Question

Please ANSWER THIS AND CORRECTLY IT'S DUE IN 30 minutes

Question 1
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

Question 2

The data given represents the number of gallons of coffee sold per hour at two different coffee shops.


Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5


Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons

Question 3
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.

Which drive-thru is able to estimate their wait time more consistently and why?

Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range

Question 4(Multiple Choice Worth 2 points)
(Comparing Data MC)

The line plots represent data collected on the travel times to school from two groups of 15 students.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above18. There are four dots above 12. The graph is titled Bus 14 Travel Times.

Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.

Bus 47, with an IQR of 8
Bus 14, with an IQR of 6
Bus 47, with a range of 8
Bus 14, with a range of 6

Question 5(Multiple Choice Worth 2 points)
(Comparing Data MC)

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

Question 6 (Essay Worth 4 points)
(Comparing Data HC)

The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.


Bay Side School Seaside School
8, 6, 5 0 5, 8
8, 6, 5, 4, 2, 0 1 0, 1, 2, 5, 6, 8
5, 3, 2, 0, 0 2 5, 5, 7, 7, 8
3 0, 6
2 4
Key: 2 | 1 | 0 means 12 for Bay Side and 10 for Seaside


Part A: Calculate the measures of center. Show all work. (2 points)

Part B: Calculate the measures of variability. Show all work. (1 point)

Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)

Answer 1

Answer below :)

Explanation:

Question 1:

When comparing the two sets of data in the histograms to determine the location with the most consistent temperature, we should use IQR as the measure of variability. The reason for this is that IQR is a robust measure of dispersion that is not affected by outliers and is especially useful when the data is skewed. In this case, the data in Sunny Town is skewed, and therefore the range may not be the best measure of variability. IQR is not affected by the shape of the data and provides a better measure of variability in both symmetric and skewed datasets.

Therefore, the correct answer is: IQR, because Sunny Town is skewed.

Question 2:

To determine which coffee shop typically sells the most amount of coffee per hour, we need to find the measure of center that best represents the data. Both the mean and the median can be used as measures of center, but the appropriate one depends on the distribution of the data. If the data is skewed, the median is more appropriate, and if it is symmetric, the mean is more appropriate.

Comparing the data from the two coffee shops, we find that Coffee Ground has a mean value of about 5 gallons, while Wide Awake has a median value of 4.5 gallons. The mean value for Coffee Ground is higher, but since the data is not given, it is not possible to determine the distribution of the data. Therefore, we should use the median as the measure of center for both coffee shops. In this case, we find that the median for Coffee Ground is 5 gallons, while the median for Wide Awake is 4.5 gallons.

Therefore, the correct answer is: Coffee Ground, with a median value of 5 gallons.

Question 3:

To determine which drive-thru is able to estimate their wait time more consistently, we need to compare the variability of the wait times between the two drive-thrus. We can use either the range or IQR as a measure of variability. The smaller the range or IQR, the more consistent the wait times.

Comparing the box plots for Super Fast Food and Burger Quick, we find that Super Fast Food has a smaller IQR of 4.5 (15.5 - 12), while Burger Quick has an IQR of 14.5 (24 - 9.5). Therefore, Super Fast Food has a more consistent wait time.

Therefore, the correct answer is: Super Fast Food, because it has a smaller IQR.

Question 4:

To determine which bus has the most consistent travel times, we need to compare the variability of the travel times between Bus 47 and Bus 14. We can use either the range or IQR as a measure of variability. The smaller the range or IQR, the more consistent the travel times.

Comparing the line plots for Bus 47 and Bus 14, we find that Bus 14 has a smaller IQR of 6 (18 - 12), while Bus 47 has an IQR of 8 (22 - 14). Therefore, Bus 14 has more consistent travel times.

Therefore, the correct answer is: Bus 14, with an IQR of 6.

Question 5:

To determine which girls' basketball team typically has the tallest players, we need to find the measure of center that best represents the data. Both the mean and the median can be used as measures of center, but the appropriate one depends on the distribution of the data. If the data is skewed, the median is more appropriate, and if it is symmetric, the mean is more appropriate.

Comparing the data from the two girls' basketball teams, we find that the Allstars have a median height of 68 inches, while the Champs have a median height of 67