Business Statistics

Chapter 4 | Measures of Dispersion 129

Example 4.7

The greater the standard deviation, the greater the magnitude of the values from their mean; smaller

the standard deviation, greater the uniformity in the observation. The formula for the calculation of

sample standard deviation is

2

1

( )

Sample standard deviation ( )

1

n

i

i

x x

s

n

=

−

=

−

∑

where

x

is the sample arithmetic mean, n the sample size, and x

i

the ith value of the variable x.

The formula used for the calculation of population standard deviation is given as

2

( )

Population standard deviation( )

n

i

i=1

x

N

− µ

σ =

∑

where m is the population arithmetic mean, x

i

the ith value of the variable x, and N = f