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 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 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 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other.right here
The correct response is:
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, or interquartile range, is a measure of variability that describes the spread of the middle 50% of the data. In this case, the IQR of 3.5 indicates that the shoe sizes for half of the players are within 3.5 shoe sizes of each other, showing how the values of the dataset vary around a single number.
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 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 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 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, on average, by 13 from the mean of 27.5 likes.
The correct response is:
The MAD is 6. This means the number of likes differ, on average, by 6 from the mean of 27.5 likes.
The MAD, or Mean Absolute Deviation, is a measure of variability that describes the average difference between each data point and the mean of the dataset. In this case, the MAD of 6 means that, on average, the number of likes differ by 6 from the mean number of likes, which is 27.5.
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
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.
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.
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.
The correct response is:
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
The range, which is the difference between the maximum and minimum values in a dataset, is best used to describe the spread of a dataset when the distribution is symmetrical and there aren't any outliers present. In this case, since the data represents race times and there are no indications of skewness or outliers, the range is the appropriate measure to describe the spread of the dataset.
Compare Measures of Variation Quick Check
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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.
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The correct response is:
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Since the data represents social studies group project grades and there are no indications of skewness or outliers, the range is the appropriate measure to describe the spread of the dataset.
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 is symmetrical
MAD; the data distribution is symmetrical
MAD; the data distribution has outliers
MAD; the data distribution has outliers
IQR; the data distribution is skewed
The correct response is:
MAD; the data distribution has outliers
In this case, the Mean Absolute Deviation (MAD) is the more appropriate measure of variability to describe the spread of the dataset because there are outliers present in the data. MAD is less sensitive to outliers compared to the Interquartile Range (IQR), making it a better choice in this scenario.