For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?

For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?

Correct Answer: 1

Step 1: Find the mean (average) of the data set. Add all the numbers together: 5 + 7 + 8 + 9 + 10 = 39.
Step 2: Divide the total by the number of values in the data set. There are 5 numbers, so 39 / 5 = 7.5. This is the mean.
Step 3: Calculate the absolute deviation for each number. This means finding the distance from each number to the mean (7.5).
Step 4: For each number, subtract the mean and take the absolute value: |5 - 7.5| = 2.5, |7 - 7.5| = 0.5, |8 - 7.5| = 0.5, |9 - 7.5| = 1.5, |10 - 7.5| = 2.5.
Step 5: Add all the absolute deviations together: 2.5 + 0.5 + 0.5 + 1.5 + 2.5 = 7.5.
Step 6: Divide the total absolute deviation by the number of values in the data set: 7.5 / 5 = 1. This is the mean absolute deviation (MAD).

Mean – The average of a set of numbers, calculated by summing the numbers and dividing by the count.
Absolute Deviation – The distance between each data point and the mean, expressed as a positive value.
Mean Absolute Deviation (MAD) – The average of the absolute deviations from the mean, providing a measure of variability in the data set.