Mean, Median, Mode, Variance, and Standard Deviation – A Quick Recap

Mean, Median, and Mode

Mean, median, and mode are all measures of central tendency.

  • Mode refers to the most frequently occurring number in a dataset,
  • Median is the middle number of an ordered dataset, and
  • Mean is calculated by piding the sum of numbers by the number of numbers

Variance and Standard Deviation

Variance and standard deviation are measures of spread in a dataset. They measure how far the points deviate from the mean on average.

Variance is calculated using the following steps:

  1. Calculate difference between each point and the mean
  2. Square the differences
  3. Sum the squares
  4. Divide the sum by the number of numbers

Standard deviation is the square root of variance.

Example

Let’s illustrate with an example. Suppose we have the following dataset:

1,1, 2, 2, 3, 3, 3, 3, 4, 4, 5

Median

There are 11 numbers in the dataset.

Therefore, median
= 6th number
= 3

Mode

Mode = 3

Mean

Mean
= (1 + 1 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 5) / 11
= 31 / 11
= 2.82

Variance

Sum of squared differences (Steps 1 to 3 above)
= (1 – mean)2 + (1 – mean)2 + (2 – mean)2 + …. + (4 – mean)2 + (5 – mean)2
= 172/11

Variance
= sum of squared differences / number of numbers
= (172/11) / (11)
=  1.42

Standard Deviation

Standard Deviation
= Square root of variance
= 1.19

Video

For a video tutorial, check out this excellent YouTube video. Note that the video uses a slightly different formula for variance. It uses the standard deviation for a sample, while in most cases, we use the standard deviation for a population.

It does not make much of a difference when your sample size is large, so either one is fine.