The shoe sizes for a varsity field hockey team are:
5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0
Which of the following is the IQR and explains how this measure of variability describes how the values of a dataset vary with a single number?
(1 point)
Responses
The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other.
The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other.
The IQR is 1.5. This means that the shoe sizes for half of the players are within 1.5 shoe sizes of each other.
The IQR is 1.5. This means that the shoe sizes for half of the players are within 1.5 shoe sizes of each other.
The IQR is 3.5. This means that the shoe sizes for the middle half of the players are within 3.5 shoe sizes of each other.
The IQR is 3.5. This means that the shoe sizes for the middle half of the players are within 3.5 shoe sizes of each other.
The IQR is 3.5.This means that the shoe sizes for half of the players are within 3.5 shoe sizes of each other.
The IQR is 3.5.This means that the shoe sizes for half of the players are within 3.5 shoe sizes of each other.
The correct answer is:
The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other.
The IQR (Interquartile Range) is a measure of variability that describes the spread of the middle 50% of a dataset. In this case, it represents the range of shoe sizes for the middle eight players, from the 25th percentile (which is 6.5) to the 75th percentile (which is 8.0). The IQR of 1.5 indicates that these shoe sizes are fairly close together, with most falling within 1.5 sizes of each other.
This dataset represents the number of likes Julia had on her last 10 Instagram posts:
17, 19, 21, 23, 28, 31, 31, 34, 35, 36
Which of the following is the MAD of the dataset and explains what the value means for this dataset?
(1 point)
Responses
The MAD is 6. This means the number of likes differ, on average, by 6 from the mean of 27.5 likes.
The MAD is 6. This means the number of likes differ, on average, by 6 from the mean of 27.5 likes.
The MAD is 13. This means the number of likes differ, on average, by 13 from the mean of 27.5 likes.
The MAD is 13. This means the number of likes differ, on average, by 13 from the mean of 27.5 likes.
The MAD is 13. This means the number of likes differ by 13 from the mean of 27.5 likes.
The MAD is 13. This means the number of likes differ by 13 from the mean of 27.5 likes.
The MAD is 6. This means the number of likes differ by 6 from the mean of 27.5 likes.
The MAD is 6. This means the number of likes differ by 6 from the mean of 27.5 likes.
The correct answer is:
The MAD is 6. This means the number of likes differ, on average, by 6 from the median of 30 likes.
The MAD (Mean Absolute Deviation) is a measure of variability that describes how much the data values deviate from the median of the dataset. In this case, the median is 30 (the middle value among the sorted list), and the MAD is the average absolute difference between each data value and the median. The MAD of 6 indicates that on average, the number of likes differs by 6 from the median value of 30. This suggests that the dataset is relatively consistent in terms of variability, with most values falling within 6 likes of the median.
Determine whether the range or interquartile range best describes the spread of a dataset.
The times (in seconds) for a high school boys’ 100-meter race:
11.0 11.2 11.7 12.2 12.4 12.6 12.8 12.9 13.1 13.3 13.8 14.2 14.3 14.3 16.5 17.6 18.0
(1 point)
Responses
IQR; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is skewed, and there are outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
The correct answer is:
IQR; the distribution is skewed, and there are outliers in the dataset.
The IQR (Interquartile Range) is a better measure of spread for datasets that are skewed or have outliers. In this case, the distribution is skewed to the right (long tail on the right side), and there are outliers at the upper end of the range (16.5, 17.6, 18.0). Using the range would be affected by the outliers and would not give an accurate representation of the spread of the data. The IQR is a more robust measure that is less affected by extreme values and would give a better understanding of the typical range of times for this race.
Compare Measures of Variation Quick Check
4 of 54 of 5 Items
Question
Which measure of variability—range or IQR—best describes the spread of the dataset?
Social studies group project grades (out of 100 points) for Mr. Chang’s first period class
85 88 90 90 92 92 95 96 99
(1 point)
Responses
IQR; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.
The correct answer is:
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
For datasets that are symmetrical and do not have outliers, the range is a simple and effective measure of variability that describes the spread of the data. In this case, the grades appear to be fairly symmetrical, with no extreme values or outliers. The range is calculated by subtracting the lowest value (85) from the highest value (99), giving a range of 14 points.
Maria surveyed girls on the amount (in $) they spent on a dress for the middle school spring fling:
79, 79, 79, 82, 84, 85, 89, 90, 99, 100, 100, 100, 129, 139, 155, 174, 189, 200, 209, 250
Which measure of variability—IQR or MAD—best describes the spread of the dataset?
(1 point)
Responses
IQR; the data distribution is symmetrical
IQR; the data distribution is symmetrical
MAD; the data distribution has outliers
MAD; the data distribution has outliers
IQR; the data distribution is skewed
IQR; the data distribution is skewed
MAD; the data distribution is symmetrical
MAD; the data distribution is symmetrical
The correct answer is:
IQR; the data distribution is skewed.
The IQR (Interquartile Range) is a better measure of variability for datasets that are skewed, which means that the distribution of the data is not symmetrical. The dataset has a long tail on the upper end, with values that are much higher than the majority of the data. Using the range or MAD (Mean Absolute Deviation) may be affected by these extreme values and would not give a good representation of the spread of the data. The IQR is a more robust measure that would describe the range of values for the middle 50% of the data, which is not affected by the outliers or extreme values.
The shoe sizes for a varsity field hockey team are:
5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0
Which of the following is the IQR and explains how this measure of variability describes how the values of a dataset vary with a single number?
(1 point)
Responses
The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other.
The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other.
The IQR is 1.5. This means that the shoe sizes for half of the players are within 1.5 shoe sizes of each other.
The IQR is 1.5. This means that the shoe sizes for half of the players are within 1.5 shoe sizes of each other.
The IQR is 3.5. This means that the shoe sizes for the middle half of the players are within 3.5 shoe sizes of each other.
The IQR is 3.5. This means that the shoe sizes for the middle half of the players are within 3.5 shoe sizes of each other.
The IQR is 3.5.This means that the shoe sizes for half of the players are within 3.5 shoe sizes of each other.
The IQR is 3.5.This means that the shoe sizes for half of the players are within 3.5 shoe sizes of each other.