what is the difference between the mean absolute deviation of the following numbers
students 1=77,80,100,75,82
student 2= 88,80,79,85,90
To find the mean absolute deviation (MAD) of a set of numbers, follow these steps:
1. Find the mean (average) of the set of numbers.
2. Calculate the absolute difference between each number and the mean.
3. Find the mean (average) of these absolute differences.
Now let's find the MAD for the given sets of numbers:
For student 1: 77, 80, 100, 75, 82
Step 1: Find the mean.
Mean = (77 + 80 + 100 + 75 + 82) / 5 = 414 / 5 = 82.8
Step 2: Calculate the absolute difference between each number and the mean.
|77 - 82.8| = 5.8
|80 - 82.8| = 2.8
|100 - 82.8| = 17.2
|75 - 82.8| = 7.8
|82 - 82.8| = 0.8
Step 3: Find the mean of the absolute differences.
MAD = (5.8 + 2.8 + 17.2 + 7.8 + 0.8) / 5 = 34.4 / 5 = 6.88
Now let's find the MAD for student 2: 88, 80, 79, 85, 90
Step 1: Find the mean.
Mean = (88 + 80 + 79 + 85 + 90) / 5 = 422 / 5 = 84.4
Step 2: Calculate the absolute difference between each number and the mean.
|88 - 84.4| = 3.6
|80 - 84.4| = 4.4
|79 - 84.4| = 5.4
|85 - 84.4| = 0.6
|90 - 84.4| = 5.6
Step 3: Find the mean of the absolute differences.
MAD = (3.6 + 4.4 + 5.4 + 0.6 + 5.6) / 5 = 19.6 / 5 = 3.92
Therefore, the MAD for student 1 is 6.88 and for student 2 is 3.92.