Mean, Median, Mode & Range Examples

These are the scores from last week's geometry test:

90, 94, 53, 68, 79, 84, 87, 72, 70, 69, 65, 89, 85, 83, 72

You earned a score of 72. Your mom asks you how you did on the test compared to the rest of the class. Calculate the three measures of the average, and decide what to tell your mom.

Mean:

Median:

Mode:

72 occurs twice, so it is the mode.

So what are you going to say to your mom? You could tell her that the average score of the class was 72, just like your score!  You wouldn't exactly be lying... although she almost certainly meant "average" in its more common usage as "mean."  

These are the top ten final scores for the combined results of the Ladies' Figure Skating event at the 2010 Winter Olympics:

Yu-Na Kim of South Korea shattered the world record with a score 18 points higher than the previous record. How would the mean and median of this group change if we left out her score?

The current median of the group is:

The current mean is:

If we eliminate Yu-Na's score, the median would be:

, or the middle number in the data set.

And the mean would be:

By removing her score, the median dropped by less than one point, but the mean dropped by more than 4 points. Yu-Na's extremely high score affected the mean much more than the median.

On your first four math tests you earned a 85, 80, 95, and a 65 (hey, anyone can have a bad day). What must you earn on your next test to have a mean score of at least 80?

To find the answer, first we'll set up an equation to find the mean of the 5 tests (after you take the next test there will be 5 of them). Let's call that final test x.

Now let's solve for x. We'll start by adding the scores on top:  

Next, multiply 80 by 5.

Finally, subtract 325 from 400.

You must earn at least a 75 on the next test to have a B average.