Unit E: Statistics and Probability

Chapter 1: Statistics

When to Use Mean, Median, and Mode

Which is the best measure of central tendency to use to find the "average" value? Mean, median, and mode determine the average value differently. Each one has its own advantages and disadvantages.

When should it be used?

  • Mean is best used for sets of data that do not have extreme values.

  • For example, mean would be a good choice to find the average weight of one-week-old Labrador puppies.

Advantages:

  • The mean can be calculated quickly by adding up all the values and dividing by the total number of values in the set of data.

  • Generally, mean is well understood. When most people refer to the word "average," they are referring to the mean.

Disadvantages:

  • Mean is not useful when a set of data has extreme values; i.e., values that are much higher or lower than the typical values in a set of data.

When should it be used?

  • Median is best used for sets of data that have extreme values that do not reflect the typical data.

  • For example, the median would be a good choice to calculate the average house price in a city. If the mean was calculated, the average could be pulled down by a few houses that sold very cheaply or inflated by a couple of very expensive houses.

Advantages:

  • Median provides an accurate middle of the data set when the set of data contains extreme values.

Disadvantages:

  • Ordering the values from least to greatest takes time.

When should it be used?

  • Mode is best used when looking for the typical or most popular data.
  • For example, a shoe store would identify the most popular size when ordering stock.

Advantages:

  • No calculations are required.
  • It is easy to identify the most frequent value.

Disadvantages:

  • There may be several modes.
  • Mode cannot be used if all the data values are different.