5.4.2 Standard Deviation and Variance

Which of the following lists of data has the largest standard deviation? -22, 25, 25, 22, 25, 23, 24, 23, 26, 24 -13, 11, 11, 11, 10, 14, 14, 10, 11, 11 -16, 14, 15, 15, 16, 16, 15, 16, 18, 14 -25, 23, 25, 22, 21, 25, 22, 21, 25, 23 -7, 14, 19, 18, 4, 16, 5, 11, 11, 12

7, 14, 19, 18, 4, 16, 5, 11, 11, 12

Which of the following lists of data has the smallest standard deviation? -30, 21, 19, 17, 16, 32, 26, 25, 19, 16 -5, 11, 15, 7, 5, 9, 8, 16, 14, 11 -25, 24, 28, 18, 32, 34, 34, 22, 28, 19 -17, 19, 17, 18, 17, 16, 16, 16, 17, 20 -9, 16, 14, 22, 20, 9, 19, 16, 21, 8

17, 19, 17, 18, 17, 16, 16, 16, 17, 20 Remember that standard deviation is a measure of how spread out the values are. The list 17, 19, 17, 18, 17, 16, 16, 16, 17, 20 has the smallest standard deviation because its values are all relatively close together.

The results from the final exam for these three classes are shown below: Algebra class: Mean Final Exam score of 85.2, standard deviation of 3.9 Statistics class: Mean Final Exam score of 81.7, standard deviation of 5.3 Calculus class: Mean Final Exam score of 84.3, standard deviation of 1.8 Based on these results, which class had most consistent scores on the final exam and which class had the greatest variation in scores on the final exam. -Algebra class had the most consistent scores,Calculus class had the greatest variation in scores. -Calculus class had the most consistent scores,Statistics class had the greatest variation in scores. -Statistics class had the most consistent scores,Calculus class had the greatest variation in scores.

Calculus class had the most consistent scores,Statistics class had the greatest variation in scores.

Suppose that you are conducting a survey on how many pets each employee has in his or her household. The mean number of pets is 4 per household, and the standard deviation is 2. Rob only owns cats, and he has 10 of them. Which of the following statements is true? -Rob's number of pets is 3 standard deviations to the left of the mean. -Rob's number of pets is 3 standard deviations to -the right of the mean. -Rob's number of pets is 6 standard deviations to the left of the mean. -Rob's number of pets is 6 standard deviations to the right of the mean.

Rob's number of pets is 3 standard deviations to the right of the mean.

The College Board analyzed SAT scores in 2015. Math scores for the group who planned to apply for financial aid and the group who did not plan to apply for financial aid were both analyzed. Test-takers who planned to apply for financial aid had a mean score of 507 and a standard deviation of 113. Test-takers who did not plan to apply for financial aid had a mean score of 556 and a standard deviation of 118. Which group had a more consistent set of scores? -Test-takers who planned to apply for financial aid had scores with a smaller mean, so this group had more consistent scores. -Test-takers who planned to apply for financial aid had scores with a smaller standard deviation, so this group had more consistent scores. -Test-takers who did not plan to apply for financial aid had scores with a larger mean, so this group had more consistent scores. -Test-takers who did not plan to apply for financial aid had scores with a larger standard deviation, so this group had more consistent scores.

Test-takers who planned to apply for financial aid had scores with a smaller standard deviation, so this group had more consistent scores.; The smaller standard deviation represents the more consistent data set. These data values are less spread out than data sets with greater standard deviations.