Question

The data set below has 7 values.Find the mean absolute deviation for the data set.If necessary, round your answer to the nearest hundredth8, 21, 19, 18, 11, 22, 20Mean absolute deviation:

Answer 1

Step-by-step explanation:

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

Lets first find the mean of the data set:

`Mean=(8+21+19+18+11+22+20)/(7)=17`

Now for the mean absolute deviation we have to find the absolute distance from each value and the mean, the MAD formula is:

`MAD=\frac{\sum_{i\left|x-\bar{x}|\right?}^{}}{n}`

In this case:

`MAD=(\left|8-17\right|+\left|21-17\right|+\left|19-17\right|+\left|18-17\right|+\left|11-17\right|+\left|22-17\right|+\left|20-17\right|)/(7)`
`MAD=(9+4+2+1+6+5+3)/(7)`
`MAD\approx4.2857`

ANSWER

The mean absolute deviation for the data set is approximately 4.29