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 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 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.
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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 find the Mean Absolute Deviation (MAD) of a dataset, you first need to find the mean of the dataset.
The dataset given is:
17, 19, 21, 23, 28, 31, 31, 34, 35, 36
To find the mean, you add up all the numbers in the dataset and divide by the number of data points. In this case, there are 10 data points.
Mean = (17 + 19 + 21 + 23 + 28 + 31 + 31 + 34 + 35 + 36) / 10 = 275 / 10 = 27.5
Now that we have the mean, we can find the MAD. To find the MAD, you calculate the absolute difference between each data point and the mean, and then find the average of these absolute differences.
The absolute differences between each data point and the mean are:
|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|
= 10.5, 8.5, 6.5, 4.5, 0.5, 3.5, 3.5, 6.5, 7.5, 8.5
The average of these absolute differences is:
(10.5 + 8.5 + 6.5 + 4.5 + 0.5 + 3.5 + 3.5 + 6.5 + 7.5 + 8.5) / 10
= 59 / 10
= 5.9
Therefore, the MAD of the dataset is 5.9. 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.