Identifying Outliers

Students were asked to report how far (in miles) they each live from school. The following distances were recorded. Please respond to the questions below.

Student

Distance

Zane

0.4

Jackson

0.5

Benjamin

1.0

Bethany

1.0

Joe

2.4

Noelle

2.7

Tianye

3.0

Anthony

3.2

Amanda

4.1

Michaela

4.2

Miranda

4.4

Joseph

5.0

John

7.5

Summary statistics for the distances are given below.

Min

Q1

Median

Q3

Max

Mean

Standard Deviation

0.4

1.0

3.0

4.3

7.5

3.03

1.97

1.Create and insert a box plot of the above data.

2.John currently lives furthest from school. Would you consider his distance from school (7.5 miles) to be "unusual"? Explain.

3.John's family is considering moving to a house that is 10 miles from school. How will this move affect the summary statistics? Change John's distance from 7.5 miles to 10 miles and complete the table based on this new data.

Min

Q1

Median

Q3

Max

Mean

4.Has the mean increased, decreased or remained unchanged? Has the median increased, decreased or remained unchanged? Explain how John's move has affected these measures of center.

5.Would this new distance of 10 miles be "unusual"now? Explain.

6.Zane lives closest to school. Using the definition of an outlier, is his distance considered an outlier? What is the relative position of Zane's distance to school from the mean? Explain your answer.