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Descriptive Statistics is broken down into Tendency and Variability."
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");
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");