The document discusses the concepts of variance and standard deviation in the context of a data set. It provides formulas for calculating variance and standard deviation, demonstrating the calculations using a specific data set (7, 9, 6, 9, 6) resulting in a variance of 2.3 and standard deviation of approximately 1.516. The conclusion emphasizes that these measures indicate the dispersion of data relative to the mean.

1. FACULTY OF EDUCATION
PREPAIRED BY: SONIYA KHAN
SEAT NO # 59
ELSA QAZI CAMPUS
TOPIC: VARIANCE
ASSIGNED BY:
DR. AMJAD ALI ARAIN

2. OBJECTIVES
VARIANCE
•To find the variance of a data
set.
STANDARD DEVIATION
•To find the standard deviation
of a data set.

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.

8. THANK YOU!
Do you have any questions?
SONIYA KHAN
SEAT No # 59