Measure of dispersion, Variance & Standard Deviation

1. Course Title: Business Statistics
BBA (Hons)
2nd
Semester
Course Instructor: Atiq ur Rehman Shah
Lecturer, Federal Urdu University of Arts,
Science & Technology, Islamabad
+92-345-5271959
aatresh@gmail.com

2. Measure of Dispersion
• Measures of dispersion express quantitatively
the degree of variation or dispersion of values
in a population or in a sample .
• Variance and Standard deviation are the two
most commonly used tools for measurement
of dispersion

3. Variance
The average of the squared differences from the
Mean.

4. Raw Data: IT Department Graduate
Level (MCS)
Number of observations = 27

6. • Frequency(F)= Total observations in each class
• X= Midpoint of class
• FiXi= Midpoint(X) multiplied with Frequency (F)
• X-µ= Midpoint minus µ.
• µ represents the arithmetic mean
• (X-µ)2
= The above formula is Squared. Keeping in
mind that the square of a negative number will
be a positive.
• F(X-µ)2
= The outcome of (X-µ)2
is multiplied with
the frequency of that class.

7. = 10.21/27
= 0.378328807
= 0.378
Variance = 0.378

8. Standard Deviation
• The standard deviation is defined as the
square root of the variance.
Standard Deviation = √Variance

9. Standard Deviation
• Standard Deviation = √Variance
= √0.378
= 0.615
Standard Deviation = 0.615

10. Standard Deviation
• Standard Deviation = √Variance
= √0.378
= 0.615
Standard Deviation = 0.615