Putting It Together: Ratios, Rates, Probabilities, and Averages

Eloyse Lesueur performing long jump in 2013

At the beginning of this module, we met Jeffrey, the long jump coach at Hamilton Middle School. He was wanting to find the mean distance for Hamilton Middle School’s long jump team given the following lengths:

  • Pedro jumped 5.51 meters
  • Elena jumped 5.87 meters
  • Roy jumped 3.92 meters

In the module we learned to find the mean of a set of numbers in the following way:

First, sum the numbers: [latex]5.51+5.87+3.92=15.3[/latex]

Then divide the total by the number of elements in the set:

[latex]15.3\div 3 = 5.1[/latex]

The mean high jump distance is 5.1 meters.

If Jeffrey’s incoming class ends up with jumps of

  • 4.54m
  • 3.89m
  • 6.02m
  • 4.54m
  • 5.31m
  • 3.91m

What are the median and mode of the jumps?

In the module we learned that you can find the median of a set of data with an even number of entries by finding the mean of the middle two values. First, we will need to sort the data from smallest to largest value.

3.89 3.91 4.54 4.54 5.31 6.02

The middle two numbers are the same, so the median is that value: [latex]4.54[/latex]

The mode of the data set is the number with the highest frequency, which is also [latex]4.54[/latex].