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 Dispersion Formula

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

SD = sqrt((1/N) * SO(xi - SO)^2)

Variables:

  • SD is the standard deviation
  • N is the total number of observations
  • xi is each individual observation
  • MO is the mean of the observations
  • SO denotes the sum of all 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 Dispersion?

Measures of dispersion are statistical calculations used to describe the variability or spread in a set of data. They provide insights into how much the data points differ from the average or mean value. Common measures of dispersion include range, variance, standard deviation, and interquartile range. These measures help in understanding the reliability of the mean, identifying outliers, and making comparisons between different data sets.

How to Calculate Measures Of Dispersion?

The following steps outline how to calculate the Measures of Dispersion using the given formula:

  1. First, determine the total number of observations (N).
  2. Next, calculate the mean of the observations (?).
  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 (?(xi - ?)^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 (?) = 15

Using the formula SD = sqrt((1/N) * ?(xi - ?)^2), calculate the standard deviation.