Question

Data set: 47, 45, 44, 41, 48 1. Find the mean. Mean = 47 + 45 + 44 + 41 + 48 5 = 225 5 = 45 2. Find each absolute deviation. Absolute deviations: 2, 0, 1, 4, 3 What is the mean absolute deviation (MAD) for the data set? MAD

Answer 1

2

Explanation:

Got it right :3

Answer 2

We have been given the data: 47,45,44,41,48

`Mean=\frac{\text{sum of observations}}{\text{number of observations}}`

On substituting the values in the above formula to find mean:

`Mean=(47+45+44+41+48)/(5)`

`Mean=(225)/(5)=45`

Now, we need to find the absolute deviation that is:

`\text{absolute deviation}=\sum{|x-\bar{x}|}`

Where
`\bar{x}` is the mean and x is the values given of x which are: 2,0,1,4

`\text{absolute deviation}=|2-45|+|0-45|+|1-45|+|4-45|=43+45+44+41`

`\Rightarrow \text{absolute deviation}=173`

Now, to find mean absolute deviation we have a formula:

`\text{mean absolute deviation}=\sum\frac{(x-\bar{x})}{N}`

`\text{mean absolute deviation}=(|47-45|+|45-45|+|44-45|+|41-45|+|48-45|)/(5)`

`\text{mean absolute deviation}=(2+0+1+4+3)/(5)`

`\text{mean absolute deviation}=2`