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
