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Describing Data: Numerical Measures Chapter 3
GOALS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Characteristics of the Mean ,[object Object],[object Object],[object Object],[object Object],[object Object]
Population Mean ,[object Object]
EXAMPLE – Population Mean
Sample Mean ,[object Object]
EXAMPLE – Sample Mean
Properties of the Arithmetic Mean ,[object Object],[object Object],[object Object],[object Object],[object Object]
Weighted Mean ,[object Object]
EXAMPLE – Weighted Mean The Carter Construction Company pays its hourly employees $16.50, $19.00, or $25.00 per hour. There are 26 hourly employees, 14 of which are paid at the $16.50 rate, 10 at the $19.00 rate, and 2 at the $25.00 rate. What is the mean hourly rate paid the 26 employees?
The Median ,[object Object],[object Object],[object Object]
Properties of the Median ,[object Object],[object Object],[object Object],[object Object]
EXAMPLES  - Median ,[object Object],[object Object],[object Object],[object Object],[object Object],The heights of four basketball players, in inches, are:  76, 73, 80, 75 Arranging the data in ascending order gives:  73, 75, 76, 80 .  Thus the median is 75.5
The Mode ,[object Object]
Example - Mode
Mean, Median, Mode Using Excel Table 2–4 in Chapter 2 shows the prices of the 80 vehicles sold last month at Whitner Autoplex in Raytown, Missouri. Determine the mean and the median selling price. The mean and the median selling prices are reported in the following Excel output. There are 80 vehicles in the study. So the calculations with a calculator would be tedious and prone to error.
Mean, Median, Mode Using Excel
The Relative Positions of the Mean, Median and the Mode
The Geometric Mean ,[object Object],[object Object],[object Object],[object Object],[object Object]
EXAMPLE – Geometric Mean ,[object Object]
EXAMPLE – Geometric Mean (2) ,[object Object]
Dispersion ,[object Object],[object Object],[object Object],[object Object]
Samples of Dispersions
Measures of Dispersion ,[object Object],[object Object],[object Object]
EXAMPLE – Range ,[object Object],Range = Largest – Smallest value = 80 – 20 = 60
EXAMPLE – Mean Deviation ,[object Object]
EXAMPLE – Variance and Standard Deviation ,[object Object]
EXAMPLE – Sample Variance ,[object Object]
Chebyshev’s Theorem ,[object Object]
The Empirical Rule
The Arithmetic Mean of Grouped Data
[object Object],The Arithmetic Mean of Grouped Data - Example
The Arithmetic Mean of Grouped Data - Example
Standard Deviation of Grouped Data
Standard Deviation of Grouped Data - Example ,[object Object]
End of Chapter 3

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Chapter 03