Using Standard Deviation to Compare Variation in Two Data Sets key The following table gives a sample of 6 bowling scores for both George and Danny George 185 135 200 185 250 155 Danny 182 185 188 185 180 190 Find the mean median and mode for each bowler s scores 185 for all 3 for both bowlers Use the following table to find 1 the variance and 2 the standard deviation for each one x Danny 182 3 9 185 0 188 3 185 0 0 180 5 25 190 5 25 0 9 The sum of the deviations is 0 as it always is and the sum of the squared deviations is 68 Divide this by n 1 6 1 5 to get 13 6 The square root of this is s the standard deviation The square root of 13 6 is 3 69 pins correct to two decimal places x George 185 0 0 135 50 2500 200 15 225 185 0 0 250 65 4225 155 30 900 Again the sum of the deviations is 0 while the sum of the squared deviations is 7850 We again divide by n 1 5 to get 1570 The square root of this is the standard deviation for George s scores The square root of 1570 is 39 62 pins correct to two decimal places Which bowler was the more consistent How do the two standard deviations show this Danny was the more consistent bowler with most of his scores right around his mean score of 185 The much smaller standard deviation for Danny shows this Remember that the standard deviation is a measure of the variation or spread of the data
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