Standard deviation measures how dispersed data values are from the average. It is the most reliable measure of dispersion and shows the average distance of each data point from the mean. While it is more difficult to calculate than other measures, standard deviation provides important information about how concentrated or spread out the data is. The presentation defines standard deviation, lists its merits and demerits, and shows how to calculate it for both populations and samples.

1. Standard Deviation
Presented by:
Sultan Sultan
AbdelrahmanAl Kilani

2. Overview
• Objectives
• Definition of Standard Deviation
• Merits and demerits of Standard Deviation
• The calculation of Standard deviation

3. Objectives
At 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

4. 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.

5. Merits of Standard Deviation
1- 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.

6. 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

7. Formula
Standard 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

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

9. 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:

10. 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.

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