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
- 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
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