Measures of Dispersion for Ungrouped Data

Standard deviation

A measure of spread in the same units as the data; the square root of the variance.

EnglishStandard deviation
Bahasa MelayuSisihan piawai
中文标准差

How it is used

For 2, 4, 6, 8, 10 the variance is 8, so the standard deviation is √8 ≈ 2.83. It says a typical value lies about 2.83 away from the mean of 6.

Where it shows up in SPM

In Measures of Dispersion for ungrouped data. Paper 2 often asks for the standard deviation as the last step after the variance, and then to compare two classes: the smaller standard deviation means the more consistent set.

Don't confuse it with

VarianceThe standard deviation is the square root of the variance, so remember to take the root at the end rather than stopping at the variance.
RangeThe range uses only the two extreme values, while the standard deviation uses every value, so it describes the spread more fully.

Open the chapter: Measures of Dispersion for Ungrouped Data →

Frequently asked questions

What does a small standard deviation tell me?

It means the values are clustered close to the mean, so the data is consistent and reliable. Comparing two sets with equal means, the one with the smaller standard deviation is more uniform.

A standard deviation of zero means every value equals the mean.

Why is the standard deviation preferred over the variance in reports?

Because it is in the same unit as the original data. If heights are in cm, the standard deviation is also in cm, which is easy to interpret, whereas the variance would be in cm² and harder to picture.

Related terms

One-hour paid trial · Same-day replyfrom RM50/hr
Book a Trial Class