Topic: Variance
Student Name: Sonia Khan
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
3. VARIANCE
• Variance is the average squared deviation from the mean of a
set of data.
• It is used to find the standard deviation
• VARIANCE FORMULA
• The variance formula includes the Summation Notation, 𝛴
which represents the sum of all the items to the right of Sigma.
• Mean is represented by 𝜇 & x̅ and n is the number of
observation.
4. NOW FIND OUT THE VARIANCE
• Data = 7, 9, 6, 9, 6
• Formula of Mean :
∑ 𝑥−
𝑛
7+9+6+9+6= 37
37
5
= 7.4
𝜇 = 7.4
5. NOW FIND OUT THE VARIANCE
Formula of Variance = 𝑆 =
∑ ( 𝑥− 𝑥− )2
𝑛−1
=
(7−7.4)2+(9−7.4)2+(6−7.4)2+(9−7.4)2+(6−7.4)2
5−1
=
(0.4)2+(1.6)2+(1.4)2+(1.6)2+(1.4)2
4
=
0.16+2.56+1.96+2.56+1.96
4
=
9.2
4
= 2.3
Variance is 2.3
6. CALCULATION OF STANDARD DEVIATION
Formula of Standard Deviation = 𝑆 =
∑ ( 𝑥− 𝑥− )2
𝑛−1
2.3 is your variance.
So, 2.3
𝜎 = 1.516
7. FINAL RESULT / CONCLUSION
• As we have seen, variance and standard deviation measures the
dispersion of data.
• The greater the value of the standard deviation, the further the
data tend to be dispersed from the mean.