Question

Find the mean absolute deviation of the following set of data.

Answer 1

Answer:

The mean absolute deviation is 5.952 ⇒ 3rd answer

Step-by-step explanation:

* Lets talk about the mean absolute deviation

- Mean absolute deviation (MAD) of a data set is the average distance

 between each data value and the mean

1- To find the mean absolute deviation of the data, start by finding

   the mean of the data set.

2- Find the sum of the data values, and divide the sum by the

   number of data values.

3- Find the absolute value of the difference between each data value

   and the mean ⇒ |data value – mean|

4- Find the sum of the absolute values of the differences.

5- Divide the sum of the absolute values of the differences by the

   number of data values

* Now lets solve the problem

- The set of data is 31.8 , 22.6 , 13.8 , 16.4 , 28.1

# Find the mean

∵ The mean = sum/ number

∴ The mean = (31.8 + 22.6 + 13.8 + 16.4 + 28.1)/5 = 112.7/5 = 22.54

# Find |data value – mean|

∵ I31.8 - 22.54I = 9.26

∵ I22.6 - 22.54I = 0.06

∵ I13.8 - 22.54I = 8.74

∵ I16.4 - 22.54I = 6.14

∵ I28.1 - 22.54I = 5.56

# Find the sum of the absolute values

∴ The sum = 9.26 + 0.06 + 8.74 + 6.14 + 5.56 = 29.76

# Find the mean absolute deviation

∵ The mean absolute deviation = sum of absolute values/number

∴ The mean absolute deviation = 29.76/5 = 5.952

* The mean absolute deviation is 5.952