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?
Responses
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 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.
The correct response 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.
Explanation: The IQR (interquartile range) is a measure of variability that describes the middle 50% of values in a dataset. It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1). In this case, the Q1 is 7.0 and the Q3 is 8.5. Therefore, the IQR is 8.5 - 7.0 = 1.5. This means that the shoe sizes for the middle half of the players (between Q1 and Q3) are within 1.5 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.
im not to sure tho
In this case, the statement is incorrect. The IQR being 3.5 means that the shoe sizes for the middle half of the players (between Q1 and Q3) are within 3.5 shoe sizes of each other, not that all the shoe sizes for half of the players are within 3.5 shoe sizes of each other. It is important to note that the IQR measures the spread of a dataset, specifically the spread of the middle 50% of the data, not the entire dataset.
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 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.
Explanation: The IQR is calculated by finding the difference between the third quartile and the first quartile. In this case, the Q1 is 7.0 and the Q3 is 8.5, so the IQR is 8.5 - 7.0 = 1.5. This means that the shoe sizes for the middle half of the players, or the values from the 25th percentile (Q1) to the 75th percentile (Q3), are within 1.5 shoe sizes of each other. The IQR gives us a sense of the spread or variability of the middle 50% of the data.
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 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, 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.
Explanation: MAD (Mean Absolute Deviation) is a measure of variability that tells us how spread out the data is from the mean. It is calculated by finding the absolute value of the difference between each data point and the mean, then taking the average of those absolute differences. In this case, the mean is 27.5 and the absolute deviations are:
|17 - 27.5| = 10.5
|19 - 27.5| = 8.5
|21 - 27.5| = 6.5
|23 - 27.5| = 4.5
|28 - 27.5| = 0.5
|31 - 27.5| = 3.5
|31 - 27.5| = 3.5
|34 - 27.5| = 6.5
|35 - 27.5| = 7.5
|36 - 27.5| = 8.5
The average of these absolute deviations is (10.5 + 8.5 + 6.5 + 4.5 + 0.5 + 3.5 + 3.5 + 6.5 + 7.5 + 8.5) / 10 = 6. Therefore, the MAD for this dataset is 6, which means that, on average, each data point is about 6 away from the mean of 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
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.
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.
Explanation: In this dataset, the range may be a better measure of spread than the interquartile range because the distribution is skewed and there are outliers present. The range will give us the difference between the largest and smallest values in the dataset, which will give us a sense of how spread out the data is overall, whereas the interquartile range would only describe the variability of the middle 50% of the data. Additionally, because there are outliers present, the range will give us a more complete picture of how spread out the entire dataset is.
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)
IQR; the distribution is relatively symmetrical and there are no outliers present in the dataset.
Explanation: In this dataset, the IQR would be a better measure of variability than the range because the distribution is relatively symmetrical and there are no outliers present. The IQR would give us a sense of the variability of the middle 50% of the data points, which in this case, would be the grades between 88 and 96. While the range would be easy to calculate (14), it would not give us an accurate measure of variability since these data points are closely grouped together.
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)
MAD; the dataset contains extreme outliers that might not be accurately represented by the IQR.
Explanation: In this dataset, the MAD (Mean Absolute Deviation) would be a better measure of variability than the IQR. This is because the dataset contains extreme outliers, such as the values of 129, 139, 155, 174, 189, 200, 209, and 250 that might not be accurately represented by the IQR. The MAD gives us a sense of the average distance from the mean of the data points, taking into account extreme values. Additionally, the MAD is not affected by extreme outliers in the same way that the range might be, making it a more robust measure of variability for this particular dataset.