Exam 2: Describing Data With Numerical Measures

The range is considered the weakest measure of variability.

If the 90th and 91st observations in a set of 100 data values are 158 and 167, respectively, then the 90th percentile value is: ______________

Numerical descriptive measures computed from sample measurements are called statistics.

Which of the following randomly selected measurements, x, might be considered a potential outlier (i.e., an unusual measurement) if it was selected from the given population?

Two classes, one with 15 students and the other with 25 students, took the same test and averaged 85 points and 75 points, respectively. If the two classes were combined, the overall average score of the 40 students would be 80 points.

Assume that 75% of the households in Michigan have incomes of $24,375 or below. Given this information, it is certain that the mean household income is less than $24,375.

If the mean value of a set of data is 83.5 and the median is 72.8, then the third quartile will be at least 83.5.

You are given n = 8 measurements: 13, 11, 15, 16, 14, 14, 13, and 15. Calculate the range. ______________ Calculate the sample mean. ______________ Calculate the sample variance. ______________ Calculate the standard deviation. ______________ Compare the range and the standard deviation. The range is approximately how many standard deviations? ______________

The following data represent the scores for a sample of 10 students on a 20-point chemistry quiz: 16 14 2 8 12 12 9 10 15 13 a. Calculate the median. ______________ b. Calculate the sample mean. ______________ c. Calculate the sample variance. ______________

Data about qualitative variables can be summarized by:

For Labrador Retriever dogs, the average weight at 12 months of age is 50 pounds with a standard deviation of 2.5 pounds. What can be said about the proportion of 12 month old Labrador Retrievers that will weigh between 46.25 pounds and 53.75 pounds? Choose the appropriate rule: ______________ Approximately what proportion of weights will fall into the interval described above? ______________ Explain. ________________________________________________________

The population mean, , is used to estimate the sample mean, .

Which of the following is not a measure of variability?

Lily recently took a biochemistry test, and it was reported back to her that her score placed her at the 97^th percentile. Therefore:

Which of the following statements about the mean is not always correct?

If two data sets have the same range, the variances in both sets will be the same.

A new manufacturing plant has 20 job openings. To select the best 20 applicants from among the 1,000 job seekers, the plant's personnel office administers a written aptitude test to all applicants. The average score on the aptitude test is 150 points with a standard deviation of 10 points. Assume the distribution of test scores is approximately mound-shaped. a. What percentage of the test scores will fall between 130 and 160 points? Approximately ______________. (Enter as a decimal percent or use the % sign.) b. How many applicants will score between 130 and 160 points? At least ______________ applicants. c. One of the applicants scored 192 points on the test. What might you conclude about this test score? ____________________________

A distribution of measurements is relatively mound-shaped with mean 70 and standard deviation 10. a. What proportion of the measurements will fall between 60 and 80? ______________ b. What proportion of the measurements will fall between 50 and 90? ______________ c. What proportion of the measurements will fall between 50 and 80? ______________ d. If a measurement is chosen at random from this distribution, what is the probability that it will be greater than 80? ______________

Which measure of center is meaningful when the data are qualitative?

The following data represents the number of minutes an athlete spends training per day. 73 74 76 77 79 79 83 84 88 84 84 85 86 86 87 87 88 91 92 92 93 97 98 98 81 82 The mean and standard deviation were computed to be 85.54 and 6.97, respectively. a. What percentage of measurements would you expect to be between 71.60 and 99.48? ______________ b. What percentage of the measurements lies in the interval (71.60, 99.48)? ______________