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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)
The MAD is
.

Answer 1

its wrong

Answer 2

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.

Answer 3

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.