Variance and Standard Deviation

Gr 11 Statistics (Ch 8)

The need for Variance and Standard Deviation Measures of dispersion:

Interquartile Range is better than the Range (not affected by outliers)

IQR measures spread around the median

Measure of central tendency Mean is better than the median

Variance and Standard Deviation measure dispersion around the mean

Abbreviations and Formulae

Standard Deviation =

Variance =

Formula:

2

22 ( )x x

n

2( )x x

n

Calculating Standard Deviation Manually

Consider the following two groups. They measured the distance that the members can throw a tennis ball. Measurements are given in cm.

Group A: 182, 186, 182, 184, 185, 184, 185 Group B 152, 194, 166, 216, 200, 176,

184 For each group:

1. Find the mean

2. Find the variance

3. Find the standard Deviation Which group is more consistent?

Calculating Standard Deviation Manually

Calculate the mean On a table:

Find the individual deviations from the mean.Square the individual deviations from the

mean.Add the deviations togetherFind the VARIANCE (The mean of the

deviations) Find the STANDARD DEVIATION

The square root of the variance

Using your calculator

See page 208 of text book

pdf (Master Maths)