MODULE 3:DESCRIPTIVE STATISTICS

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Descriptive Statistics• Population parameter: a number calculated from all the

population measurements that describes some aspect of the population

• Sample statistic: a number calculated using the sample measurements that describes some aspect of the sample

• Interval or Ratio level data

• Make inferences about populations

• Describe the variable of interest

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Descriptive Statistics

• Measures of Central Tendency

• Mean, Median, Mode, Percentiles

• Measures of Variation

• Range, IQR, MAD, Variance, Standard Deviation, Coefficient of

Variation

• Measures of Shape

• Skewness, Box and Whisker Plot, Outliers

• Measures of Location

• Z score or Standard Score

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Measures of Central Tendency

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Measures of Central Tendency• Percentiles, Deciles, Quartiles

• For a set of measurements arranged in increasing order, the pth percentile is a value such that p percent of the measurements fall at or below the value and (100-p) percent of the measurements fall at or above the value

• The first quartile Q1 is the 25th percentile • The second quartile (median) is the 50th percentile• The third quartile Q3 is the 75th percentile• The interquartile range IQR is Q3 - Q1

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Percentiles

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Measures of Variation

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Descriptions of the spread or dispersion of a set of data.

Measures of Variation

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Measures of Variation

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Measures of Variation

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Measures of Variation

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Measures of Variation

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Measures of Shape

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Measures of Shape

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Measures of Shape

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Measures of Shape

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Measures of Shape

The “Box” in the plot ….

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Hinge Hinge

Median

Measures of Location

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Normal Populations: Empirical Rule

Empirical Rule

•68% of the population measurements lie within

one standard deviation of the mean

•95% of the population measurements lie within

two standard deviations of the mean

•99.7% of the population measurements lie within

three standard deviations of the mean

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Non-Normal Populations: Chebychev’s Theorem

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Computer Applications

Descriptive Statistics: Price

Variable Mean StDev Variance CoefVar Minimum Q1 Median Q3

Price 98.03 57.96 3359.38 59.12 1.00 42.50 98.00 149.75

N for

Variable Maximum Range IQR Mode Mode Skewness

Price 199.00 198.00 107.25 10, 16, 38, 148 4 -0.03

The data contain at least five mode values. Only the smallest four are shown.

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