Compare Measures of Variation Practice
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Question
Here are the science test scores from Ms. O’Donnell’s class:
55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100
Find the MAD.
(1 point)
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no
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To find the MAD (Mean Absolute Deviation), we first need to find the mean of the data set:
(55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17 = 82.35
Next, we find the absolute difference between each data point and the mean:
|55 - 82.35| = 27.35
|60 - 82.35| = 22.35
|70 - 82.35| = 12.35
|70 - 82.35| = 12.35
|75 - 82.35| = 7.35
|75 - 82.35| = 7.35
|75 - 82.35| = 7.35
|80 - 82.35| = 2.35
|80 - 82.35| = 2.35
|85 - 82.35| = 2.65
|85 - 82.35| = 2.65
|85 - 82.35| = 2.65
|85 - 82.35| = 2.65
|90 - 82.35| = 7.65
|90 - 82.35| = 7.65
|95 - 82.35| = 12.65
|100 - 82.35| = 17.65
Then, we find the sum of these absolute differences:
27.35 + 22.35 + 12.35 + 12.35 + 7.35 + 7.35 + 7.35 + 2.35 + 2.35 + 2.65 + 2.65 + 2.65 + 2.65 + 7.65 + 7.65 + 12.65 + 17.65 = 152.45
Finally, we find the MAD by dividing this sum by the number of data points:
MAD = 152.45 / 17 = 8.97
Therefore, the MAD for the science test scores is 8.97.
I apologize for the mistake. Let's recalculate the Mean Absolute Deviation (MAD) using the correct procedure:
1. Find the mean of the data set:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1265 / 17
Mean = 74.41
2. Calculate the absolute deviations for each data point from the mean:
|55 - 74.41| = 19.41
|60 - 74.41| = 14.41
|70 - 74.41| = 4.41
|70 - 74.41| = 4.41
...
|100 - 74.41| = 25.59
3. Find the average of these absolute deviations:
MAD = (19.41 + 14.41 + 4.41 + 4.41 + ... + 25.59) / 17
MAD = 221.81 / 17
MAD ≈ 13.05
Therefore, the Mean Absolute Deviation (MAD) for the science test scores is approximately 13.05. Thank you for your patience.
I apologize for the error in my previous responses. Let's calculate the Mean Absolute Deviation (MAD) correctly for the given data set:
First, find the mean of the data set:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1260 / 17
Mean = 74.12
Next, calculate the absolute deviations for each data point from the mean:
|55 - 74.12| = 19.12
|60 - 74.12| = 14.12
|70 - 74.12| = 4.12
|70 - 74.12| = 4.12
...
|100 - 74.12| = 25.88
Then, find the average of these absolute deviations:
MAD = (19.12 + 14.12 + 4.12 + 4.12 + ... + 25.88) / 17
MAD = 228.84 / 17
MAD ≈ 13.46
Therefore, the Mean Absolute Deviation (MAD) for the science test scores is approximately 13.46. Thank you for your patience and understanding.
I apologize for the errors in my previous responses. Let's compute the Mean Absolute Deviation (MAD) correctly for the given data set:
1. Find the mean of the data set:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1260 / 17
Mean = 74.12
2. Calculate the absolute deviations for each data point from the mean:
|55 - 74.12| = 19.12
|60 - 74.12| = 14.12
|70 - 74.12| = 4.12
|70 - 74.12| = 4.12
...
|100 - 74.12| = 25.88
3. Find the sum of these absolute deviations:
Sum of Absolute Deviations = 19.12 + 14.12 + 4.12 + 4.12 + 0.88 + 0.88 + 0.88 + 5.88 + 5.88 + 10.88 + 10.88 + 10.88 + 10.88 + 15.88 + 15.88 + 20.88 + 25.88
Sum of Absolute Deviations = 174.84
4. Calculate the Mean Absolute Deviation (MAD):
MAD = Sum of Absolute Deviations / Number of Data Points
MAD = 174.84 / 17
MAD ≈ 10.29
Therefore, the Mean Absolute Deviation (MAD) for the science test scores is approximately 10.29. Thank you for your patience.