Question

What is the mean and the mean absolute deviation (MAD) for the data set shown?

2, 3, 4, 5, 6, 7, 8

A) Mean: 5; MAD: 2.0
B) Mean: 5; MAD: 2.5
C) Mean: 4.5; MAD: 2.0
D) Mean: 4.5; MAD: 2.5

Answer 1

The mean of the data set provided is 5. The mean absolute deviation (MAD) is approximately 1.71, which is not among the provided choices and suggests a possible error in the question's answer options.

Step-by-step explanation:

To calculate the mean of the data set, you add all the numbers together and then divide by the total count of the numbers. For the data set provided (2, 3, 4, 5, 6, 7, 8), you would calculate the mean as follows:

1. Add all numbers: 2 + 3 + 4 + 5 + 6 + 7 + 8 = 35
2. Divide by the number of values (7 in this case): 35 ÷ 7 = 5

The mean is therefore 5.

To calculate the mean absolute deviation (MAD) for this data set, follow these steps:

1. Find the absolute deviations from the mean for each number in the data set: |2 - 5|, |3 - 5|, |4 - 5|, |5 - 5|, |6 - 5|, |7 - 5|, |8 - 5|
2. The absolute deviations are: 3, 2, 1, 0, 1, 2, 3
3. Add all the absolute deviations: 3 + 2 + 1 + 0 + 1 + 2 + 3 = 12
4. Divide by the number of values (7 in this case): 12 ÷ 7 = approximately 1.71

The mean absolute deviation (MAD) is approximately 1.71. However, since this option is not available, we can confirm that the calculation in the question may be incorrect or that the correct answer is not provided among the available options.