Chapter 12 – Probability and Statistics12.6 – Statistical Measures

12.6 – Statistical Measures• Today we will learn how to:• Use measures of central tendency to represent a set of data

• Find measures of variation for a set of data

12.6 – Statistical Measures• Measures of Central Tendency• Univariate data – data with one variable

• Measure of Central Tendency – number that describes a set of data• Represents the center or middle of the data

• Mean, median, mode

12.6 – Statistical Measures• Measures of Tendency• Mean

• the data are spread out, and you want an average of the value

• Median• the data contain outliers

• Mode• The data are tightly clustered around one or two values

12.6 – Statistical Measures• Example 1• A new internet company has 3 employees who are each paid

$300,000, ten who are paid $100,000 and sixty who are paid $50,000. Which measure of central tendency best represents the pay at this company?

12.6 – Statistical Measures• Measure of Variation (Dispersion) – measures how spread out

or scattered a set of data is• Range – difference between greatest and least values

• Variance – how much the data values differ from the mean

• Standard Deviation – how much the data values differ from the mean

12.6 – Statistical Measures• Variance – σ2 (sigma)• Find the mean (x3 - x bar)

• Find the difference between each value in the set of data and the mean

• Square each different

• Find the mean of the squares

12.6 – Statistical Measures• Standard Deviation (σ) • Square root of the variance

• If a set of data consists of the n values x1, x2, …, xn, and has mean x3 , then the standard deviation σ is given by the following formula• σ = √(x1 - x3 )2 + (x2 - x3 )2 + … + (xn - x3 )2

n

12.6 – Statistical Measures• Example 2• This table shows the lengths

in thousands of miles some of the longest rivers in the world. Find the standard deviation of these data

River Length(thousands of

miles)Nile 4.16

Amazon 4.08

Missouri 2.35

Rio Grande 1.90

Danube 1.78

12.6 – Statistical Measures

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