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)
The MAD is
the mean absolute deviation.
To find the MAD, we need to find the mean of the data set first.
Adding up all the scores, we get:
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1460
There are 17 scores in total, so the mean is:
mean = sum/number of scores = 1460/17 = 85.88 (rounded to the nearest hundredth)
Next, we need to find the absolute deviation for each score, which is the absolute value of the difference between each score and the mean. Then, we total up all the deviations:
|(55-85.88)| + |(60-85.88)| + |(70-85.88)| + |(70-85.88)| + |(75-85.88)| + |(75-85.88)| + |(75-85.88)| + |(80-85.88)| + |(80-85.88)| + |(85-85.88)| + |(85-85.88)| + |(85-85.88)| + |(85-85.88)| + |(90-85.88)| + |(90-85.88)| + |(95-85.88)| + |(100-85.88)|
= 30.88 + 25.88 + 15.88 + 15.88 + 10.88 + 10.88 + 10.88 + 5.88 + 5.88 + 0.88 + 0.88 + 0.88 + 0.88 + 4.12 + 4.12 + 9.12 + 14.12
= 147.96
Finally, to find the MAD, we divide the sum of the absolute deviations by the number of scores:
MAD = sum of absolute deviations/number of scores = 147.96/17 = 8.7047
So, the MAD is approximately 8.7047.
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).
The MAD is
the mean absolute deviation.
To find the MAD, we need to find the mean of the data set first.
Adding up all the scores, we get:
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1430
There are 17 scores in total, so the mean is:
mean = sum/number of scores = 1430/17 = 84.12 (rounded to the nearest hundredth)
Next, we need to find the absolute deviation for each score, which is the absolute value of the difference between each score and the mean. Then, we total up all the deviations:
|(55-84.12)| + |(60-84.12)| + |(70-84.12)| + |(70-84.12)| + |(75-84.12)| + |(75-84.12)| + |(75-84.12)| + |(80-84.12)| + |(80-84.12)| + |(85-84.12)| + |(85-84.12)| + |(85-84.12)| + |(85-84.12)| + |(90-84.12)| + |(90-84.12)| + |(95-84.12)| + |(100-84.12)|
= 29.12 + 24.12 + 14.12 + 14.12 + 8.12 + 8.12 + 8.12 + 4.12 + 4.12 + 0.88 + 0.88 + 0.88 + 0.88 + 5.88 + 5.88 + 10.88 + 15.88
= 158.12
Finally, to find the MAD, we divide the sum of the absolute deviations by the number of scores:
MAD = sum of absolute deviations/number of scores = 158.12/17 = 9.3000
So, the MAD is approximately 9.3000.
calculated by finding the mean (average) of the scores and then finding the absolute difference between each score and the mean. Finally, you take the mean of these absolute differences to get the MAD.
Step 1: Find the mean
Adding up all the scores and dividing by the total number of scores:
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1395
There are 17 scores, so dividing 1395 by 17 gives us the mean:
1395 / 17 = 82.0588 (approximately 82.06)
Step 2: Find the absolute differences
Finding the absolute difference between each score and the mean:
|55 - 82.06| = 27.06
|60 - 82.06| = 22.06
|70 - 82.06| = 12.06
|70 - 82.06| = 12.06
|75 - 82.06| = 7.06
|75 - 82.06| = 7.06
|75 - 82.06| = 7.06
|80 - 82.06| = 2.06
|80 - 82.06| = 2.06
|85 - 82.06| = 2.94
|85 - 82.06| = 2.94
|85 - 82.06| = 2.94
|85 - 82.06| = 2.94
|90 - 82.06| = 7.94
|90 - 82.06| = 7.94
|95 - 82.06| = 12.94
|100 - 82.06| = 17.94
Step 3: Find the mean of the absolute differences
Adding up all the absolute differences and dividing by the number of scores:
27.06 + 22.06 + 12.06 + 12.06 + 7.06 + 7.06 + 7.06 + 2.06 + 2.06 + 2.94 + 2.94 + 2.94 + 2.94 + 7.94 + 7.94 + 12.94 + 17.94 = 170.96
There are 17 scores, so dividing 170.96 by 17 gives us the MAD:
170.96 / 17 = 10.05 (approximately 10.05)
Therefore, the MAD of the science test scores is 10.05.