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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To find the Mean Absolute Deviation (MAD), we need to subtract the mean of the scores from each individual score, take the absolute value of each difference, and then find the average of those absolute differences.
First, let's find the mean of the scores:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1380 / 17
Mean ≈ 81.176
Next, we'll subtract the mean from each score and find the absolute value of the differences:
|55 - 81.176| ≈ 26.176
|60 - 81.176| ≈ 21.176
|70 - 81.176| ≈ 11.176
|70 - 81.176| ≈ 11.176
|75 - 81.176| ≈ 6.176
|75 - 81.176| ≈ 6.176
|75 - 81.176| ≈ 6.176
|80 - 81.176| ≈ 1.176
|80 - 81.176| ≈ 1.176
|85 - 81.176| ≈ 3.824
|85 - 81.176| ≈ 3.824
|85 - 81.176| ≈ 3.824
|85 - 81.176| ≈ 3.824
|90 - 81.176| ≈ 8.824
|90 - 81.176| ≈ 8.824
|95 - 81.176| ≈ 13.824
|100 - 81.176| ≈ 18.824
Now, let's find the average of these absolute differences:
MAD = (26.176 + 21.176 + 11.176 + 11.176 + 6.176 + 6.176 + 6.176 + 1.176 + 1.176 + 3.824 + 3.824 + 3.824 + 3.824 + 8.824 + 8.824 + 13.824 + 18.824) / 17
MAD = 150 / 17
MAD ≈ 8.824
Therefore, the Mean Absolute Deviation (MAD) of the science test scores is approximately 8.824.
I apologize if my previous response was incorrect. Let me recalculate the MAD for you.
To find the Mean Absolute Deviation (MAD), we need to subtract the mean of the scores from each individual score, take the absolute value of each difference, and then find the average of those absolute differences.
First, let's find the mean of the scores:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1380 / 17
Mean ≈ 81.176
Next, we'll subtract the mean from each score and find the absolute value of the differences:
|55 - 81.176| ≈ 26.176
|60 - 81.176| ≈ 21.176
|70 - 81.176| ≈ 11.176
|70 - 81.176| ≈ 11.176
|75 - 81.176| ≈ 6.176
|75 - 81.176| ≈ 6.176
|75 - 81.176| ≈ 6.176
|80 - 81.176| ≈ 1.176
|80 - 81.176| ≈ 1.176
|85 - 81.176| ≈ 3.824
|85 - 81.176| ≈ 3.824
|85 - 81.176| ≈ 3.824
|85 - 81.176| ≈ 3.824
|90 - 81.176| ≈ 8.824
|90 - 81.176| ≈ 8.824
|95 - 81.176| ≈ 13.824
|100 - 81.176| ≈ 18.824
Now, let's find the average of these absolute differences:
MAD = (26.176 + 21.176 + 11.176 + 11.176 + 6.176 + 6.176 + 6.176 + 1.176 + 1.176 + 3.824 + 3.824 + 3.824 + 3.824 + 8.824 + 8.824 + 13.824 + 18.824) / 17
MAD = 150 / 17
MAD ≈ 8.824
Therefore, the Mean Absolute Deviation (MAD) of the science test scores is approximately 8.824.
I apologize for the confusion. Let's recalculate the MAD correctly.
To find the Mean Absolute Deviation (MAD), we need to subtract the mean of the scores from each individual score, take the absolute value of each difference, and then find the average of those absolute differences.
First, let's find the mean of the scores:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1415 / 17
Mean ≈ 83.235
Next, we'll subtract the mean from each score and find the absolute value of the differences:
|55 - 83.235| ≈ 28.235
|60 - 83.235| ≈ 23.235
|70 - 83.235| ≈ 13.235
|70 - 83.235| ≈ 13.235
|75 - 83.235| ≈ 8.235
|75 - 83.235| ≈ 8.235
|75 - 83.235| ≈ 8.235
|80 - 83.235| ≈ 3.235
|80 - 83.235| ≈ 3.235
|85 - 83.235| ≈ 1.765
|85 - 83.235| ≈ 1.765
|85 - 83.235| ≈ 1.765
|85 - 83.235| ≈ 1.765
|90 - 83.235| ≈ 6.765
|90 - 83.235| ≈ 6.765
|95 - 83.235| ≈ 11.765
|100 - 83.235| ≈ 16.765
Now, let's find the average of these absolute differences:
MAD = (28.235 + 23.235 + 13.235 + 13.235 + 8.235 + 8.235 + 8.235 + 3.235 + 3.235 + 1.765 + 1.765 + 1.765 + 1.765 + 6.765 + 6.765 + 11.765 + 16.765) / 17
MAD = 152.235 / 17
MAD ≈ 8.951
Therefore, the Mean Absolute Deviation (MAD) of the science test scores is approximately 8.951.
I apologize for the incorrect calculations. Let me try again to find the Mean Absolute Deviation (MAD) correctly.
To find the MAD, we need to subtract the mean of the scores from each individual score, take the absolute value of each difference, and then find the average of those absolute differences.
First, let's find the mean of the scores:
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1380 / 17
Mean ≈ 81.176
Next, we'll subtract the mean from each score and find the absolute value of the differences:
|55 - 81.176| ≈ 26.176
|60 - 81.176| ≈ 21.176
|70 - 81.176| ≈ 11.176
|70 - 81.176| ≈ 11.176
|75 - 81.176| ≈ 6.176
|75 - 81.176| ≈ 6.176
|75 - 81.176| ≈ 6.176
|80 - 81.176| ≈ 1.176
|80 - 81.176| ≈ 1.176
|85 - 81.176| ≈ 3.824
|85 - 81.176| ≈ 3.824
|85 - 81.176| ≈ 3.824
|85 - 81.176| ≈ 3.824
|90 - 81.176| ≈ 8.824
|90 - 81.176| ≈ 8.824
|95 - 81.176| ≈ 13.824
|100 - 81.176| ≈ 18.824
Now, let's find the average of these absolute differences:
MAD = (26.176 + 21.176 + 11.176 + 11.176 + 6.176 + 6.176 + 6.176 + 1.176 + 1.176 + 3.824 + 3.824 + 3.824 + 3.824 + 8.824 + 8.824 + 13.824 + 18.824) / 17
MAD = 150 / 17
MAD ≈ 8.824
Apologies for the confusion earlier. The correct Mean Absolute Deviation (MAD) for the given science test scores is approximately 8.824.