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Date Submitted: 11/29/2011 06:55 PM
Section A.2
Measures of Central Tendency and Dispersion
A5
A.2
Measures of Central Tendency and Dispersion Mean, Median, and Mode
In many real-life situations, it is helpful to describe data by a single number that is most representative of the entire collection of numbers. Such a number is called a measure of central tendency. The most commonly used measures are as follows. 1. The mean, or average, of n numbers is the sum of the numbers divided by n. 2. The median of n numbers is the middle number when the numbers are written in order. If n is even, the median is the average of the two middle numbers. 3. The mode of n numbers is the number that occurs most frequently. If two numbers tie for most frequent occurrence, the collection has two modes and is called bimodal.
What you should learn
• How to find and interpret the mean, median, and mode of a set of data • How to determine the measure of central tendency that best represents a set of data • How to find the standard deviation of a set of data • How to create and use box-and-whisker plots
Why you should learn it
Measures of central tendency and dispersion provide a convenient way to describe and compare sets of data. For instance, in Exercise 36 on page A13, the mean and standard deviation are used to analyze the price of gold for the years 1981 through 2000.
Example 1
Comparing Measures of Central Tendency
On an interview for a job, the interviewer tells you that the average annual income of the company’s 25 employees is $60,849. The actual annual incomes of the 25 employees are shown below. What are the mean, median, and mode of the incomes? Was the person telling you the truth? $17,305, $478,320, $45,678, $18,980, $17,408, $25,676, $28,906, $12,500, $24,540, $33,450, $12,500, $33,855, $37,450, $20,432, $28,956, $34,983, $36,540, $250,921, $36,853, $16,430, $32,654, $98,213, $48,980, $94,024, $35,671
Solution
The mean of the incomes is Mean 17,305 1,521,225 25 478,320 45,678...