Question

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The data given represents the height of basketball players, in inches, on two different girls' teams.


Allstars
73 62 60
63 72 65
69 68 71
66 70 67
60 70 71
Champs
62 69 65
68 60 70
70 58 67
66 75 70
69 67 60


Compare the data and use the correct measure of center to determine which team typically has the tallest players. Explain your answer.

The Allstars, with a mean of about 67.1 inches
The Champs, with a mean of about 66.4 inches
The Allstars, with a median of about 68 inches
The Champs, with a median of about 67 inches









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 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.

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 skewed
IQR, because Desert Landing is symmetric
Range, because Sunny Town is skewed
Range, because Desert Landing is symmetric

Answer 1

To determine which team typically has the tallest players, we need to compare the measures of center for both teams.

For the first question, the measure of center we should use is the median. The median represents the middle value in a data set when the values are arranged in ascending or descending order. It is not affected by extreme values, making it a good measure to use when comparing heights.

For the Allstars team, the median height is about 68 inches. This means that half of the players on the Allstars team have a height greater than or equal to 68 inches.

For the Champs team, the median height is about 67 inches. This means that half of the players on the Champs team have a height greater than or equal to 67 inches.

Comparing the medians, we can conclude that the Allstars team typically has taller players, as their median height is greater than the median height of the Champs team.

Therefore, the Allstars team typically has the tallest players.

For the second question about comparing the variability of temperatures, we should use the measure of variability known as the interquartile range (IQR). The IQR is calculated by finding the difference between the first quartile (Q1) and the third quartile (Q3).

Since the data for Sunny Town is skewed, with a shaded bar stopping at 10 above 60 to 69 and decreasing frequencies for higher temperature intervals, the IQR should be used for Sunny Town. The IQR helps to identify the range in which the middle 50% of the data falls and is less sensitive to extreme values.

Since the data for Desert Landing is symmetric, with a higher frequency in the middle temperature intervals and a gradual decrease in frequencies towards the extremes, the IQR is not necessary. Instead, the range can be used to determine the measure of variability. The range is calculated by finding the difference between the highest and lowest values in the data set.

Therefore, the appropriate measure of variability for Sunny Town is the IQR, and for Desert Landing, it is the range.

Explanation:

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