BackGraphical Analysis In Exercises 21–24, you are asked to compare three data sets.
(c) Estimate the sample standard deviations. Then determine how close each of your estimates is by finding the sample standard deviations.
i.
ii.
iii.
Find the standard deviation of the sample below. Round your answer to the nearest tenth.
In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.
Super Bowl Jersey Numbers Listed below are the jersey numbers of the 11 offensive players on the starting roster of the New England Patriots when they won Super Bowl LIII. What do the results tell us?
12 26 46 15 11 87 77 62 60 69 61
In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.
Super Bowl Ages Listed below are the ages of the same 11 players used in the preceding exercise. How are the resulting statistics fundamentally different from those found in the preceding exercise?
41 24 30 31 32 29 25 26 26 25 30
Identifying Significant Values with the Range Rule of Thumb. In Exercises 33–36, use the range rule of thumb to identify the limits separating values that are significantly low or significantly high.
U.S. Presidents Based on Data Set 22 “Presidents” in Appendix B, at the time of their first inauguration, presidents have a mean age of 55.2 years and a standard deviation of 6.9 years. Is the minimum required 35-year age for a president significantly low?
Estimating Standard Deviation with the Range Rule of Thumb. In Exercises 29–32, refer to the data in the indicated exercise. After finding the range of the data, use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the standard deviation computed using all of the data.
Audiometry Use the hearing measurements from Data Set 7 “Audiometry.” Does it appear that the amounts of variation are different for the right threshold measurements and the left threshold measurements?
In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.
Jaws 3 Listed below are the number of unprovoked shark attacks worldwide for the last several years. What extremely important characteristic of the data is not considered when finding the measures of variation?
70 54 68 82 79 83 76 73 98 81
In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.
Smart Thermostats Listed below are selling prices (dollars) of smart thermostats tested by Consumer Reports magazine. Are any of the resulting statistics helpful in selecting a smart thermostat for purchase?
250 170 225 100 250 250 130 200 150 250 170 200 180 250
In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.
California Smokers In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of California adults?
[IMAGE]
In Exercises 21–24, find the coefficient of variation for each of the two samples; then compare the variation. (The same data were used in Section 3-1.)
Pulse Rates Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 “Body Data” in Appendix B). Does there appear to be a difference?
[IMAGE]
Large Data Sets from Appendix B. In Exercises 25–28, refer to the indicated data set in Appendix B. Use software or a calculator to find the range, variance, and standard deviation. Express answers using appropriate units, such as “minutes.”
Earthquakes Use the magnitudes (Richter scale) of the 600 earthquakes listed in Data Set 24 “Earthquakes” in Appendix B. In 1989, the San Francisco Bay Area was struck with an earthquake that measured 7.0 on the Richter scale. If we add that value of 7.0 to those listed in the data set, do the measures of variation change much?
Comparing Values. In Exercises 13–16, use z scores to compare the given values.
Tallest and Shortest Men The tallest adult male was Robert Wadlow, and his height was 272 cm. The shortest adult male was Chandra Bahadur Dangi, and his height was 54.6 cm. Heights of men have a mean of 174.12 cm and a standard deviation of 7.10 cm. Which of these two men has the height that is more extreme?
Significant Values. In Exercises 9–12, use the range rule of thumb to identify (a) the values that are significantly low, (b) the values that are significantly high, and (c) the values that are neither significantly low nor significantly high.
IQ Scores The Wechsler test is used to measure intelligence of adults aged 16 to 80. The mean test score is 100 and the standard deviation is 15.
Percentiles. In Exercises 17–20, use the following radiation levels (in W/kg) for 50 different cell phones. Find the percentile corresponding to the given radiation level.
0.48 W/kg
Percentiles. In Exercises 17–20, use the following radiation levels (in W/kg) for 50 different cell phones. Find the percentile corresponding to the given radiation level.
1.47 W/kg