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:
| 7 | 8 | 8 | 9 | 9 | 9 | 10 | 11 | 14 | 14 | 15 |
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;
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");
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);
Deviation is a measure 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");