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Uploaded byDr. Amjad Ali Arain
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VARIANCE

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.

Education◦
FACULTY OF EDUCATION PREPAIRED BY: SONIYA KHAN SEAT NO # 59 ELSA QAZI CAMPUS TOPIC: VARIANCE ASSIGNED BY: DR. AMJAD ALI ARAIN
OBJECTIVES VARIANCE •To find the variance of a data set. STANDARD DEVIATION •To find the standard deviation of a data set.
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.
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
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
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
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.
THANK YOU! Do you have any questions? SONIYA KHAN SEAT No # 59