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Statistic Variability (Spread)

Descriptive Statistics is broken down into Tendency and Variability.

Variability uses these measures:

  • Min and Max
  • Variance
  • Deviation
  • Distribution
  • Skewness
  • Kurtosis

The Variance

In statistics, the Variance is the average of the squared differences from the Mean Value.

In other words, the variance describes how far a set of numbers is Spread Out from the mean (average) value.

Mean value is described in the previous chapter.

This table contains 11 values:

7889991011141415

Calculate the Variance:

// Calculate the Mean (m)
let m = (7+8+8+9+9+9+10+11+14+14+15)/11;

// Calculate the Sum of Squares (ss)
let ss = (7-m)**2 + (8-m)**2 + (8-m)**2 + (9-m)**2 + (9-m)**2 + (9-m)**2 + (9-m)**2 + (10-m)**2 + (11-m)**2 + (14-m)**2 + (15-m)**2;

// Calculate the Variance
let variance = ss / 11;

Try it Yourself »

Or use a math library like math.js:

const values = [7,8,8,9,9,9,10,11,14,14,15];
let variance = math.variance(values, "uncorrected");

Try it Yourself »



Standard Deviation

Standard Deviation is a measure of how spread out numbers are.

The symbol is σ (Greek letter sigma).

The formula is the variance (the square root of the variance).

The Standard Deviation is (in JavaScript):

// Calculate the Mean (m)
let m = (7+8+8+9+9+9+10+11+14+15)/11;

// Calculate the Sum of Squares (ss)
let ss = (7-m)**2 + (8-m)**2 + (8-m)**2 + (9-m)**2 + (9-m)**2 + (9-m)**2 + (9-m)**2 + (10-m)**2 + (11-m)**2 + (14-m)**2 + (15-m)**2;

// Calculate the Variance
let variance = ss / 11;

// Calculate the Standard Deviation
let std = Math.sqrt(variance);

Try it Yourself »

Deviation is a mesure of Distance.

How far (on average), all values are from the Mean (the Middle).

Or if you use a math library like math.js:

const values = [7,8,8,9,9,9,9,10,11,14,15];
let std = math.std(values, "uncorrected");

Try it Yourself »