1.6

1.6 The Standard Deviation

The IQR is a measure of spread using the median to start

The standard deviation is a measure of spread using mean to start.

The standard deviation tells you how data is spread about the mean.

We’re going to use the standard deviation to measure the dispersal of samples.

s is the standard deviation for a sample but is the standard deviation of a population.

is the mean of a sample, is the mean of a population.

where, x is any value, is the mean of the sample, and n is the number in the sample.

Do p. 150#1 on paper, 2 on the GDC

Grouped Discrete Data

Do #3

Grouped Continuous Data

use the class midpoint for x.

Variance is a term used for the square of the standard deviation.

p.152#4-7

the coefficient of variation (CV) is a measure of dispersion of a probability distribution. It is defined as the ratio of the standard deviation $\ \sigma$ to the mean $\ \mu$ :

$c_{v} = {\sigma \over \mu }$

The coefficient of variation is a dimensionless number. For distributions of positive-valued random variables, it allows comparison of the variation of populations that have significantly different mean values. It is often reported as a percentage (%) by multiplying the above calculation by 100.