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

The coefficient of variation, expressed as a percent, is used to describe the standard deviation relative to the mean. It allows us to compare variability of data sets with different measurement units and is calculated as follows: $\text { coefficient of variation } = 100 ( \mathrm {~s} / \overline { \mathrm { x } } )$ Find the coefficient of variation for the following sample of weights (in pounds): 138 134 186 105 197 136 172 152 116 125

Find the variance for the given data. Round your answer to one more decimal place than the original 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: 61 33 18 51 56 18 A) $15.0 \mathrm { mi } ^ { 2 }$ B) $17.9 \mathrm { mi } ^ { 2 }$ C) $10,914.2 \mathrm { mi } ^ { 2 }$ D) $366.7 \mathrm { mi } ^ { 2 }$

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. -The maximum value of a distribution is 42.7 and the minimum value is 2.3.

Use the empirical rule to solve the problem. -At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.5 and 3.7?

The weights (in pounds) of 30 newborn babies are listed below. Find $Q _ { 1 }$ . 5.5 5.7 5.8 6.0 6.1 6.1 6.3 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 variance for the given data. Round your answer to one more decimal place than the original 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: \ 425 \ 332 \ 453 \ 353 \ 260 \ 366 A) $4720.6$ dollars $^ { 2 }$ B) $3933.8$ dollars $^ { 2 }$ C) $798,264.4$ dollars ² D) $4720.5$ dollars ²

Scores on a test have a mean of 74 and a standard deviation of 12. Michelle has a score of 50. Convert Michelle's score to a z-score.

The mean of a set of data is -1.82 and its standard deviation is 3.91. Find the z score for a value of 4.51.

Find the median for the given sample data. -The distances (in miles) driven in the past week by each of a company's sales representatives are listed below. 29 99 246 270 379 389 Find the median distance driven.

Find the median for the given sample data. -The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a fifteen-minute period. 22 24 22 25 25 22 27 24 32 28 28 26 21 28 22 17 12 24 24 24

Find the mean of the data summarized in the given frequency distribution. -The test scores of 40 students are summarized in the frequency distribution below. Find the mean score. Score Students 50-59 6 60-69 5 70-79 6 80-89 11 90-99 12

Find the number of standard deviations from the mean. Round your answer to two decimal places. -The test scores on the Chapter 3 mathematics test have a mean of 62 and a standard deviation of 11. Andrea scored 86 on the test. How many standard deviations from the mean is that?

Use the empirical rule to solve the problem. -The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg?

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. -A distribution of data has a maximum value of 60, a median value of 53, and a minimum of 46.

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?

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. -The following is a set of data showing the water temperature in a heated tub at different time intervals. 113.9 114.0 116.4 115.0 116.0 115.6 112.7 115.5

The quadratic mean (or root mean square) is usually used in physical applications. In power distribution systems, for example, voltages and currents are usually referred to in terms of their root mean square value. The quadratic mean of a set of values is obtained by squaring each value, adding the results, dividing by the number of values (n), and then taking the square root of that Result, expressed as $\text { quadratic mean } = \sqrt { \frac { \sum x ^ { 2 } } { n } }$ Find the root mean square of these power supplies (in volts): 56, 53, 22, 20.

Find the midrange for the given sample data. - 1.6 2.4 3.2 1.0 1.2 3.7 1.9 3.3 2.2 2.6 1.9

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 14.5 seconds at a school where the mean time for the 100 meter sprint is 17.6 seconds and the standard deviation is 2.1 seconds.

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. - 24.4 11.8 38.9 29.7 11.2 14.6