Question

The dot plot below shows how many customers purchased different numbers of shirts at a sale last weekend.

What is the mean absolute deviation of the data set shown?
A. 1.16
B. 3
C. 2
D. 3.3

Answer 1

the answer is 1.16 shirts

Explanation:

the mean absolute deviation is found by finding the average of the difference between each data point and the mean of the data.

1st...find the mean of the data by adding all the numbers according to the data plotted and dividing the by the numbers listed; which in this case is 10

1 +2+ 2+ 3+ 3+ 3+ 4+ 4+ 5+ 6 = 3.3

mean is 3.3

then find the difference between the mean and each data point

Data Point = 1 2 2 3 3 3 4 4 5 6

Difference from mean = 2.3 1.3 1.3 0.3 0.3 0.3 0.7 0.7 1.7 2.7

Find the average of these differences by adding the (differences from Mean) by 10

2.3 + 1.3 + 1.3 + 0.3 + 0.3 + 0.3 + 0.7 + 0.7 + 1.7 + 2.7

10

the mean absolute deviations is 1.16 shirts

Answer 2

mode: 3

median: 3

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mean:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 2 = 8

5 x 1 = 5

6 x 1 = 6

1 + 4 + 9 + 8 + 5 + 6 = 33 ÷ 10 = 3.3

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mean: 3.3

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Interquartile Range: 4 - 2 = 2

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Range: 6 - 1 = 5

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Mean Absolute Deviation:

3.3 - 1 = 2.3

3.3 - 2 = 1.3

3.3 - 2 = 1.3

3.3 - 3 = 0.3

3.3 - 3 = 0.3

3.3 - 3 = 0.3

3.3 - 4 = 0.7

3.3 - 4 = 0.7

3.3 - 5 = 1.7

3.3 - 6 = 2.7

____________________________

1.3 · 2 = 2.6

0.3 · 3 = 0.9

0.7 · 2 = 1.4

____________________________

2.3 + 2.6 + 0.9 + 1.4 + 1.7 + 2.7 = 11.6/10 = 1.16

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So your mean absolute deviation would be 1.16 :)!