Exam 3: Describing, Exploring, and Comparing Data

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. -The race speeds for the top eight cars in a 200-mile race are listed below. 181.0 180.6 189.2 182.2 175.6 180.0 177.9 181.8

Provide an appropriate response. -Which of the following statements regarding percentiles is true? (More than one statement may be true). A : In any data set, P90 is greater than P80 $B$ : In any data set, $\frac { P _ { 10 } + P _ { 90 } } { 2 }$ is equal to $Q _ { 2 }$ $C :$ In a set of 20 test scores, the percentile of the second highest score is 95

Find the midrange for the given sample data. -Listed below are the amounts of weight change (in pounds) for 12 women during their first year of work after graduating from college. Positive values correspond to women who gained weight and negative values Correspond to women who lost weight. What is the midrange? 1 -1 4 -18 8 -9 8 0 24 -10 7 7

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. -Listed below are the amounts of weight change (in pounds) for 12 women during their first year of work after graduating from college. Positive values correspond to women who gained weight and negative values Correspond to women who lost weight. 15 -5 14 8 -1 10 -6 1 0 4 -3 9

Find the variance for the given data. Round your answer to one more decimal place than the original data. - 7 7 2 5 1

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. -Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69. Men aged 20-29: 117 122 129 118 131 123 Men aged 60-69: 130 153 141 125 164 139

Solve the problem. -Construct a data set for which the range is misleading as a measure of variation. Explain why the range is misleading and suggest an alternative measure of variation.

Listed below are the amounts of weight change (in pounds) for 12 women during their first year of work after graduating from college. Positive values correspond to women who gained weight and negative values Correspond to women who lost weight. What is the mean weight change? 3 -8 3 -9 11 -9 14 0 13 -5 14 7

Use the following duration times (seconds) of 24 eruptions of the Old Faithful geyser in Yellowstone National Park. The duration times are sorted from lowest to highest. 110 120 178 213 234 234 235 237 240 243 245 245 250 250 251 252 254 255 255 259 260 266 269 273 Describe how to calculate the limits to determine outliers for this data set? Identify any outliers.

Find the standard deviation of the data summarized in the given frequency distribution. -The test scores of 40 students are summarized in the frequency distribution below. Find the standard deviation. Score Students 50-59 5 60-69 7 70-79 9 80-89 10 90-99 9

Find the mode(s) for the given sample data. -Listed below are the lengths (in inches) of each snake in the Clarmont Zoo's reptile house. 9 15 22 13 16 101 29 10 14 17 102

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

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. 22.6 16.1 36.1 36.0 23.8 20.3

Find the midrange for the given sample data. -The test scores of 40 students are summarized in the frequency distribution below. Find the mean score. Score Students 50-59 5 60-69 15 70-79 6 80-89 5 90-99 9

Determine which score corresponds to the higher relative position. -Which score has a higher relative position, a score of 60 on a test for which x = 53 and s = 10, or a score of 240.3 on a test for which x = 206 and s = 49?

The mean of a set of data is 108.06 and its standard deviation is 115.45. Find the z score for a value of 489.67.

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 body temperature of 96.7° F given that human body temperatures have a mean of 98.20° F and a standard deviation of 0.62°.

Solve the problem. -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): 110, 105, 10, 72.

Find the mode(s) for the given sample data. - 97 25 97 13 25 29 56 97

Find the percentile for the data value. -In a data set with a range of 55.4 to 105.4 and 400 observations, there are 276 observations with values less than 86. Find the percentile for 86.