![]() ![]() To find out the total variability in our data set, we would perform this calculation for all of the 100 students' scores. It is important to note that scores above the mean have positive deviations (as demonstrated above), whilst scores below the mean will have negative deviations. Therefore, if we took a student that scored 60 out of 100, the deviation of a score from the mean is 60 - 58.75 = 1.25. For example, the mean score for the group of 100 students we used earlier was 58.75 out of 100. Perhaps the simplest way of calculating the deviation of a score from the mean is to take each score and minus the mean score. Absolute Deviation and Mean Absolute Deviation How we calculate the deviation of a score from the mean depends on our choice of statistic, whether we use absolute deviation, variance or standard deviation. The average deviation of a score can then be calculated by dividing this total by the number of scores. To find the total variability in our group of data, we simply add up the deviation of each score from the mean. The absolute and mean absolute deviation show the amount of deviation (variation) that occurs around the mean score. The absolute deviation, variance and standard deviation are such measures. To get a more representative idea of spread we need to take into account the actual values of each score in a data set. Quartiles are useful, but they are also somewhat limited because they do not take into account every score in our group of data. ![]()
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