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7.5 The Variance and Standard Deviation. Definitions. The Formula. Let’s try! Find the mean Calculate the variance. 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

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7 5 the variance and standard deviation
7.5 The Variance and Standard Deviation

Definitions

The Formula

Let’s try!

Find the mean

Calculate the variance

  • 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


7 5 the variance and standard deviation1
7.5 The Variance and Standard Deviation

Another Formula!!

Another Example!!

Calculate the variance of this information.

  • This formula calculates the variance as well, but it can be a little simpler than the other…

  • Try it out… does it work?


7 5 the variance and standard deviation2
7.5 The Variance and Standard Deviation

Definitions

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):

Variance:

  • Definition:

    • Tells us how spread out the data is.

  • Formula(s):


7 5 the variance and standard deviation3
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 deviation4
7.5 The Variance and Standard Deviation

  • Problems to complete from 7.5

    • Pg. 373 #1, 2


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