Basic statistics

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. Also answer the given questions.

Perception of Time: Statistics students participated in an experiment to test their ability to determine when one minute (or 60 seconds) has passed. The results are given below in seconds. Identify at least one good reason why the mean from this sample might not be a good estimate of the mean for the population of adults.

53 52 75 62 68 58 49 49

Old Faithful Geyser: Listed below are intervals (in minutes) between eruptions of Old Faithful Geyser in Yellowstone National Park. After each eruption, the Nation Park Service provides an estimate of the length of time to the next eruption. Based on these values, what appears to be the best single value that could be used as an estimate of the time to the next eruption? Is that estimate likely to be accurate to within 5 minutes?

98 92 95 87 96 90 65 92 95 93 98 94

Body Temperatures: Researchers at the University of Maryland collected body temperature readings from a sample of adults, and eight of those temperatures are listed below (in degrees Fahrenheit). Does the mean of this sample equal 98.6, which is commonly believed to be the mean body temperature of adults?

98.6 98.6 98.0 98.0 99.0 98.4 98.4 98.4

Personal Income: Listed below are the amounts of personal income per capita (in dollars) for the first five states listed in alphabetical order: Alabama, Alaska, Arizona, Arkansas, and California (data from the US Bureau of Economic Analysis). When the 45 amounts from the other states are included, the mean of the 50 state amounts is $29,672.52. Is $29,672.52 the mean amount of personal income per capita for all individuals in the United States? In general, can you find the mean for some characteristic of all residents of the United States by finding the mean for each state, then finding the mean of those 50 results?

$25,128 $32,151 $26,182 $23,512 $32,996

Find the range, variance, and standard deviation for the given sample data. Also answer the given questions. Present the calculations in table form.

Perception of Time: Statistics students participated in an experiment to test their ability to determine when one minute (or 60 seconds) has passed. The results are given below in seconds. Identify at least one good reason why the mean from this sample might not be a good estimate of the mean for the population of adults.

53 52 75 62 68 58 49 49

Cereal: A dietician obtains the amounts of sugar (in centigrams) from 100 centigrams (or 1 gram) in each of 10 different cereals, including Cheerios, Corn Flakes, Fruit Loops, and 7 others. Those values are listed below. Is the standard deviation o those values likely to be a good estimate of the standard deviation of the amounts of sugar in each gram of cereal consumed by the population of all Americans who eat cereal? Why or why not?

3 24 30 47 43 7 47 13 44 39

Express all z scores with two decimal places.

Heights of Presidents: With a height of 67 in., William McKinley was the shortest president of the past century. The presidents of the past century have a mean height of 71.5 in. and a standard deviation of 2.1 in.
A.) What is the difference between McKinley's height and the mean height of presidents of the past century?
B.) How many standard deviations is that [the difference found in part (A)]?
C.) Convert McKinley's height to a z score.
D.) If we consider "usual" heights to be those that convert z scores between -2 and 2, is McKinley's height usual or unusual?

World's Tallest Woman: Sandy Allen is the world's tallest woman with a height of 91.25 in. (or 7 ft. 7.25 in.). Women have heights with a mean of 63.6 in. and a standard deviation of 2.5 in.
A.) What is the difference between Sandy Allen's height and the mean height of women?
B.) How many standard deviations is that [the difference found in part (A)]?
C.) Convert Sandy Allen's height to a z score.
D.) Does Sandy Allen's height meet the criterion of being unusual by corresponding to a z score that does not fall between -2 and 2?