![]() The existence of an outlier can result in a misleading representation of the spread in data values.Īn alternative measure of dispersion is called the standard deviation. The range depends on only the highest and lowest data values. The range of 60% does not capture the fact that if the outlier is removed then there is a spread of only 6% for the four remaining data values. Refer back to Example 2 and the measures that were calculated for five test scores.The student’s mean score is 81% and the range in marks is 60%. Comparing the results for the seven versus six salaries, which of the three measures was most impacted by the outlier?.Comparing the results for the seven versus six salaries, which of the three measures was least impacted by the outlier?. ![]() Remove the outlier and recalculate the mean, median and the range for the six remaining salaries.Which of the seven salaries is an outlier?.Determine the mean, median and the range for these seven salaries.The following seven values are salaries at a local computer company. A measure of dispersion is used to describe the spread of data. In this section we will consider two measures of dispersion. When we analyze data it is important to consider how dispersed or spread out the data values are. Student B’s test scores range from a low score of 62% to a high score of 74% so the spread in marks is 12 percentage points. Student A’s test scores range from a low score of 32% to a high score of 95% so the spread in marks is 63 percentage points. They indicate where the data clusters.Ĭonsider student A’s scores on five tests: 32% 95% 89% 74% 55% The mean, or average, is (32 + 95 + 89 + 74 + 55)/5 = 69% and the median is 74%.Ĭonsider student B’s scores on the same five tests: 68% 69% 72% 74% 62% The mean, or average, is (68 + 69 + 72 + 74 + 62)/5 = 69% and the median is 69%.īoth student’s have the same test average of 69% but there is a substantial difference in the spread or dispersion of their scores. We have seen that measures of central tendency, including the mean and median, are used to identify a central position within a data set. ![]()
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