Exam 3: Statistics for Describing, Exploring, and Comparing Data

Find the percentile for the data point. -The test scores of 32 students are listed below. Find P46. 32 37 41 44 46 48 53 55 56 57 59 63 65 66 68 69 70 71 74 74 75 77 78 79 80 82 83 86 89 92 95 99

Find the midrange for the given sample data. -Fred, a local mechanic, gathered the following data regarding the price, in dollars, of an oil and filter change at twelve competing service stations: 32.95 24.95 26.95 28.95 18.95 28.95 30.95 22.95 24.95 26.95 29.95 28.95 Compute the range.

Find the range for the given data. -The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m)are listed below. $0.146\quad0.119\quad0528\quad0.346\quad0.616\quad0.245$ Compute the range.

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results. -The test scores of 40 students are summarized in the frequency distribution below. Find the standard deviation. Score Students 50-59 8 60-69 6 70-79 10 80-89 5 90-99 11

Provide an appropriate response. -The Empirical Rule and Chebyshev's Theorem both relate the percent of data points to the number of standard deviations above or below the mean. What is the significant difference between the two and why do the percents for ±2 SD and ±3 SD differ so much?

Solve the problem. -Elaine gets quiz grades of 60, 69, and 68. She gets a 65 on her final exam. Find the weighted mean if the quizzes each count for 10% and the final exam counts for 70% of the final grade.

Find the mean of the data summarized in the given frequency distribution. -The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. Speed (mph) Cars 30-39 3 40-49 17 50-59 51 60-69 16 70-79 13

Solve the problem. -The race speeds for the top eight cars in a 200-mile race are listed below. Use the range rule of thumb to find the standard deviation. Round results to the nearest tenth. $187.5\quad185.7\quad189.2\quad186.7\quad175.6\quad188.3\quad179.7\quad185.4$

Find the mean, median, mode, and midrange for each of the two samples, then compare the two sets of results. -A comparison is made between summer electric bills of those who have central air and those who have window units. May June July Aug Sept Central \ 32 \ 64 \ 80 \ 90 \ 65 Window \ 15 \ 84 \ 99 \ 120 \ 40

Find the range for the given data. -Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter, he got the following scores: 27 34 13 49 51 Compute the range.

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. -When investigating times required for drive-through service, the following results (in seconds)were obtained. Restaurant A 120 67 89 97 124 68 72 96 Restaurant B 115 126 49 56 98 76 78 95

Solve the problem. -If the standard deviation of a set of data is zero, what can you conclude about the set of values?

Find the midrange for the given sample data. -Compute the variance. To get the best deal on a microwave oven, Jeremy called six appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $\$ 476\quad \$ 477 \quad\$ 645 \quad\$ 334 \quad\$ 667 \quad\$ 237$

In a data set containing n values, the 67th percentile can be found as follows: $\mathrm { P } _ { 67 } = \frac { 67 } { 100 } \cdot \mathrm { n }$

Provide an appropriate response. -Without calculating the standard deviation, compare the standard deviation for the following three data sets. (Note: All data sets have a mean of 30.)Which do you expect to have the largest standard deviation and which do you expect to have the smallest standard deviation? Explain your answers in terms of the formula s= 30,30,30,30,30,30,30,30,30,30 20,25,25,30,30,30,30,35,35,40 20,20,20,25,25,35,35,40,40,40

Find the midrange for the given sample data. -Compute the variance. The owner of a small manufacturing plant employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below: 30 26 67 24 41 57

Determine which score corresponds to the higher relative position. -Data set: $6\quad3\quad21\quad15\quad6\quad15\quad30\quad27\quad33\quad9\quad3\quad30\quad18\quad3\quad30 \text {; }$ data point 21

Solve the problem. Round results to the nearest hundredth. -The mean of a set of data is 3.77 and its standard deviation is 3.39. Find the z score for a value of 6.19.

Find the mode(s)for the given sample data. - 1.4 2.6 3.1 1.0 1.3 3.5 1.9 3.4 2.1 2.7 1.9

Solve the problem. -The data set below consists of the scores of 15 students on a quiz. For this data set, which measure of variation do you think is more appropriate, the range or the standard deviation? Explain your thinking. 90 90 91 91 89 90 89 91 91 90 60 90 89 90 91