Outliers Warmup

A value that is much higher or much lower than the other values in a set of data.

• Outlier

• Mean

• Median

• Mode

Answer explanation

An outlier is a value that significantly differs from the other values in a dataset, being much higher or lower. This makes 'Outlier' the correct choice, while mean, median, and mode refer to measures of central tendency.

Identify the outlier for the given data?

23, 34, 27, 7, 30, 26, 28, 31, 34

• 7

• 23

• 31

• 34

Answer explanation

The number 7 is significantly lower than the other values in the dataset, which range from 23 to 34. This makes 7 the outlier, as it does not fit the pattern of the other numbers.

Your math grades are 90, 85, 0, 90, 80, 100, and 90. Which grade is the outlier?

• 90

• 0

• 80

• 100

Answer explanation

The grade 0 is significantly lower than the others, which are mostly in the 80s and 90s. This makes 0 the outlier in the set of grades.

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 measures of center?

• The median will decrease

• The mean will decrease

• The mean will increase

• The median will increase

Answer explanation

Removing the outlier 42 lowers the total sum of the data set, which decreases the mean. The median, being the middle value, remains unchanged since it is not affected by extreme values.

The data in the table represents 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.

Answer explanation

Mr. Smith's age, being higher than the current mean, raises the overall average age of the class, thus increasing the mean of the data.

Consider the data set below:

2, 5, 12, 15, 19, 4, 6, 11, 16, 18, 12, 12, 42

What is the value of the median with the outlier included?

Answer explanation

To find the median, first sort the data: 2, 4, 5, 6, 11, 12, 12, 12, 15, 16, 18, 19, 42. With 13 numbers, the median is the 7th value, which is 12. Thus, the median with the outlier included is 12.