Question

the following is a list of shoe sizes for a group of 12 people. 4.5, 7, 6, 5, 9.5, 10, 7.5, 7.5, 11, 9, 6.5, 8 which of the following box plots best represents the numerical data?

Explanation:

Step1: Order the data

First, we order the shoe sizes: \( 4.5, 5, 6, 6.5, 7, 7.5, 7.5, 8, 9, 9.5, 10, 11 \)

Step2: Find the minimum, Q1, median, Q3, maximum

• Minimum: \( 4.5 \)
• There are 12 data points, so the median is the average of the 6th and 7th values. The 6th value is \( 7.5 \) and the 7th value is \( 7.5 \), so median \( = \frac{7.5 + 7.5}{2} = 7.5 \)
• Q1 (25th percentile) is the median of the first 6 values: \( 4.5, 5, 6, 6.5, 7, 7.5 \). The median of these is \( \frac{6 + 6.5}{2} = 6.25 \)
• Q3 (75th percentile) is the median of the last 6 values: \( 7.5, 8, 9, 9.5, 10, 11 \). The median of these is \( \frac{9 + 9.5}{2} = 9.25 \)
• Maximum: \( 11 \)

Step3: Analyze the box plots

We check which box plot has minimum \( 4.5 \), Q1 around \( 6.25 \), median \( 7.5 \), Q3 around \( 9.25 \), and maximum \( 11 \). The first box plot (with the x - axis from 3 to 12) has the correct minimum (\( 4.5 \)), maximum (\( 11 \)), and the box should be centered around the median and have the correct quartiles.

Answer:

The first box plot (the one with the x - axis labeled from 3 to 12 and the box plot with the left whisker starting near 4.5, box with Q1 around 6 - 7, median at 7.5, Q3 around 9 - 10, and right whisker to 11)