Question

Use the data to answer the following questions: 68, 63, 67, 66, 65, 87, 69, 61, 86, 82, 28

a. what is the outlier of the data and explain why you consider it as an outlier.
b. Find the mean of the data set with the outlier, show all your work.
c. calculate the mean of the date without the outlier, show all your work.

Answer 1

Rewrite given data in increasing order:

28, 61, 63, 65, 66, 67, 68, 69, 82, 86, 87

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. As you can see that number 28 lies an abnormal distance from other values.

Answer A: 28

The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values.

`\text{mean with outlier}=(28+61+63+65+66+67+68+69+82+86+87)/(11)=(742)/(11)=67.454545...\approx67.45.`

Answer B: 67.45

`\text{mean without outlier}=(61+63+65+66+67+68+69+82+86+87)/(11)=(742)/(10)=71.4.`

Answer C: 71.4