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MAT 181- Chapter: 3 Practice Problems-Measures of Center and Variation

Name___________________________________ Date:________________

Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values.

1) Andrew asked seven of his friends how many cousins they had. The results are listed below. Find the mean number of cousins.

18 12 7 13 7 2 7

Find the median for the given sample data.

2) A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.

80 39 214 152 264 239 232

Find the median number of newspapers sold.

Find the midrange for the given sample data.

3) 49 52 52 52 74 67 55 55

Find the mean of the data summarized in the given frequency distribution.

4) The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed.

Speed (mph)	# of Cars (f)	Midpoint (x)	(f*x)
30-39	4
40-49	19
50-59	50
60-69	15
70-79	12

Solve the problem.

5) Michael gets test grades of 73, 77, 82, and 86. He gets a 93 on her final exam. Find the weighted mean if the tests each count for 15% and the final exam counts for 40% of the final grade. Round to one decimal place.

Grades	Percentage (%)

Find the standard deviation and variance for the given data. Round your answer to one more decimal place than the original data.

6) 18 20 18 2 7

x	(x-xbar)	(x-xbar)^2

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth.

7) The heights in feet of people who work in an office are as follows.

5.8 6.1 5.9 5.4 5.6 5.8 5.9 6.2 6.1 5.8

Use the empirical rule to solve the problem.

8) At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.3 and 3.5?

Solve the problem.

9) 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:

Coefficient of variation = 100 (s/ )

Find the coefficient of variation for the following sample of weights (in pounds):

130 127 186 105 197

153 172 150 116 125

Solve the problem. Round results to the nearest hundredth.

10) The mean of a set of data is 5.73 and its standard deviation is 3.44. Find the z- score for a value of 13.87.

Find the number of standard deviations from the mean. Round your answer to two decimal places.

11) The annual snowfall in a town has a mean of 38 inches and a standard deviation of 10 inches. Last year there were 63 inches of snow. How many standard deviations from the mean is that?

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.

12) A body temperature of 99.5° F given that human body temperatures have a mean of 98.20° F and a standard deviation of 0.62°.

Determine which score corresponds to the higher relative position.

13) Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150?

Find the percentile for the data value.

14) Data set: 55 38 30 66 67 68 44;

Data value: 55

Find the indicated measure.

15) Use the given sample data to find.

49 52 52 52 74 67 55 55

Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.

16) The test scores of 32 students are listed below. Construct a boxplot for the data set.

32 37 41 44 46 48 53 55

57 57 59 63 65 66 68 69

70 71 74 74 75 77 78 79

81 82 83 86 89 92 95 99