Course Title: Business StatisticsBBA (Hons)

2nd Semester

Course Instructor: Atiq ur Rehman ShahLecturer, Federal Urdu University of Arts,

Science & Technology, Islamabad+92-345-5271959

aatresh@gmail.com

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

Variance

The average of the squared differences from the Mean.

Raw Data: IT Department Graduate Level (MCS)

Number of observations = 27

• 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.

= 10.21/27 = 0.378328807 = 0.378

Variance = 0.378

Standard Deviation

• The standard deviation is defined as the square root of the variance.

Standard Deviation = √Variance

Standard Deviation

• Standard Deviation = √Variance = √0.378

= 0.615

Standard Deviation = 0.615