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Compare Measures of Variation Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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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)
The MAD is
.
Step 1: Find the mean (average)
To find the mean, add up all the numbers and divide by the total number of numbers.
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1410
There are 17 numbers, so the mean is 1410/17 ≈ 82.94
Step 2: Find the absolute deviation for each number
To find the absolute deviation, subtract the mean from each number.
|55 - 82.94| = 27.94
|60 - 82.94| = 22.94
|70 - 82.94| = 12.94
|70 - 82.94| = 12.94
|75 - 82.94| = 7.94
|75 - 82.94| = 7.94
|75 - 82.94| = 7.94
|80 - 82.94| = 2.94
|80 - 82.94| = 2.94
|85 - 82.94| = 2.06
|85 - 82.94| = 2.06
|85 - 82.94| = 2.06
|85 - 82.94| = 2.06
|90 - 82.94| = 7.06
|90 - 82.94| = 7.06
|95 - 82.94| = 12.06
|100 - 82.94| = 17.06
Step 3: Find the absolute deviations' mean
Add up all the absolute deviations and divide by the total number of numbers.
27.94 + 22.94 + 12.94 + 12.94 + 7.94 + 7.94 + 7.94 + 2.94 + 2.94 + 2.06 + 2.06 + 2.06 + 2.06 + 7.06 + 7.06 + 12.06 + 17.06 = 153.28
There are 17 absolute deviations, so the mean is 153.28/17 ≈ 9
Therefore, the Mean Absolute Deviation (MAD) is 9.
its wrong
My apologies for the error. Let's find the correct MAD.
Step 1: Find the mean (average)
To find the mean, add up all the numbers and divide by the total number of numbers.
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1465
There are 17 numbers, so the mean is 1465/17 ≈ 86.18
Step 2: Find the absolute deviation for each number
To find the absolute deviation, subtract the mean from each number.
|55 - 86.18| = 31.18
|60 - 86.18| = 26.18
|70 - 86.18| = 16.18
|70 - 86.18| = 16.18
|75 - 86.18| = 11.18
|75 - 86.18| = 11.18
|75 - 86.18| = 11.18
|80 - 86.18| = 6.18
|80 - 86.18| = 6.18
|85 - 86.18| = 1.18
|85 - 86.18| = 1.18
|85 - 86.18| = 1.18
|85 - 86.18| = 1.18
|90 - 86.18| = 3.82
|90 - 86.18| = 3.82
|95 - 86.18| = 8.82
|100 - 86.18| = 13.82
Step 3: Find the absolute deviations' mean
Add up all the absolute deviations and divide by the total number of numbers.
31.18 + 26.18 + 16.18 + 16.18 + 11.18 + 11.18 + 11.18 + 6.18 + 6.18 + 1.18 + 1.18 + 1.18 + 1.18 + 3.82 + 3.82 + 8.82 + 13.82 = 168.28
There are 17 absolute deviations, so the mean is 168.28/17 ≈ 9.90
Therefore, the Mean Absolute Deviation (MAD) is 9.90.
To find the MAD (Mean Absolute Deviation), follow these steps:
Step 1: Find the mean (average) of the data set.
To find the mean, add up all the numbers in the data set and divide by the number of data points.
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1445
1445 / 17 = 85 (rounded to the nearest whole number)
Step 2: Find the absolute deviation for each data point.
Subtract the mean from each data point and take the absolute value of the result (ignoring any negative signs).
55 - 85 = 30
60 - 85 = 25
70 - 85 = 15
70 - 85 = 15
75 - 85 = 10
75 - 85 = 10
75 - 85 = 10
80 - 85 = 5
80 - 85 = 5
85 - 85 = 0
85 - 85 = 0
85 - 85 = 0
85 - 85 = 0
90 - 85 = 5
90 - 85 = 5
95 - 85 = 10
100 - 85 = 15
Step 3: Find the mean of the absolute deviations.
Add up all the absolute deviations and divide by the number of data points.
30 + 25 + 15 + 15 + 10 + 10 + 10 + 5 + 5 + 0 + 0 + 0 + 0 + 5 + 5 + 10 + 15 = 160
160 / 17 = 9.411764705882353 (rounded to decimal places)
Therefore, the Mean Absolute Deviation (MAD) is approximately 9.412.