Numerical Descriptive Measures (PPT)

Basic Business Statistics (8th Edition)
Chapter 3 - Numerical Descriptive Measures

Chapter Topics

• Measures of central tendency
• Mean, median, mode, geometric mean, midrange
• Quartile
• Measure of variation
• Range, Interquartile range, variance and standard deviation, coefficient of variation
• Shape
• Symmetric, skewed, using box-and-whisker plots

Chapter Topics

• Coefficient of correlation
• Pitfalls in numerical descriptive measures and ethical considerations

Summary Measures

• Measures of Central Tendency
• Mean (Arithmetic Mean)
• Mean (arithmetic mean) of data values
• Sample mean

Population mean

• Mean (Arithmetic Mean)
• The most common measure of central tendency
• Affected by extreme values (outliers)

Median

• Robust measure of central tendency
• Not affected by extreme values
• In an ordered array, the median is the “middle” number
• If n or N is odd, the median is the middle number
• If n or N is even, the median is the average of the two middle numbers

Mode

• A measure of central tendency
• Value that occurs most often
• Not affected by extreme values
• Used for either numerical or categorical data
• There may may be no mode
• There may be several modes

Geometric Mean
Useful in the measure of rate of change of a variable over time

Geometric mean rate of return
Measures the status of an investment over time

Measures of Variation
Range
Measure of variation
Difference between the largest and the smallest observations:
Ignores the way in which data are distributed
Interquartile Range
Measure of variation
Also known as midspread
Spread in the middle 50%
Difference between the first and third quartiles
Not affected by extreme values

Variance
Important measure of variation
Shows variation about the mean

Standard Deviation

• Most important measure of variation
• Shows variation about the mean
• Has the same units as the original data

Comparing Standard Deviations

• Coefficient of Variation
• Measures relative variation
• Always in percentage (%)
• Shows variation relative to mean
• Is used to compare two or more sets of data measured in different units

Chapter Summary

• Described measures of central tendency
• Mean, median, mode, geometric mean, midrange
• Discussed quartile
• Described measure of variation
• Range, interquartile range, variance and standard deviation, coefficient of variation
• Illustrated shape of distribution
• Symmetric, skewed, box-and-whisker plots

Chapter Summary

• Discussed correlation coefficient
• Addressed pitfalls in numerical descriptive measures and ethical considerations

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