Chapter 3

Gas prices in a metropolitan area range from $2.75 to $3.18, with an average of $2.93. Use the range rule of thumb to estimate the standard deviation.

$0.108

Following are the closing prices (in dollars) of a certain stock for the past 20 trading days. Find the population standard deviation for the closing prices. 134.50 132.05 146.49......

$9.14

A consumer advocacy group tested the "on-air" lifetimes a random sample of 120 cell phone batteries. The mean lifetime was 3.2 hours with a standard deviation of 0.1 hours. The lifetimes are approximately bell-shaped. Estimate the number of batteries with lifetimes between 3.0 hours and 3.4 hours.

114

Given that the mean of a set of data is 25 and the standard deviation is 3, what is the coefficient of variation?

12%

Use the boxplot to identify the maximum value, minimum value, median, first quartile, third quartile, and interquartile range.

12, 7, 9, 8, 11, 4

Indicate which student has the higher z score.

The theater major has a higher score than the art major.

​​​Class Frequency ​0 - 4 13​ ​5 - 9 11​​ 10 - 14 17 ​​15 - 19 15​ ​20 - 24 12​

12.6

For the data set below, find the outlier(s). 178 123 171 163 147 201 196 166 170 171 177

123 and 201

If the mean of five values is 8.8 and four of the values are 6, 7, 6, and 12, find the fifth value.

13

What is the midrange of the following data set? 7, 13, 12, 14, 6, 14, 20, 20, 20

13

A student received the following grades last semester. Find the student's semester grade point average. A/4.0 F/0.0 B/3.0 B/3.0 D/1.0

2.13

Find the median for the following data set: 29​ 22 ​16 ​26 ​16

22

For the data set below, find the upper outlier boundary. 160 176 193 144 163 146 152 158 154 184 129

221

Find the median for the following data set: 27​ 33 ​18 ​32 ​21 ​14

24

For the data set below, find the 15th percentile. 64 95 74 70 32 58 24 46 25 17 59 51 7 60 36 67 67 54 33 60

24.5

The number of incidents in which police were needed for a sample of 9 schools in Allegheny County is 8, 39, 6, 12, 45, 16, 3, 0, 15. Find the first and third quartiles for the data.

27.5

The following table presents the heights (in inches) of a sample of college basketball players. Frequency 2 5 2 5 3 Considering the data to be a population, approximate the variance of the heights.

28.0

The average weekly earnings in dollars for various industries are listed below. Find the percentile rank of 634. 737, 634, 569, 671, 597, 701, 766, 542, 788, 819

35th

The following data represent the total price, in dollars, of 20 randomly-selected gasoline purchases at a certain convenience store. 26.25 27.89 39.21 41.08 41.27.....

39.95

Given the following data set, find the approximate value that corresponds to the 75th percentile. 10, 44, 15, 23, 14, 18, 72, 56

50

Use the boxplot to identify the maximum value, minimum value, median, first quartile, third quartile, and interquartile range.

500, 350, 450, 400, 475, 75

Find the population variance for the following data set: 16​ 21 ​30 ​27 ​37

52.6

Find the population variance for the following data set: 16 ​21 ​30 ​27 ​37

52.6

Find the sample variance for the following data set: 15 22 29 28 35

57.7

Find the sample standard deviation for the following data set: 23 27 12 17 16

6

Following are heights, in inches, for a sample of college basketball players. 83 82 71 88 80 88 72 81 70 72 82 73 73 74 87 82 85 84 76 86 Find the sample standard deviation for the heights of the basketball players.

6.2

For the data set below, find the first quartile. 62 65 75 72 68 63 65 67 78 70 74

65

A student has an average of 78 on seven chapter tests. If the student's scores on six of the tests are 76, 74, 76, 80, 83, and 91, what was the score on the remaining test?

66

A paint manufacturer discovers that the mean volume of paint in a gallon-sized pail is 1 gallon with a standard deviation of 0.1 gallons. The paint volumes are approximately bell-shaped. Estimate the percent of pails with volumes between 0.90 gallons and 1.10 gallons.

68%

Assuming the population is bell-shaped, between what two values will approximately 68% of the population be?

69 to 85

For the data set below, list the outliers, if any. 38 42 44 38 45......

7 and 92

Approximate the sample standard deviation given the following frequency distribution. Class Freq 0-4 17 5-9 16 10-14 9 15-19 18 20-24 17

7.5

Check the following data set for outliers. 73, 82, 84, 84, 86, 87, 89, 91

73 is an outlier

Find the weighted mean for a particular student's scores on three exams if the first one was worth 75 points and the student received a score of 70% , the second was worth 50 points and the student received a score of 80% , and the third was worth 30 points and the student received a score of 95%?

78.1

The costs per load (in cents) of 26 dishwashing detergents tested by a consumer organization are shown here. Find the standard deviation of the sample.

8.5

The average age of Stokes County school board members over the last 40 years has been 51, but members have ranged from 32 to 67. Use the range rule of thumb to estimate the standard deviation of the members' ages.

8.8

Following are heights, in inches, for a sample of college basketball players. 84 78 78 84 80 81 78 79 79 78 78 79 79 77 7782 84 82 82 83 Find the mean height of the basketball players.

80.1 in

If a data set has 25 values and a standard deviation 9.4, then the variance is _________

88.4

A soft-drink bottling company fills and ships soda in plastic bottles with a target volume of 354 milliliters. The filling machinery does not deliver a perfectly consistent volume of liquid to each bottle, and the three quartiles for the fill volume are and q3=357 find the IQR

9

Which of the following is the properly rounded mean for the given data? 7, 8, 13, 9, 10, 11

9.7

Use the boxplot to identify the maximum value, minimum value, median, first quartile, third quartile, and interquartile range.

95, 65, 80, 70, 90, 20

If a distribution is negatively skewed as shown in the figure below, the mean will fall to the right of the median and the mode will fall to the left of the median.

false

Assuming the population is bell-shaped, approximately what percentage of the population values are between 29 and 89?

almost all (greater than 95%)

For a set of data with a mean of 24 and a variance of 36, approximately of the values will fall between 18 to 30.

true

A data set has a mean of 162 and a standard deviation of 11. Compute the coefficient of variation.

0.07

Given that the variance for a data set is , what is the standard deviation?

1.10

Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of a bluefish is 276 millimeters with a standard deviation of 60mm. For pompano, the mean is 127mm with a standard deviation of 3. Stewart caught a bluefish that was long. What was the z-score for this length?

1.33

A population has a mean mew=53 and standard deviation 14. Find the z-score for a population value of 29.

1.7

For the data set below, find the IQR. 70 63 73 65 61 62 74 63 74 68 78

11

The average resident of Metro City produces 630 pounds of solid waste each year, and the standard deviation is approximately 70 pounds. Use Chebyshev's theorem to find the weight range that contains at least of all residents' annual garbage weights.

Between 490 and 770 lbs

Which score indicates the highest relative position? I. A score of 2.6 on a test with = 5.0 and s = 1.6 II. A score of 650 on a test with = 800 and s = 200 III. A score of 48 on a test with = 57 and s = 6

II

The number of incidents in which police were needed for a sample of 9 schools in Allegheny County is 8, 39, 6, 12, 45, 16, 3, 0, 15. Find the first and third quartiles for the data.

Q1 = 6; Q3 = 16

A_______ is the midpoint in a data array.

median

For the data shown in the histogram, which of the following choices best describes the relationship between the median and the mean?

median < mean

A data set contains three unique values. Which of the following must be true?

none of these

____________are either extremely high or extremely low data values compared with the rest of the data.

outliers

A report states that the mean household income last year for a certain rural county was $44,100 and the median was $35,300. If a histogram were constructed for the incomes of all households in the county, would you expect it to be skewed to the right, to the left, or approximately symmetric?

skewed right

Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of a bluefish is 282 millimeters with a standard deviation of For pompano, the mean is with a standard deviation of 31mm Stewart caught a bluefish that was long, and Gina caught a pompano that was long. Who caught the longer fish, relative to fish of the same species?

stewart

Given the following boxplot where m is the median value, what statement could be made about the distribution of the data?

the distribution is approximately symmetric

A distribution in which approximately of the data values fall within one standard deviation of the mean behaves according to

the empirical rule

In a unimodal, symmetrical distribution as shown in the figure below,

the mean, the median, and the mode are the same.