Exercise Set 1.3:
Standard Deviation and Variance
Math 2311
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Section 1.3 Exercises
1. From section 1.2, exercise 1: Twelve babies spoke for the first time at the following ages (in months): 8 9 10 11 12 13 15 15 18 20 20 26 The mean age (in months) was found to be 14.75. If this is population data, find the variance and standard deviation. 2. Suppose the data given in exercise 1 is a sample of ages taken from a larger population. Find the variance and standard deviation of the sample. 3. A survey was conducted to gather ratings of the quality of service at local restaurants. Respondents rated on a scale of 0 (terrible) to 100 (excellent). The data are given below. Find the mean, variance and standard deviation of the sample. 32, 34, 40,43, 44, 47, 48, 50, 54, 58, 63, 80, 85, 92 4. A sample of 15 adults who live in a large urban area were asked to indicate the number of parking tickets that each had received over the last 5 years.The data are given below. Find the mean, variance and standard deviation of the sample. 3, 0, 1, 2, 2, 6, 1, 3, 0, 1, 0, 2, 2, 5, 4 5. Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores? 6. Give an example of a data set with 5 values for which the standard deviation is zero. 7. A researcher wants to see if birds that build larger nests lay larger eggs. He selects two random samples of nests: one of small nests and the other of large nests. He weighs one egg from each nest. The data are summarized below. What can be said about the variability of each group? Small nests Large nests Sample size 60 159 Sample mean (g) 37.2 35.6 Sample variance 24.7 39.0