College Math

College Math Study Guide

tendency as they denote different ways to describe the average of the data collected. In other words, they describe the centrality of the data in a single value. Standard deviation and variance are used to explain the measures of dispersion that is how much the numbers in a set differs from the mean. We shall study all these measures one by one now. is the average of all the values, and is calculated by adding up the values of all the observations and then dividing the sum by the number of observations. It should, however, be noted that the mean is influenced by outliers, that is, extreme values. The formula to calculate mean is given by: = ∑ Where, M = mean value ΣX = sum of all observations N = number of observations Let us solve an example to understand it better. Suppose a series of distribution has the following values: 67, 68, 65, 62, 63, 64, 69, 69, 70, 63. The mean of the distribution can be computed as follows: N = 10 ΣX = 67+ 68+ 65+ 62+ 63+ 64+ 69+ 69+ 70+ 63 = 660 M = 660/10 = 66 It should be noted that the value of mean is highly influenced by any extreme value, and is termed as an outlier. Suppose, in the above example the 10 th value of 63 is substituted by 150. Then the value of mean will change drastically, calculated as: N = 10 ΣX = 67+ 68+ 65+ 62+ 63+ 64+ 69+ 69+ 70+ 150 = 747 M = 747/10 = 74.7 There is one more case when we are given tally charts or frequency tables. For instance, suppose a football team maintain a record of the number of goals for its matches, and following summary has been provided to us. 5.7 Mean Mean

©2018

Achieve

Page 91

of 120