Enter the total number of observations, each individual observation, and the mean of the observations into the calculator to determine the standard deviation.

Measures Of Variability Formula

The following formula is used to calculate the measures of variability, specifically the standard deviation. 

SD = sqrt((1/N) * Σ(xi - μ)^2)

Variables:

  • SD is the standard deviation
  • N is the total number of observations
  • xi is each individual observation
  • μ is the mean of the observations

To calculate the standard deviation, subtract the mean from each individual observation and square the result. Sum up all these squared results and divide by the total number of observations. Finally, take the square root of the result to get the standard deviation.

What is a measure of variability?

Measures of variability, also known as measures of dispersion, are statistical calculations that describe the spread or dispersion of a set of data. They provide information about the range, interquartile range, variance, and standard deviation of the data set. These measures help to understand how much the data points differ from each other and from the central tendency (mean, median, or mode) of the data set. They are essential in statistical analysis to assess the reliability and predictability of data.

How to Calculate Measures Of Variability?

The following steps outline how to calculate the Standard Deviation (SD) using the formula: SD = sqrt((1/N) * Σ(xi – μ)^2).

  1. First, determine the total number of observations (N).
  2. Next, calculate the mean of the observations (μ).
  3. Next, subtract the mean from each individual observation (xi) and square the result.
  4. Next, sum up all the squared differences obtained in the previous step (Σ(xi – μ)^2).
  5. Next, divide the sum of squared differences by the total number of observations (1/N).
  6. Finally, take the square root of the result obtained in the previous step to calculate the Standard Deviation (SD).

Example Problem:

Use the following variables as an example problem to test your knowledge.

Total number of observations (N) = 10

Individual observations (xi) = 5, 7, 9, 11, 13, 15, 17, 19, 21, 23

Mean of the observations (μ) = 15