Compare Measures of Variation Quick Check
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Question
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 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.
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 correct answer is:
The MAD is 6. This means the number of likes differ, on average, by 6 from the mean of 27.5 likes.
To calculate the Mean Absolute Deviation (MAD), we need to find the difference between each data point and the mean, then take the average of those differences.
Given the dataset of Julia's last 10 Instagram posts: 17, 19, 21, 23, 28, 31, 31, 34, 35, 36
Step 1: Calculate the mean
Mean = (17 + 19 + 21 + 23 + 28 + 31 + 31 + 34 + 35 + 36) / 10
Mean = 275 / 10
Mean = 27.5
Step 2: Find the differences between each data point and the mean
Differences = |17 - 27.5|, |19 - 27.5|, |21 - 27.5|, |23 - 27.5|, |28 - 27.5|, |31 - 27.5|, |31 - 27.5|, |34 - 27.5|, |35 - 27.5|, |36 - 27.5|
Step 3: Calculate the average of the differences
MAD = (|17 - 27.5| + |19 - 27.5| + |21 - 27.5| + |23 - 27.5| + |28 - 27.5| + |31 - 27.5| + |31 - 27.5| + |34 - 27.5| + |35 - 27.5| + |36 - 27.5|) / 10
MAD = (|-10.5| + |-8.5| + |-6.5| + |-4.5| + |0.5| + |3.5| + |3.5| + |6.5| + |7.5| + |8.5|) / 10
MAD = (10.5 + 8.5 + 6.5 + 4.5 + 0.5 + 3.5 + 3.5 + 6.5 + 7.5 + 8.5) / 10
MAD = 59.5 / 10
MAD = 5.95
Therefore, the MAD of the dataset is approximately 5.95. This means that, on average, the number of likes differs by 5.95 from the mean of 27.5 likes.
The correct answer choice is:
The MAD is 6. This means the number of likes differ, on average, by 6 from the mean of 27.5 likes.