Question

The data set represents the ages of players in a chess club. 27, 34, 38, 16, 22, 45, 54, 60. What is the mean absolute deviation of the data set?

Answer 1

Explanation:

In order to find the mean absolute deviation of the given data,first find the sum of the given data and then decide the sum of the given data with the sum by the number of data values.

Thus, sum of the given data=27+34+38+16+22+45+54+60=296 and then divide with the sum by the number of data values that is =
`(296)/(8)=37`.

Now, find the the absolute value of the difference between each data value and the mean(Data value-mean) that is:

Data Absolute value

27 27-37=-10

34 34-37=-3

38 38-37=1

16 16-37=-21

22 22-37=-15

45 45-37=8

54 54-37=17

60 60-37=23

Now, Find the sum of the absolute values of the differences that is

-10+(-3)+1+(-21)+(-15)+8+17+23=0

Now, Divide the sum of the absolute values of the differences by the number of data values that is =
`(0)/(8)=0`.

Thus, the mean absolute deviation =0

Answer 2

The mean absolute deviation of the data set is:

12.25

Explanation:

The data points are given as follows:

27, 34, 38, 16, 22, 45, 54, 60.

Total number of data points= 8

The mean of these data points is the average of the data points and is calculated as follows:

`Mean(x')=(27+34+38+16+22+45+54+60)/(8)\\\\i.e.\\\\Mean(x')=(296)/(8)\\\\i.e.\\\\Mean(x')=37`

The absolute deviation of these data points is calculated as follows:

x Absolute deviation|x-x'|

27 |27-37|=10

34 |34-37|=3

38 |38-37|=1

16 |16-37|=21

22 |22-37|=15

45 |45-37|=8

54 |54-37|=17

60 |60-37|=23

Now, the mean of these absolute deviation i.e. Mean absolute deviation (MAD) is:

`MAD=(\sum |x-x'|)/(8)\\\\i.e.\\\\MAD=(10+3+1+21+15+8+17+23)/(8)\\\\i.e.\\\\MAD=(98)/(8)\\\\i.e.\\\\MAD=12.25`