the minimum (65) to Q1 (70), a box from Q1 (70) to Q3 (90) with a line at the median (82), and a whisker from Q3 (90) to the maximum (95). By comparing with the given plots, the correct plot should be the one that matches these values. Assuming the first plot (option 1) has these characteristics (left whisker from 65, Q1 at 70, median at 82, Q3 at 90, right whisker to 95), the answer is the plot labeled as 1 (the one with the left whisker starting at 65, box from 70 - 90, median at 82, and right whisker to 95). If we consider the options as 1), 2), 3), 4), the correct one is 1).