![]() Calculating the standard deviation rather than the variance rectifies this problem. Therefore, the figure of 211.89, our variance, appears somewhat arbitrary. This means we cannot place it on our frequency distribution and cannot directly relate its value to the values in our data set. Secondly, the variance is not in the same units as the scores in our data set: variance is measured in the units squared. If our data contains outliers (in other words, one or a small number of scores that are particularly far away from the mean and perhaps do not represent well our data as a whole), this can give undo weight to these scores. First, because the deviations of scores from the mean are 'squared', this gives more weight to extreme scores. However, there are two potential problems with the variance. Conversely, if the scores are spread closely around the mean, the variance will be a smaller number. ![]() If the scores in our group of data are spread out, the variance will be a large number. Therefore, for our 100 students the mean absolute deviation is 12.81, as shown below:Īs a measure of variability, the variance is useful. Adding up all of these absolute deviations and dividing them by the total number of scores then gives us the mean absolute deviation (see below). Since we are only interested in the deviations of the scores and not whether they are above or below the mean score, we can ignore the minus sign and take only the absolute value, giving us the absolute deviation. However, the problem is that because we have both positive and minus signs, when we add up all of these deviations, they cancel each other out, giving us a total deviation of zero. 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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