Five kids from the neighborhood are heading to the store to get some snacks. Kid #1 has $1, Kid #2 has $2, Kid #3 has $3, Kid #4 has $4, and Kid #5 has $5. Two weeks later, the family of Kid #5 won the lottery, and the kids got together to go to the store to get some snacks again. This time around, Kid #1 has $1, Kid #2 has $2, Kid #3 has $3, Kid #4 has $4, and Kid #5 has a wad of cash that totals $5,000. What's the average (mean) amount of cash the five kids have this time? What's the median? How have the mean and median changed since the first time they got snacks? Which one—the mean or the median—is a better reflection of how much money the neighborhood kids have? Finally, think of some examples in everyday life where the median is usually reported instead of the mean. Why do you think that is?

Quick answer:

The mean amount of cash the kids have before Kid #5's family wins the lottery is $3, and the median is $3. After the lottery winnings, the mean is $1,002, but the median is still $3. This means that the median is a better reflection of how much money the neighborhood kids have.

Expert Answers

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In the second scenario, after the lottery winnings, the mean is $1,002, and the median is $3.

In the first scenario, before the lottery winnings, the mean is $3, and the median is also $3.

You'll notice that the median is $3 in both scenarios, but the mean goes from $3 all the way up to $1,002.

In situations where there is an outlier, it is better to use the median as a way to represent the data points that you have. In the second scenario, there is one outlier. That outlier is Kid #5, who brought $5,000 to the store. If you want an accurate representation of the majority of the data (that is, Kids #1–4), using the median is a good way to show that the vast majority of the kids (80%) have only a few dollars.

Here is a scenario in everyday life where the median is a better representation of data. Think of a nice, small town with one hundred houses. Let's say 99 of those houses are small, cute little houses worth around $250,000. In the corner of this same town, one very successful millionaire owns a giant mansion worth $3,000,000. In this scenario, think of the millionaire as Kid #5 from earlier. It would be better to report the median property value of $250,000, because it represents the vast majority of homeowners in the area. It gives the reader of this data a better idea of what the town is like. The outlying millionaire would skew the data if you chose to represent the home values using the mean rather than the median.

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