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The data below show the numbers of hours Mrs. Diaz volunteered at the library each month
for eight months.
20, 12, 27, 23, 18, 20, 30, 26
The mean of the data set is 22 hours. What is the mean absolute deviation of the data?
4.5
2
4
2.2

Respuesta :

MrRoyal

Answer:

A. 4.5

Step-by-step explanation:

Given:

20, 12, 27, 23, 18, 20, 30, 26

Mean = 22

Required:

Calculate the Mean Absolute Deviation (M.A.D)

Since, we have the mean; we start calculating M.A.D by subtracting the mean from each data

20 - 22 = -2

12 - 22 = -10

27 - 22 = 5

23 - 22 = 1

18 - 22 = -4

20 -22 = -2

30 - 22 = 8

26 - 22 = 4

The we find absolute value of the result above

|-2| = 2

|-10| = 10

|5| = 5

|1| = 1

|-4| = 4

|-2| = 2

|8| = 8

|4| = 4

Lastly, we calculate the mean of the above to give M.A.D

[tex]M.A.D = \frac{2 + 10 + 5 + 1 + 4 + 2 + 8 + 4}{8}[/tex]

[tex]M.A.D = \frac{36}{8}[/tex]

[tex]M.A.D = 4.5[/tex]

Option A is correct.

The value of the mean absolute deviation is 4.5 hours if the mean of the data set is 22 hours, option first is correct.

What is the mean absolute deviation?

It is defined as the measure to show the variation in data set in other words between the mean and every data value, the distance is known as the MAD.

We have data:

20, 12, 27, 23, 18, 20, 30, 26

Mean of the data X = 22 hours

∑(x - X) = 36

MAD = 36/8 = 4.5 hours

Thus, the value of the mean absolute deviation is 4.5 hours if the mean of the data set is 22 hours.

Learn more about the mean absolute deviation here:

brainly.com/question/10528201

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