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.
To find the Mean Absolute Deviation (MAD), we follow these steps:
1. Find the mean (average) of the data set.
mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
mean ≈ 80
2. Find the absolute deviation of each data point from the mean. Absolute deviation is obtained by finding the difference between each data value and the mean, ignoring the negative symbol.
Absolute deviations from the mean:
|55 - 80| = 25
|60 - 80| = 20
|70 - 80| = 10
|70 - 80| = 10
|75 - 80| = 5
|75 - 80| = 5
|75 - 80| = 5
|80 - 80| = 0
|80 - 80| = 0
|85 - 80| = 5
|85 - 80| = 5
|85 - 80| = 5
|85 - 80| = 5
|90 - 80| = 10
|90 - 80| = 10
|95 - 80| = 15
|100 - 80| = 20
3. Calculate the mean of the absolute deviations.
mean of absolute deviations = (25 + 20 + 10 + 10 + 5 + 5 + 5 + 0 + 0 + 5 + 5 + 5 + 5 + 10 + 10 + 15 + 20) / 17
mean of absolute deviations ≈ 8.824
Therefore, the Mean Absolute Deviation (MAD) for Ms. O'Donnell's class science test scores is approximately 8.824.
To find the Mean Absolute Deviation (MAD), follow these step-by-step instructions:
Step 1: Calculate the mean (average) of the data set.
To find the mean, add up all the test scores and divide by the total number of scores:
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1340
1340 ÷ 17 (total number of scores) = 78.82 (rounded to two decimal places)
Step 2: Calculate the deviation (absolute difference) for each test score.
For each score, subtract the mean from the score and take the absolute value of the difference. This will give you the deviation for each score.
Here are the deviations for each score:
|55 - 78.82| = 23.82
|60 - 78.82| = 18.82
|70 - 78.82| = 8.82
|70 - 78.82| = 8.82
|75 - 78.82| = 3.82
|75 - 78.82| = 3.82
|75 - 78.82| = 3.82
|80 - 78.82| = 1.18
|80 - 78.82| = 1.18
|85 - 78.82| = 6.18
|85 - 78.82| = 6.18
|85 - 78.82| = 6.18
|85 - 78.82| = 6.18
|90 - 78.82| = 11.18
|90 - 78.82| = 11.18
|95 - 78.82| = 16.18
|100 - 78.82| = 21.18
Step 3: Calculate the mean of the absolute differences.
Add up all the deviation values obtained in Step 2 and divide by the total number of scores.
23.82 + 18.82 + 8.82 + 8.82 + 3.82 + 3.82 + 3.82 + 1.18 + 1.18 + 6.18 + 6.18 + 6.18 + 6.18 + 11.18 + 11.18 + 16.18 + 21.18 = 166.82
166.82 ÷ 17 (total number of scores) = 9.81 (rounded to two decimal places)
So, the Mean Absolute Deviation (MAD) for Ms. O'Donnell's class's science test scores is 9.81.