Mean, Median, and Mode


The mean is a number that shows the center of the data. Another word for mean is average and it is mathematically symbolized as x̄ (x-bar). However, when calculating the mean of the whole population, you use the Greek letter μ (mu) instead.

To calculate the average of a sample, you sum all the observations, then divide by the number of observations (n). The formula changes slightly for population average. The formulas are below:



  • Σ(x) represents the total sum of the observations.
  • n/N represents the number of observations.


The median of a set of numbers arranged in order of magnitude is the middle value of an odd number of measurements, or the mean of the two middle values of an even number of measurements. Median is symbolized as x̃ (x-tilda) or with a capital M.

Question:   Find the median of the following data:   574   635   645   695   736   746   794   894

Solution:   The numbers are in ascending order (always make sure they’re arranged in order of magnitude). There are an even number of observations (n = 8), therefore you take the average value of observation 4 and 5. null

If you’re still confused, two more examples are demonstrated below.


The mode of a set of numbers is the value(s) that occurs most often in the set.

  • The set:   1   3   3   5   6   7   7   7   9   → 7
  • The set:   1   1   3   3   5   5   7   7   → 1, 3, 5, and 7
  • The set:   1   3   3   3   5   6   7   7   7   9   → and 7

More details on finding the mode can be found in this video.


The mid-range is simply the value midway between the two extreme values, such as the range.

The mid-range for the values   3,   5,   6,   6,   7,   11,   11,   15   is: null

Let’s review how to calculate the mean, median, and mode with 2 sample problems.