Question

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

Answer 1

Answer:

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

1. Find the mean of the data set, by finding the sum of the data, and divide the sum by the number of data
2. Find the absolute value of the difference between each data value and the mean: I data value – mean I.
3. Find the sum of the absolute values of the differences.
4. 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