Mean and Outliers

The data set below has an outlier of 42.
2, 5, 12, 15, 19, 4, 6, 11, 16, 18, 12, 12, 42
What effect does removing the outlier have on the distribution of the data?

• The mean will decrease

• The median will decrease

• The mean will increase

• The median will increase

Given the following data set
6, 9, 12, 14, 7, 9, 6, 8, 25, 12, 14
What is the mean of the data set without the outlier(s)?

• 9.2

• 9.7

• 11.1

• 12.4

The table below shows the lengths of fences a company installed during a week. 
Which statement is true?

• The 275-foot fence caused the mean to be significantly lower than the median.

• The 275-foot fence caused the median to be significantly lower than the mean.

• The 2,250-foot fence caused the mean to be significantly greater than the median.

• The 2,250-foot fence caused the median to be significantly greater than the mean.

A bowler had the following scores after 5 games:
 196, 205, 197, 280, and 202.
How much does the bowler’s mean score increase if the outlier is considered, compared to if the outlier is not considered?

• 13

• 16

• 19

• 22

If a student with a GPA of 1.5 is added to the group, how would the mean and median be affected?

• The mean and median would stay the same.

• The mean would decrease and the median would stay the same.

• The mean would stay the same the median would decrease.

• The mean and median would decrease.

The prices at several different stores for a pair of shoes are shown below.
$78, $79, $81, $82, $83
Two days later, another store has the same shoes on sale for $65. How does the new price affect the data?

• Only the range was affected.

• The median increased, and the range increased.

• The mean increased, and the range increased.

• The mean decreased and the range increased.

Gabriella’s quiz grades are shown below.
88, 92, 92, 96, 98
Gabriella scored a 20 on her sixth quiz. What effect does this score have?

• The low score causes the median to increase.

• The low score causes the median to decrease.

• The low score causes the mean to increase.

• The low score causes the mean to decrease.

The data below represent the ages of several people in a class.What effect does Mr. Smith’s age have on the data set?

• Mr. Smith’s age increases the mode of the data.

• Mr. Smith’s age decreases the mean of the data.

• Mr. Smith’s age increases the mean of the data.

• Mr. Smith’s age increases the median of the data.

Jacob recorded the ages of the people at a picnic. The data set is listed below.
12, 12, 14, 15, 16, 20, 24, 28, 32, 35, 36
What effect does the arrival of Jacob’s 72-year old grandfather have on the difference between the mean and the median ages of people at the picnic?

• The difference increases by about 2.1.

• The difference increases by about 3.3

• The difference increases by about 4.1

• The difference increases by about 4.3

The hourly salaries of the workers at a restaurant are shown below.
$7.75, $8.50, $7.25, $9.00, $30.00, $8.25, $7.75, $9.00
Which statement is true?

• The worker who earns $7.25 an hour causes the mean to be a better representation of the typical salary than the median.

• The worker who earns $7.25 an hour causes the median to be  a better representation of typical salary than the mean.

• The worker who earns $30.00 an hour causes the mean to be a better representation of the typical salary than the median.

• The worker who earns $30.00 an hour causes the median to be a better representation of the typical salary than the mean.