Statistics: Mean, Variance, and Standard Deviation

Statistical Calculations

While the evaluator is not a full statistical package, you can compute common statistics by expressing the formulas directly.

Arithmetic Mean

The mean (average) is the sum divided by the count:

mean = (x1 + x2 + ... + xn) / n

Example: Mean of 4, 8, 15, 16, 23, 42:

(4 + 8 + 15 + 16 + 23 + 42) / 6 = 108 / 6 = 18

Variance

Variance measures how spread out the data is:

variance = ((x1-mean)^2 + (x2-mean)^2 + ...) / n

Using the dataset above (mean=18):

((4-18)^2 + (8-18)^2 + (15-18)^2 + (16-18)^2 + (23-18)^2 + (42-18)^2) / 6
= (196 + 100 + 9 + 4 + 25 + 576) / 6
= 910 / 6 = 151.667

Standard Deviation

Standard deviation is the square root of variance:

sqrt(151.667) = 12.315

Weighted Mean

When values have different weights:

weighted_mean = (w1*x1 + w2*x2 + ...) / (w1 + w2 + ...)

Example: Grade calculation (homework=30%, midterm=30%, final=40%):

(0.3*85 + 0.3*78 + 0.4*92) / (0.3+0.3+0.4) = 85.7

Or simply:

0.3*85 + 0.3*78 + 0.4*92 = 85.7

Geometric Mean

Useful for growth rates:

geometric_mean = (x1 * x2 * ... * xn)^(1/n)

Example: Average growth factor over 3 periods (1.1, 1.05, 1.15):

(1.1 * 1.05 * 1.15)^(1/3) = 1.0996