Slide 1 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 1 Measures of central tendency n Learning Objectives Calculate the mode, median and mean from grouped and ungrouped data Calculate quartiles, deciles, percentiles and fractiles Calculate and interpret the geometric mean Determine the significance of the skewness of a distribution Chapter S3

Slide 2 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 2 The mode The number that occurs most frequently in a set of numbers n Where

Slide 3 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 3 The median The middle observation in a set Odd number of observations ( n ) Even number of observations ( n )

Slide 4 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 4 The mean n The sum of the observations divided by the number of observations Where:

Slide 5 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 5 Quartiles Quartiles divide data into four equal parts. n First quartile—Q 1 25% of observations are below Q 1 and 75% above Q 1 n Second quartile—Q 2 50% of observations are below Q 2 and 50% above Q 2 n Third quartile—Q 3 75% of observations are below Q 3 and 25% above Q 3

Slide 6 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 6 Geometric mean n Measure of the average rate of change over time. For example, the average growth rate of savings over several years.

Slide 7 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 7 Skewness The skewness of a distribution is measured by comparing the relative positions of the mean, median and mode. n Distribution is symmetrical Mean = Median = Mode n Distribution skewed right Median lies between mode and mean, and mode is less than mean n Distribution skewed left Median lies between mode and mean, and mode is greater than mean

Slide 8 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 8 Summary arithmetic mean: n The arithmetic mean: –most familiar measure –most commonly used measure –used to make inferences about a population –may be distorted by a few outlying measures –value cannot be calculated for open-ended frequency distribution