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
.
wrong
To find the Mean Absolute Deviation (MAD) of the given set of scores, follow these steps:
Step 1: Find the mean (average) of the scores.
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1475
Mean = 1475 ÷ 17 = 86.76 (rounded to two decimal places)
Step 2: Find the absolute deviation for each score by subtracting the mean from each individual score.
Absolute deviations:
|55 - 86.76| = 31.76
|60 - 86.76| = 26.76
|70 - 86.76| = 16.76
|70 - 86.76| = 16.76
|75 - 86.76| = 11.76
|75 - 86.76| = 11.76
|75 - 86.76| = 11.76
|80 - 86.76| = 6.76
|80 - 86.76| = 6.76
|85 - 86.76| = 1.76
|85 - 86.76| = 1.76
|85 - 86.76| = 1.76
|85 - 86.76| = 1.76
|90 - 86.76| = 3.24
|90 - 86.76| = 3.24
|95 - 86.76| = 8.24
|100 - 86.76| = 13.24
Step 3: Find the mean of the absolute deviations.
31.76 + 26.76 + 16.76 + 16.76 + 11.76 + 11.76 + 11.76 + 6.76 + 6.76 + 1.76 + 1.76 + 1.76 + 1.76 + 3.24 + 3.24 + 8.24 + 13.24 = 183.52
Mean = 183.52 ÷ 17 = 10.79 (rounded to two decimal places)
Therefore, the Mean Absolute Deviation (MAD) is approximately 10.79.
To find the Mean Absolute Deviation (MAD) of a set of numbers, you need to calculate the average difference between each number and the mean of the set.
Here's how you can calculate the MAD for the science test scores:
1. Calculate the mean of the set by adding up all the numbers and dividing by the total count. In this case, there are 17 scores, so summing up all of them:
Average = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Average = 1360 / 17
Average = 80
2. Find the difference between each score and the mean. Subtract the mean from each score:
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. Take the absolute value of each difference. This removes any negative signs:
|-25| = 25
|-20| = 20
|-10| = 10
|-10| = 10
|-5| = 5
|-5| = 5
|-5| = 5
|0| = 0
|0| = 0
|5| = 5
|5| = 5
|5| = 5
|5| = 5
|10| = 10
|10| = 10
|15| = 15
|20| = 20
4. Calculate the average of these absolute differences:
MAD = (25 + 20 + 10 + 10 + 5 + 5 + 5 + 0 + 0 + 5 + 5 + 5 + 5 + 10 + 10 + 15 + 20) / 17
MAD = 170 / 17
MAD = 10
Therefore, the Mean Absolute Deviation (MAD) for the science test scores is 10.
The median is 80
To find the MAD, we first find the absolute deviations from the median for each score:
|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
Next, we find the mean of these absolute deviations:
(25 + 20 + 10 + 10 + 5 + 5 + 5 + 0 + 0 + 5 + 5 + 5 + 5 + 10 + 10 + 15 + 20) / 17 = 180 / 17 ≈ 10.59
Therefore, the MAD is approximately 10.59.