Understanding Mean, Variance and Standard Deviation

mean list

This command reports the mean of numbers in the given list, summation of numbers is performed and then divided by the total number of items in the list.

• Using the command:  mean[3 9 6 2] 
• Using manual calculation: (3 + 9 + 6  + 2) / 4  or  sum[3 9 6 2] / length[3 9 6 2]

To do this manually:

1. Get the sum of numbers.
2. Divide the resulting number by the the size or length of numbers. If you added 5 different numbers, then divided it by 5.
3. Or, use both sum[] and length[] commands.

variance list

This reports the sample variance of  a list of numbers. In NetLogo, please take note that this command computes an unbiased estimate of the variance for a sample, rather than for a whole population, using Bessel's correction.

• Using the command: variance [3 9 6 2] 
•  Using manual calculation:  ((-2 * -2) + (4 * 4) + (1 * 1) + (-3 * -3)) / 3 

To do this manually:

1. Get the mean of numbers. In the example above, the mean is 5.
2. For each number: subtract the mean and square the result. So for the first number, 3 - 5 = -2. Then the squared result is -2 * -2.
3. Get the sum of the squared differences and divide it by one less than the number of items in the list.

standard-deviation list

A command that reports the sample standard deviation of a list of numbers.  In NetLogo, like variance, please take note that this command computes an unbiased estimate of the variance for a sample, rather than for a whole population, using Bessel's correction.

• Using the command: standard-deviation[3 9 6 2] 
•  Using manual calculation:  show sqrt(((-2 * -2) + (4 * 4) + (1 * 1) + (-3 * -3)) / 3)

To do this manually:

1. Get the variance of numbers.
2. Then, just take the square root of the resulting number from Step 1.

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