Course Guide - USAID Teacher Education Project

Unit 4 Information HandlingWeek 2 Session, 2: Measures of Central Tendency—The Arithmetic Mean,Deciding on Measures of Central Tendency1. What are the important concepts?a) The arithmetic mean is calculated by adding all the items in the data set, thendividing by the number of items. This measure of central tendency implies that eachitem in the data set has the same value. Sometimes the mean is not an integer.b) When calculating the arithmetic mean, teachers need to think about whether theyconsider this a practice activity in calculation (with sums and division being done byhand), or if this is an activity in Information Handling, which would be an appropriateplace for students to use what they know about addition and division and to use abasic hand-held calculator.c) The arithmetic mean is often called the "average." However, all measures ofcentral tendency that consider what is typical of a data set can be considered to be anaverage. Hence the mode and the median should be considered averages, too.d) When reading articles containing statistics, students need to be alert to whichmeasure of central tendency the writer has chosen to use, and for what purpose.Consider the following data set:0, 0, 0, 0, 0, 50, 50, 100, 100, 100, 4000.1) The mean is a useful measure of central tendency to communicate an evendistribution.However, the mean is influenced by all the data, including extremes andoutliers. In the above data set, the many 0s and the large outlier have adramatic effect on the mean, 440.If these data show salaries of 11 people in a work group (5 volunteers earningno money, 5 interns receiving a small amount (50 or 100), and a projectdirector earning 4000), then the mean average salary for the organizationwould be 440. Using the mean would make it appear that the five personsrepresented by 0 had a 440 income, which is not true.On the other hand, if the data represents 11 people contributing money toshare with each other on the basis of need, each person would receive a 440share. Which would be true.2) In situations where the data is "skewed," as in the data set above, themedian may be a more realistic measure, because it is not influenced byoutliers. Thus, the median of this data set is 50, quite different from the meanof 440.This is why the median is often used in situations such as real estate valuessince in a neighbourhood there may be many similarly priced homes and an