Savannah recorded the average rainfall amount, in inches, for two cities over the course of 6 months.

City A: {3, 2.5, 4, 4.5, 3, 1}

City B: {6, 4, 1.5, 3.5, 2, 4}

What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth. Show your work.

M. A. D City A:

M. A. D. City B:

M. A. D City A: 0.8

M. A. D City B: 1.2

Step-by-step explanation:

To find the mean absolute deviation of the data

Find the mean of the data set, by finding the sum of the data, and divide the sum by the number of data Find the absolute value of the difference between each data value and the mean: I data value - mean I. Find the sum of the absolute values of the differences. Divide the sum of the absolute values of the differences by the number of data

Let us do these steps with Cities A and B

City A: {3, 2.5, 4, 4.5, 3, 1}

The sum of the data = 3 + 2.5 + 4 + 4.5 + 3 + 1 = 18

The number of the data is 6

The mean = 18 : 6 = 3

Find the absolute difference

I3 - 3I = 0

I2.5 - 3I = 0.5

I4 - 3I = 1

I4.5 - 3I = 1.5

I3 - 3I = 0

I1 - 3I = 2

The sum of the absolute differences = 0 + 0.5 + 1 + 1.5 + 0 + 2 = 5

MDA = 5 : 6 = 0.83333 ≅ 0.8 ⇒ to the nearest tenth

M. A. D City A: 0.8

City B: {6, 4, 1.5, 3.5, 2, 4}

The sum of the data = 6 + 4 + 1.5 + 3.5 + 2 + 4 = 21

The number of the data is 6

The mean = 21 : 6 = 3.5

Find the absolute difference

I6 - 3.5I = 2.5

I4 - 3.5I = 0.5

I1.5 - 3.5I = 2

I3.5 - 3.5I = 0

I2 - 3.5I = 1.5

I4 - 3.5I = 0.5

The sum of the absolute differences = 2.5 + 0.5 + 2 + 0 + 1.5 + 0.5 = 7

MDA = 7 : 6 = 1.166666 ≅ 1.2 ⇒ to the nearest tenth

M. A. D City B: 1.2