Standard Deviation

Presented by:

Sultan Sultan

Abdelrahman Al Kilani

Overview• Objectives

• Definition of Standard Deviation

• Merits and demerits of Standard Deviation

• The calculation of Standard deviation

ObjectivesAt the end of this presentation you should be able to :

- Define the standards deviation

- List the merit and demerit of obtaining standards deviation

- Calculate the variance and standard deviation

Standard Deviation- Standard deviation measures the dispersion of data.

- It shows the average absolute distance of each point from the mean

- The greater the value of standard deviation, the further the data tend to be dispersed from the mean.

Merits of Standard Deviation1- It is the most reliable measure of dispersion

2- It is most widely used measure of dispersion or variability

3- Its computation is based on all the observations.

Demerits of Standard Deviation

1- It is relatively difficult to calculate and understand.

2- It cannot be used for comparing the dispersion of two, or more series given in different units.

3- It is affected very much by the extreme values

FormulaStandard deviation has a symbol (σ) if the data represent a population and (s) if the data represent a sample

σ = (𝒙− 𝒙 )𝟐

𝒏

s = (𝒙− 𝒙 )𝟐

𝒏−𝟏

Population

Sample

Example:

find the standard deviation for a population data: 6, 4, 5, 7, 8

σ = (𝒙− 𝒙 )𝟐

𝒏=

𝟏𝟎

𝟓= 𝟐 = 1.4

(𝒙 − 𝒙)𝟐𝒙 − 𝒙Xn

06-6=061

44-6=-242

15-6 = -153

17-6 = 174

28-6 = 285

10 (𝑥 − 𝑥)2 =

Solution:

Summary- Standard deviation measure the dispersion of data.

- It is the most reliable

- The greater the value of standard deviation, the further the data tend to be dispersed from the mean.

References

Stacey B., Laurel S. (1st edtion). Statistics for Nursing and Allied Health