Measures of Dispersion for Ungrouped Data
Variance
A measure of how spread out data is around the mean; the square of the standard deviation.
| English | Variance |
|---|---|
| Bahasa Melayu | Varians |
| 中文 | 方差 |
How it is used
For 2, 4, 6, 8, 10 the mean is 6, so variance = (16+4+0+4+16)/5 = 40/5 = 8. Using the other form, Σx²/N − x̄² = 220/5 − 36 = 8 gives the same answer.
Where it shows up in SPM
In Measures of Dispersion for ungrouped data. Paper 2 typically asks you to build a table of x and x², apply σ² = Σx²/N − x̄², and then take the square root for the standard deviation.
Don't confuse it with
Open the chapter: Measures of Dispersion for Ungrouped Data →
Frequently asked questions
Which variance formula should I use in the exam?
Both σ² = Σ(x − x̄)²/N and σ² = Σx²/N − x̄² are correct and give the same value. The second is usually faster because you only tabulate x and x² and avoid subtracting the mean from every value.
Can the variance ever be negative?
No. It is a sum of squared distances divided by a positive count, so it is always zero or positive.
A variance of zero means every value is identical. If your working gives a negative answer, you have made an arithmetic slip.