7.5 The Variance and Standard Deviation

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Presentation transcript:

7.5 The Variance and Standard Deviation Definitions The Formula Variance measures the dispersal of the information. Basically, how spread out is the data? If the variance is small: The data is concentrated about the mean If the variance is large: The data is more spread out about the mean Let’s try! Find the mean Calculate the variance Value Prob 0.1 1 0.3 2 0.5 3

7.5 The Variance and Standard Deviation Another Formula!! Another Example!! This formula calculates the variance as well, but it can be a little simpler than the other… Try it out… does it work? Calculate the variance of this information. Value (X) Freq 3 1 8 2 5 12 4 13 9 Value (X) X2 Prob 0.1 1 0.3 2 4 0.5 3 9

7.5 The Variance and Standard Deviation Definitions Variance: Definition: Tells us how spread out the data is. Formula(s): Standard Deviation: Definition: Statistic used to measure the dispersal about the mean The reason this is good is because Var(X) is based upon the X values, whereas the standard deviation is “generic” Formula(s):

7.5 The Variance and Standard Deviation Examples State the variance from the previous two examples. What do they tell us about the data? Calculate the standard deviation of both. What does this tell us about the data?

7.5 The Variance and Standard Deviation Problems to complete from 7.5 Pg. 373 #1, 2