This exercise is designed to help you explore how outliers affect standard deviation (a measure of spread). Here is a data set ( n = 47 ) that is nearly normal (as can be seen in the histogram provided after the data set). 36.9 41.8 41.8 42.6 42.6 43.6 43.8 44.7 45.2 45.2 45.6 46.4 46.4 47.4 48 48.3 49.1 49.3 50.1 50.6 50.8 51 51 51.5 52.6 52.8 54.5 55.1 55.6 56.4 57.7 57.9 59.2 60.1 60.7 61.5 62 62.3 63 63.4 64 64 66.8 68.2 68.2 69.6 71.7 2 4 6 8 10 data 35 40 45 50 55 60 65 70 75 Frequency Part 1 Use Excel or StatDisk to find the sample standard deviation for this data set. You should be able to select the table and copy it directly to Excel or other such programs. Report the standard deviation using the rounding rules suggested in class (two more decimal places than the original data). SD = Part 2 When you collected this data, you knew there was an extreme value that seemed a little out of the ordinary (as demonstrated in the histogram). This value is 106.5. 2 4 6 8 10 data 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 Frequency Upon careful consideration, you decide to include the outlier 106.5. Calculate the standard deviation of the original data set with this outlier included ( n = 48 ). SD = Part 3 Because the value was so extreme, you decided to return to the original data collected to make sure this extreme value was not incorrectly entered or calculated wrong. When you do this, you actually find that the value was incorrect, and the correct value appears to be even more extreme; the value should be 141.3 (not 106.5). (Histogram with the correct outlier shown below.) 2 4 6 8 10 data 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 Frequency Calculate the sample standard deviation of the original data set with the correct outlier included ( n = 48 ). SD = Part 4 Briefly describe how an outlier affects the standard deviation of a data set. (This part of the exercise is not automatically graded by the computer.)