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How to Calculate Means from Raw Data

In this lesson, we’ll calculate another measure of central tendency which is often referred to as the average but in statistics, it’s called the mean. Let’s look again at Matthew and Timothy, our two competitive bowlers from our lesson on the mode. Remember, we used the mode to decide who was the better bowler. The mode, or the most frequent score, suggested Matthew was the best bowler because his mode score of 177 was higher than Timothy’s mode score of 174. However, the mean could also be used to represent the scores of the two bowlers. This measure of central tendency uses all the scores, not just the most frequent, to calculate the single score to represent all the scores for each bowler. Remember I said that the mean is the same as the average? So to calculate the mean score for Matthew, we first add up all of his scores and then divide by the number of scores. One hundred and seventy-one plus 173 plus 166 plus 177 plus 177 plus 171 plus 175 plus 177 plus 182 plus 168 and that total equals 1737. The second step in calculating the mean is to divide the total by the number of scores. In this case, there were ten scores in Matthew’s column so, we divide by ten. This gives us a mean of 173.7, which is a score that can represent all of Matthew’s scores. In statistics, the mean is represented by the symbol x-bar. Let’s find the mean score representing Timothy’s bowling performance. This time, the total of all the scores equal 1747. Once again, we divide the total 1747 by the number of scores which is ten. Now, we can see that the mean score for timothy is 174.7.

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