Question

Find the mean absolute deviation for the set below. S= {65, 90, 85, 70, 70, 95, 55}

a) 11
b) 13
c) 15
d) 17

Answer 1

To find the mean absolute deviation (MAD), you need to find the mean of the set and then calculate the average of the absolute differences between each number and the mean. For the given set S={65, 90, 85, 70, 70, 95, 55}, the mean absolute deviation is 10.

Step-by-step explanation:

To find the mean absolute deviation (MAD) for the given set, we follow these steps:

1. Find the mean of the set, which is the sum of all the numbers divided by the total number of numbers.
2. Subtract each number in the set from the mean and calculate the absolute value of each difference.
3. Find the mean of these absolute differences to determine the MAD.

Let's calculate the MAD for the set S={65, 90, 85, 70, 70, 95, 55}:

1. Step 1: Find the mean: (65 + 90 + 85 + 70 + 70 + 95 + 55) / 7 = 70
2. Step 2: Subtract each number from the mean and calculate the absolute value of each difference:
3. |65 - 70| = 5
4. |90 - 70| = 20
5. |85 - 70| = 15
6. |70 - 70| = 0
7. |70 - 70| = 0
8. |95 - 70| = 25
9. |55 - 70| = 15
10. Step 3: Find the mean of these absolute differences: (5 + 20 + 15 + 0 + 0 + 25 + 15) / 7 = 10

Therefore, the mean absolute deviation for the set is 10. The answer is not one of the options provided: (a) 11, (b) 13, (c) 15, or (d) 17.