Mean, Median, Mode, Range 05:07 minutes

Video Transcript

Transcript Mean, Median, Mode, Range

This year, the Annual Bratwurst Eating Contest will be held in Austin, Texas, and a team from the US, a team from Canada and of course, the German team will compete.

It's too bad. Kornelius, a member of the German team is otherwise engaged, so he can’t attend the contest. But Stephan, the captain of the German team, has an ace up his sleeve. I wonder what he's up to. The winner of the Annual Bratwurst Eating Contest is the team with the highest mean number of brats consumed. But, teams will be rewarded for the biggest range as well as excellence in the three methods of calculating the central tendency of a set: Mean, Median and Mode.

Calculating the mean

Let’s help the judges calculate the mean. The mean is the sum of all elements in a set divided by the total number of elements in the set. The mean is also known as the average of a data set. To calculate the mean for each team, we first have to add the number of brats consumed by each member of each team, and then divide that sum by the number of team members, or addends.

Germany has a mean of 43, while team USA has a mean of 36. The Canadian team has a mean of 23 – as you can see, to calculate their mean score, we divided the sum of the bratwurst eaten by 4 since there are only 4 members of their team and therefore, 4 addends. Does the mean truly reflect the center of the data for each team? Some of the numbers seem to be too high or too low… Numbers that are higher or lower than the other numbers in a data set are called outliers, and they can skew the mean, higher or lower. So... maybe the mean is not the best measure of central tendency.

Let’s investigate this situation a little more. Take a look at the range. The range is the difference between the maximum and minimum values, highest and lowest, respectively, in a data set. A high range indicates a large difference between the maximum and minimum values in a set and may be an indicator of the presence of outliers. Wow, the range of the data for the German team is 65!

Is there an outlier? Let's take another look at the data. One member of the German team ate 90 bratwurst! Hmmm, that seems strange. Uh oh! I hope this doesn't cause an international incident, but the Americans just pointed out that one of the members of the German team is a Yeti, and he's the team member that ate 90 bratwurst! Since there's no precedent for having a Yeti on a team, the judges hold a quick meeting to decide what to do. Will the German team be disqualified?

Calculating the median

The judges have decided. To be fair to the teams from America and Canada, the judges will use the median to determine the winner. When outliers are included in a data set, the median, the central value of a data set, may give the best measure of central tendency. To find the median, order the data from lowest to highest. The median is the middle number. If there are an even number of elements in the set, you simply have to average the two middle values.

How about that? The German team is still the winner of the contest! This doesn’t seem fair, but the evidence is clear. The Germans have the highest mean AND median, so the they win first place.

Determining the mode

There's also a prize for the team with the highest mode, or the data value that is repeated the most. Let’s take a look. The Germans and Americans have no data values that repeat, so both teams have NO mode but for the Canadians, the value 23 repeats twice, so they take the prize for the highest mode!

Well, lookey here, it seems like they've all succumb to food coma. I guess their eyes were bigger than their stomachs. Most of them, anyway.