Question

PLEASE HELP DUE IN 15 MINUTES

The histograms display the frequency of temperatures in two different locations in a 30-day period.

A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.

A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.

When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?

IQR, because Sunny Town is symmetric
IQR, because Beach Town is skewed
Range, because Sunny Town is skewed
Range, because Beach Town is symmetric

Answer 1

variability that takes into account the spread of the data. The interquartile range (IQR) is a good measure of variability to use because it is less sensitive to extreme values than the range.

Option A states that IQR should be used because Sunny Town is symmetric. However, Sunny Town is not symmetric, as evidenced by the fact that the shaded bar is not centered within the interval. Therefore, Option A is incorrect.

Option B states that IQR should be used because Beach Town is skewed. However, whether the data is skewed or not does not affect the choice of measure of variability. Therefore, Option B is incorrect.

Option C states that range should be used because Sunny Town is skewed. However, range is not a good measure of variability to use for skewed data because it is sensitive to extreme values. Therefore, Option C is incorrect.

Option D states that range should be used because Beach Town is symmetric. However, Beach Town is not symmetric, as evidenced by the fact that the shaded bar is not centered within the interval. Therefore, Option D is incorrect.

Therefore, the correct answer is A: IQR, because it is a good measure of variability to use for any type of data, and we cannot assume that either location is symmetric or skewed based on the given information.

Explanation:

Answer 2

IQR, because Sunny Town is symmetric and Beach Town is skewed.

Explanation:

The measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is IQR (Interquartile Range) because it is more resistant to outliers and provides a measure of the spread of the middle 50% of the data.

In the given histograms, the shape of the distribution for Sunny Town is approximately symmetric, while the shape of the distribution for Beach Town is approximately skewed to the right. Therefore, we should use IQR to determine the consistency of temperature in both locations.

Hence, the correct answer is: IQR, because Beach Town is skewed.