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Averages

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Challenge

Averages (discover)
The mean, median, and mode are all ways of representing typical values in a data set. The data below represent the number of text messages sent by a group of people. Change the data and see how it impacts the mean, median, and mode. Can you modify a data value so that the mean changes but not the median? How about the other way around? Enter the data set 2, 3, 3, 2, 4, 3, 5, and 9. Notice that the last value of the data set is much larger than the rest of the values. Extreme values in the data, called outliers, change the value of the mean much more than the median or the mode. It is better to use the median as an average when a data set contains extreme values.

Related Concepts

Linear Functions, Mean, Median, Mode, Scatter Plot, Slope of a Line

Fun Facts

Cell phone companies offer many plans with different amounts of included minutes and messages, different base prices, and different costs for going over the number of included minutes and messages. Companies carefully design their plans to earn the most amount of money, not necessarily the most number of customers. To do this, they analyze data from cell phone users and calculate averages to find a single value that is typical for different groups of customers. They also use linear functions to represent the relationships between the base price, included minutes, and overage rate to help decide how to set the amounts for each plan.