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

Use the empirical rule to solve the problem. -The amount of Jen's monthly phone bill is normally distributed with a mean of $78 and a standard deviation of $9. What percentage of her phone bills are between $51 and $105?

Find the range for the given data. -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: 2.6 5.4 1.6 4.9 6.7 3.8 Compute the range.

Solve the problem. -The 10% trimmed mean of a data set is found by arranging the data in order, deleting the bottom 10% of the values and the top 10% of the values and then calculating the mean of the remaining values. What advantages do you think that the trimmed mean has as compared to the mean?

Provide an appropriate response. -Describe any similarities or differences in the two distributions represented by the following boxplots. Assume the two boxplots have the same scale.

Find the standard deviation of the data summarized in the given frequency distribution. -A weight of 220 pounds among a population having a mean weight of 161 pounds and a standard deviation of 23.5 pounds.

Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. -A time for the 100 meter sprint of 20.0 seconds at a school where the mean time for the 100 meter sprint is 17.7 seconds and the standard deviation is 2.1 seconds.

Which of the following statements regarding percentiles is true? (More than one statement may be true). A : In any data set, $\mathrm { P } _ { 90 }$ is greater than $\mathrm { P } _ { 80 }$ B: In any data set, $\frac { \mathrm { P } _ { 10 } + \mathrm { P } _ { 90 } } { 2 }$ is equal to $\mathrm { Q } _ { 2 }$ C: In a set of 20 test scores, the percentile of the second highest score is 95

Find the midrange for the given sample data. -18, 17, 1, 18, and 4

Find the percentile for the data point. -The weights (in pounds) of 30 newborn babies are listed below. Find $\mathrm { P } _ { 16 }$ . 5.5 5.7 5.8 5.9 6.1 6.1 6.4 6.4 6.5 6.6 6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2 7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7

Find the median for the given sample data. -The weights (in ounces)of 14 different apples are shown below. 5.5 4.2 6.9 4.6 4.5 5.5 4.2 5.0 6.2 4.6 5.5 5.0 4.6 4.7

Provide an appropriate response. -The test scores of 32 students are listed below. Construct a boxplot for the data set. 57 57 59 63 65 66 68 69 70 71 74 74 75 77 78 79 81 82 83 86 89 92 95 99

Provide an appropriate response. -We want to compare two different groups of students, students taking Composition 1 in a traditional lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation?

Find the range for the given data. -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: $\$ 111 \quad \$ 552 \quad \$ 158 \quad \$ 668 \quad\$ 355 \quad\$ 312$ Compute the range.

Determine which score corresponds to the higher relative position. -In a data set with a range of 66.5 to 121.4 and 200 observations, there are 138 data points with values less than 87.7. Find the percentile for 87.7.

Find the range for the given data. -A class of sixth grade students kept accurate records on the amount of time they spent playing video games during a one-week period. The times (in hours)are listed below: 25.5 11.7 9.2 26.2 11.1 29.2 17.3 23.8 14.5 22.9 Compute the range.

Find the standard deviation of the data summarized in the given frequency distribution. -A test score of 54.0 on a test having a mean of 73 and a standard deviation of 10.

Suppose that all the values in a data set are converted to z-scores. Which of the statements below is true? A: The mean of the z-scores will be zero, and the standard deviation of the z-scores will be the same as the standard deviation of the original data values. B: The mean and standard deviation of the z-scores will be the same as the mean and standard deviation of the original data values. C: The mean of the z-scores will be 0, and the standard deviation of the z-scores will be 1. D: The mean and the standard deviation of the z-scores will both be zero.

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results. -When investigating times required for drive-through service, the following results (in seconds)were obtained. Restaurant A 120 123 153 128 124 118 154 110 Restaurant B 115 126 147 156 118 110 145 137

Solve the problem. -The ages of the members of a gym have a mean of 47 years and a standard deviation of 10 years. What can you conclude from Chebyshev's theorem about the percentage of gym members aged between 32 and 62?

Solve the problem. Round results to the nearest hundredth. -Scores on a test have a mean of 71 and a standard deviation of 9. Michelle has a score of 89. Convert Michelle's score to a z-score.