Measures of Central Tendency and Dispersion

Dr.Srilakshminarayana.G

Median Middle value whensorted in order ofmagnitude

50th percentile

Mode Most frequently-occurring value

Mean Average

Measures of Central Tendency or Location

Example-1Fortune published a list of the 10 largest green companiesthose that followenvironmental policies. Their annual revenues, in $ billions, are given below.

Company Revenue $ BillionHonda $84.2Continental Airlines 13.1Suncor 13.6Tesco 71.0Alcan 23.6PG&E 12.5S.C. Johnson 7.0Goldman Sachs 69.4Swiss RE 24.0Hewlett-Packard 91.7

Example-2

The daily expenditure on food by a traveller, in dollars in summer2006, was as follows:

17.5, 17.6, 18.3, 17.9, 17.4, 16.9, 17.1, 17.1, 18.0, 17.2, 18.3, 17.8, 17.1, 18.3, 17.5, 17.4.

Find the mean, standard deviation, and variance.

Example-3The number of U.S. cars in service by top car rental companies in a recent yearaccording to Auto Rental News follows.

Company Number of Cars in ServiceEnterprise 643,000Hertz 327,000National/Alamo 233,000Avis 204,000Dollar/Thrifty 167,000Budget 144,000Advantage 20,000U-Save 12,000Payless 10,000ACE 9,000Fox 9,000Rent-A-Wreck 7,000Triangle 6,000

Example-4The following table shows changes in bad loans and in provisionsfor bad loans, from 2005 to 2006, for 19 lending institutions.

Verify the reported averages, and find the medians. Whichmeasure is more meaningful, in your opinion? Also find thestandard deviation and identify outliers for change in bad loansand change in provision for bad loans.

Examples from the data sets uploaded

Marks Scored by Students Customer Data Department Store Time taken to deliver a product Investments made by people in real estate Number of defective items produced Number of accidents in the city Items stored (inventory)

Measures of Variability or Dispersion Range

Difference between maximum and minimum values Interquartile Range

Difference between third and first quartile (Q3 - Q1) Variance

Average*of the squared deviations from the mean Standard Deviation

Square root of the variance

Definitions of population variance and sample variance differ slightly.