Question

100 points!!!!!!!!!!!!!!!!!!!

The box plot shows the number of jumping jacks completed in a workout class by the class members. A box plot uses a number line from 14 to 54, with tick marks every one unit. The box extends from 26 to 49 on the number line. A line in the box is at 40. The lines outside the box end at 15 and 52. The graph is Jumping Jacks Completed, and the line is labeled Number of Jumping Jacks. Which of the following lists the range and IQR for this data? The range is 23, and the IQR is 37. The range is 40, and the IQR is 37. The range is 40, and the IQR is 23. The range is 37, and the IQR is 23.

Answer 1

To determine the range and IQR (interquartile range) based on the given box plot, let's first define these terms:

- Range: The range is the difference between the maximum and minimum values in a data set.
- IQR: The IQR is the range of the middle 50% of the data values. It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1).

In the given box plot:

- The lines outside the box represent the minimum and maximum values.
- The box represents the middle 50% of the data, with the line inside the box representing the median (or second quartile, Q2).
- The distance between the lower whisker and the bottom edge of the box represents the first quartile (Q1), and the distance between the upper whisker and the top edge of the box represents the third quartile (Q3).

Based on the information provided in the box plot, we can determine the range and IQR as follows:

- The minimum value is represented by the lower whisker, which ends at 15.
- The maximum value is represented by the upper whisker, which ends at 52.
- Q1 is located at the bottom edge of the box, which is 26.
- Q3 is located at the top edge of the box, which is 49.

Now we can calculate the range and IQR:

- Range: maximum value - minimum value = 52 - 15 = 37
- IQR: Q3 - Q1 = 49 - 26 = 23

Therefore, the correct statement is:

The range is 37, and the IQR is 23.

Answer 2

The range is 37, and the IQR is 23.

Explanation:

A box plot (also known as a "box and whisker plot"), is a graph displaying the distribution of a set of data based on a five-number summary.

Five-number summary

• Minimum value is at the end of the left whisker.
• Lower quartile (Q₁) is the left side of the box.
• Median (Q₂) is the vertical line inside the box.
• Upper quartile (Q₃) is the right side of the box
• Maximum value is at the end of the right whisker.

From the given information, the five-number summary of the Jumping Jacks box plot is:

• Minimum = 15
• Lower quartile (Q₁) = 26
• Median (Q₂) = 40
• Upper quartile (Q₃) = 49
• Maximum = 52

Range

The range is the difference between the maximum and minimum values. Therefore, the range for the data is:

`\sf Range = 52 - 15 = \boxed{\sf 37}`

Interquartile range (IQR)

The IQR is the difference between the upper quartile and the lower quartile. Therefore, the IQR for the data is:

`\sf IQR = Q_3 - Q_1 = 49 - 26 = \boxed{\sf 23}`

Summary

The range is 37, and the IQR is 23.