Deck 3: Statistics for Describing, Exploring, and Comparing Data

Question 1

Provide an appropriate response.
The Empirical Rule and Chebyshev's Theorem both relate the percent of data points to the number of standard deviations above or below the mean. What is the significant difference between the two and why do the percents for ±2 SD and ±3 SD differ so much?

Answer 1

Answers will vary.

Question 2

Provide an appropriate response.

-The mean of a data set is always/sometimes/never (select one)one of the data points in a set of data. Explain your answer with brief examples.

Answer 2

The mean of a data set is sometimes one of the data points in a set of data.The mean, or average, of a data set is calculated by summing all the data points and then dividing by the number of data points. It represents the central value of the data set. The mean does not necessarily have to be one of the actual data points—it can be a value that doesn't appear in the data set at all. However, in some cases, the mean can indeed be one of the data points.
Here are two examples to illustrate this:
1. Example where the mean is not one of the data points:
Consider the data set {1, 2, 3, 4, 6}. The mean is calculated as (1 + 2 + 3 + 4 + 6) / 5 = 16 / 5 = 3.2. In this case, the mean (3.2) is not one of the data points in the set.
2. Example where the mean is one of the data points:
Consider the data set {2, 3, 4, 5, 6}. The mean is calculated as (2 + 3 + 4 + 5 + 6) / 5 = 20 / 5 = 4. In this case, the mean (4) is one of the data points in the set.
Therefore, the mean can sometimes be one of the data points, but it is not always the case.

Question 3

Provide an appropriate response.
We want to compare two different groups of students, students taking Composition 1 in a traditional lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation?

Answer 3

Answers will vary.

Question 4

Find the mean for the given sample data.

-Frank's Furniture employees earned the following amounts last week: $$\begin{array} { l l l l l } \$ 453.83 & \$ 529.91 & \$ 439.27 & \$ 309.23 & \$ 453.86 \\\$ 533.25 & \$ 457.25 & \$ 156.42 & \$ 152.64 &\end{array}$$ What was the mean amount earned by an employee last week? Round your answer to the nearest cent.

A)$387.30
B)$435.71
C)$497.95
D)$380.63

Question 5

Answer the question.

-The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a fifteen-minute period. $\begin{array} { l } 30&32&30&33\\33&30&35&32\\40&36&36&34\\29&36&30&25\\20&32&32&32\end{array}$

A)32
B)31.85
C)33
D)36

Question 6

Answer the question.

-The distances traveled (in miles)to 7 different swim meets are given below: $$15,30,30,44,60,70,79$$ Find the median distance traveled.

A)60 miles
B)30 miles
C)47 miles
D)44 miles

Question 7

Provide an appropriate response.
A company advertises an average of 42,000 miles for one of its new tires. In the manufacturing process there is some variation around that average. Would the company want a process that provides a large or a small variance? Justify your answer.

Question 8

Answer the question.
A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below. 78, 43, 228, 194, 259, 236, 235 Find the median number of newspapers sold.

A)194 newspapers
B)228 newspapers
C)182 newspapers
D)235 newspapers

Question 9

Answer the question.

-The weights (in ounces)of 21 cookies are shown. Find the median weight. $$\begin{array} { l l l l l l l } 0.67 & 1.42 & 0.83 & 1.62 & 0.75 & 0.82 & 1.03 \\1.42 & 1.53 & 0.93 & 0.67 & 1.21 & 1.04 & 0.83 \\0.47 & 1.21 & 0.82 & 1.04 & 1.72 & 0.75 & 0.56\end{array}$$

A)1.42 ounces
B)0.93 ounces
C)0.83 ounces
D)0.88 ounces

Question 10

Find the mean for the given sample data.

-Six college buddies bought each other Christmas gifts. They spent: $$\begin{array} { l l l } \$ 122.34 & \$ 233.13 & \$ 222.32 \\\$ 130.44 & \$ 165.25 & \$ 197.41\end{array}$$ What was the mean amount spent? Round your answer to the nearest cent.

A)$178.48
B)$267.72
C)$202.18
D)$214.18

Question 11

Provide an appropriate response.
Without calculating the standard deviation, compare the standard deviation for the following three data sets. (Note: All data sets have a mean of 30.)Which do you expect to have the largest standard deviation and which do you expect to have the smallest standard deviation? Explain your answers in terms of the formula

Question 12

Provide an appropriate response.
Explain how two data sets could have equal means and modes but still differ greatly. Give an example with two data sets to illustrate.

Question 13

Provide an appropriate response.
The two most frequently used measures of central tendency are the mean and the median. Compare these two measures for the following characteristics: Takes every score into account? Affected by extreme scores? Advantages.

Question 14

Find the median for the given sample data.
-20, -27, -46, -27, -49, -27, -49

A)-27
B)-46
C)-35
D)-49

Question 15

Provide an appropriate response.
Marla scored 85% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 85 percentile in mathematics. Explain the difference in these two scores.

Question 16

Find the mean for the given sample data.

-The local Tupperware dealers earned these commissions last month: $\$ 4302.51\quad\$ 1814.26\quad\$ 2783.74\quad\$ 3967.53$
$\$ 3942.30 \quad \$ 4788.74 \quad \$ 2593.47$
$\$ 4184.57 \quad \$ 3071.59 \quad \$ 3949.90$
What was the mean commission earned? Round your answer to the nearest cent.

A)$3933.18
B)$4424.83
C)$3539.86
D)$3533.86

Question 17

Find the median for the given sample data.

-The normal monthly precipitation (in inches)for August is listed for 20 different U.S. cities. Find the median of the data. $\begin{array} { l l l l l } 3.5 & 1.6 & 2.4 & 3.7 & 4.1 \end{array}$
$\begin{array} { l l l l l } 3.9 & 1.0 & 3.6 & 4.2 & 3.4 \end{array}$
$\begin{array} { l l l l l } 3.7 & 2.2 & 1.5 & 4.2 & 3.4 \end{array}$
$\begin{array} { l l l l l } 2.7 & 0.4 & 3.7 & 2.0 & 3.6 \end{array}$

A)3.50 in.
B)3.45 in.
C)3.40 in.
D)2.94 in.

Question 18

Answer the question.

-The normal monthly precipitation (in inches)for August is listed for 20 different U.S. cities. Find the mean of the data. $\begin{array} { l l l l l } 3.5 & 1.6 & 2.4 & 3.7 & 4.1 \end{array}$
$\begin{array} { l l l l l } 3.9 & 1.0 & 3.6 & 4.2 & 3.4 \end{array}$
$\begin{array} { l l l l l } 3.7 & 2.2 & 1.5 & 4.2 & 3.4 \end{array}$
$\begin{array} { l l l l l } 2.7 & 0.4 & 3.7 & 2.0 & 3.6 \end{array}$

A)2.94 in.
B)3.09 in.
C)3.27 in.
D)2.80 in.

Question 19

Provide an appropriate response.
Describe how to find the percentile for a given score in a set of data. How does this process relate to the definition of a percentile score?

Question 20

Find the mean for the given sample data.

-Bill kept track of the number of hours he spent exercising each week. The results for four months are shown below. Find the mean number of hours Bill spent exercising per week. Round your answer to two decimal places. $$\begin{array} { l l l l l l } 6.90 & 6.60 & 6.70 & 6.90 & 7.20 & 6.90 \\7.40 & 6.70 & 8.10 & 6.90 & 6.90 & 6.70 \\8.80 & 6.60 & 6.60 & 7.70 & 7.20 & 7.40\end{array}$$

A)7.33
B)7.12
C)6.75
D)7.54

Question 21

Find the median for the given sample data.
7.22, 7.41, 7.56, 7.22, 7.88, 7.99, 7.62

A)7.41
B)7.557
C)7.22
D)7.56

Question 22

Find the mode(s)for the given sample data.

-The speeds (in mi/h)of the cars passing a certain checkpoint are measured by radar. The results are shown below. $$\begin{array} { l l l l l } 42.8&41.8&40.1&43.5&43.7\\43.7&41.8&44.3&42.3&43.5\\42.8&44.3&43.5&44.9&41.8\\41.8&41.8&40.1&44.0&42.8\end{array}$$

A)42.8, 43.5, 41.8
B)42.8
C)41.8
D)42.70

Question 23

Find the mode(s)for the given sample data.

- $$\begin{array} { l l l l l l } 49 & 52 & 52 & 74 & 67 & 55\end{array}$$

A)61.5
B)25
C)12.5
D)53.5

Question 24

Find the mode(s)for the given sample data.

-The weights (in ounces)of 18 cookies are shown. Find the midrange. $\begin{array} { l l l l l l } 0.63 & 1.28 & 0.87 & 0.99 & 0.81 & 1.43 \end{array}$
$\begin{array} { l l l l l l } 1.28 & 1.20 & 0.63 & 1.45 & 1.37 & 1.08 \end{array}$
$\begin{array} { l l l l l l } 1.37 & 1.45 & 0.81 & 1.37 & 0.99 & 0.87 \end{array}$

A)1.040
B)1.030
C)1.130
D)1.08

Question 25

Find the mode(s)for the given sample data.

- $$\begin{array} { l l l l l l l l l l l } 1.4 & 2.6 & 3.1 & 1.0 & 1.3 & 3.5 & 1.9 & 3.4 & 2.1 & 2.7 & 1.9\end{array}$$

A)2.1
B)1.9
C)2.20
D)2.25

Question 26

Find the median for the given sample data.

-The weights (in ounces)of 14 different apples are shown below. $\begin{array} { l l l l l l } 5.5 & 4.2 & 6.9 & 4.6 & 4.5 &5.5& 4.2 \end{array}$
$\begin{array} { l l l l l l l } 5.0 & 6.2 & 4.6 & 5.5 & 5.0 & 4.6 & 4.7 \end{array}$

A)None
B)5.05
C)5.5, 4.6
D)5.5

Question 27

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

-The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. $$\begin{array} { r | r } \text { Speed (mph) } & \text { Cars } \\\hline 30 - 39 & 3 \\40 - 49 & 17 \\50 - 59 & 51 \\60 - 69 & 16 \\70 - 79 & 13\end{array}$$

A)59.2 mph
B)54.5 mph
C)62.0 mph
D)56.4 mph

Question 28

Find the median for the given sample data.
98, 69, 32, 69, 29, 98

A)98, 69
B)98
C)69
D)65.8

Question 29

Solve the problem.
The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. Given n values (all positive), the geometric mean is the nth root of their product. The average growth factor for money compounded at annual interest rates of 49%, 19%, 24%, and 13% can be found by computing the geometric mean of 1.49, 1.19, 1.24, and 1.13. Find that average growth factor.

A)0.0116
B)1.5762
C)0.6211
D)1.2555

Question 30

Find the mode(s)for the given sample data.

-A meteorologist records the number of clear days in a given year in each of 21 different U.S. cities. The results are shown below. Find the midrange. $$\begin{array} { c c c c c c c } 72 & 143 & 52 & 84 & 100 & 98 & 101 \\120 & 99 & 121 & 86 & 60 & 59 & 71 \\125 & 130 & 104 & 74 & 83 & 55 & 169\end{array}$$

A)117
B)98
C)112
D)110.5

Question 31

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

-The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height. Round your answer to one decimal place. $$\begin{array} { r | r } \text { Height (in.) } & \text { Frequency } \\\hline 70 - 71 & 2 \\72 - 73 & 4 \\74 - 75 & 12 \\76 - 77 & 9 \\78 - 79 & 10 \\80 - 81 & 7 \\82 - 83 & 1\end{array}$$

A)74.9 in.
B)78.3 in.
C)76.5 in.
D)13.5 in.

Question 32

Find the mode(s)for the given sample data.

- $$\begin{array} { c c c c c c c c } 3 & 6 & 9 & 0 & 4 & 1 & 11 & 5 \\9 & 14 & 3 & 8 & 2 & 15 & 0 & 9\end{array}$$

A)8
B)7.5
C)15
D)5.5

Question 33

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

-A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the mean salary. $$\begin{array} { r | c } \text { Salary } ( \$ ) & \text { Employees } \\\hline 5,001 - 10,000 & 16 \\10,001 - 15,000 & 14 \\15,001 - 20,000 & 15 \\20,001 - 25,000 & 17 \\25,001 - 30,000 & 18\end{array}$$

A)$17,500
B)$17,937.50
C)$19,731.25
D)$16,143.75

Question 34

Find the mode(s)for the given sample data.

-The speeds (in mph)of the cars passing a certain checkpoint are measured by radar. The results are shown below. Find the midrange. $\begin{array} { l l l l l } 44.5 & 41.4 & 42.6 & 40.7 & 43.3 \end{array}$
$\begin{array} { l l l l l } 40.0 & 44.7 & 41.4 & 44.5 & 42.5 \end{array}$
$\begin{array} { l l l l l } 43.7 & 41.4 & 40.7 & 43.7 & 41.4 \end{array}$

A)42.25
B)42.35
C)4.70
D)42.5

Question 35

Find the mean, median, mode, and midrange for each of the two samples, then compare the two sets of results.
The Body Mass Index (BMI)is measured for a random sample of men and women. Interpret the results by determining whether there is a difference between the two data sets that is not apparent from a comparison of the measures of center. If there is, what is it?

Question 36

Find the mean, median, mode, and midrange for each of the two samples, then compare the two sets of results.
A comparison is made between summer electric bills of those who have central air and those who have window units.

Question 37

Find the mode(s)for the given sample data.

-Bill kept track of the number of hours he spent exercising each week. The results for 15 weeks are shown below. Find the midrange.
$\begin{array}{lllll}7.2 & 7.0 & 7.2 & 7.4 & 7.5 \\7.5 & 6.5 & 8.0 & 8.1 & 7.4 \\8.7 & 7.0 & 7.5 & 8.9 & 7.5\end{array}$

A)7.5
B)7.60
C)2.4
D)7.70

Question 38

Find the median for the given sample data.
62, 25, 62, 13, 25, 29, 56, 62

A)41.8
B)62
C)42.5
D)25

Question 39

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

-The test scores of 40 students are summarized in the frequency distribution below. Find the mean score. $$\begin{array} { l | r } \text { Score } & \text { Students } \\\hline 50 - 59 & 7 \\60 - 69 & 5 \\70 - 79 & 10 \\80 - 89 & 6 \\90 - 99 & 12\end{array}$$

A)74.5
B)73.4
C)69.6
D)77.3

Question 40

Find the median for the given sample data.
20, 21, 46, 21, 49, 21, 49

A)49
B)21
C)46
D)32.4

Question 41

Find the range for the given data.

-Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores: $\begin{array} { l l l l l } 7 & 16 & 3 & 13 & 12\end{array}$
Compute the range.

A)13
B)5
C)16
D)3

Question 42

Find the midrange for the given sample data.
18, 17, 1, 18, and 4

A)98.3
B)56.2
C)70.3
D)70.2

Question 43

Find the midrange for the given sample data.
15.0, 13.4, 14.0, 17.3, and 10.3

A)6.48
B)6.38
C)5.19
D)47.32

Question 44

Solve the problem.
The 10% trimmed mean of a data set is found by arranging the data in order, deleting the bottom 10% of the values and the top 10% of the values and then calculating the mean of the remaining values. What advantages do you think that the trimmed mean has as compared to the mean?

Question 45

Solve the problem.

-The quadratic mean (or root mean square)is usually used in physical applications. In power distribution systems, for example, voltages and currents are usually referred to in terms of their root mean square value. The quadratic mean of a set of values is obtained by squaring each value, adding the results, dividing by the number of values (n), and then taking the square root of that result, expressed as $$\text { quadratic mean } = \sqrt { \frac { \sum x ^ { 2 } } { n } }$$ Find the root mean square of these power supplies (in volts): 19, 57, 28, 45.

A)20.0 volts
B)37.2 volts
C)74.5 volts
D)40.1 volts

Question 46

Find the range for the given data.

-Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter, he got the following scores: $\begin{array}{lllll}27 & 34 & 13 & 49 & 51\end{array}$
Compute the range.

A)38
B)51
C)7
D)13

Question 47

Find the midrange for the given sample data.

-Compute the variance. The owner of a small manufacturing plant employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below: $$\begin{array} { l l l l l l } 30 & 26 & 67 & 24 & 41 & 57\end{array}$$

A)56.9
B)313.4
C)300.1
D)47.5

Question 48

Find the midrange for the given sample data.
3.8, 1.9, 8.8, 3.3, and 4.2

A)10.84
B)6.81
C)6.71
D)5.45

Question 49

Solve the problem.

-The harmonic mean is often used as a measure of center for data sets consisting of rates of change, such as speeds. It is found by dividing the number of values (n)by the sum of the reciprocals of all values, expressed as $\frac { n } { \sum ( 1 / x ) }$ Pierre drives to work (a distance of 57 miles)at a speed of 73 mi/h and returns home at a speed of 53 mi/h. What is his average speed for the round trip? Use the harmonic mean.

A)63.0 mi/h
B)62.2 mi/h
C)61.4 mi/h
D)63.3 mi/h

Question 50

Find the range for the given data.

-To get the best deal on a microwave oven, Jeremy called six appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $$\$ 111 \quad \$ 552 \quad \$ 158 \quad \$ 668 \quad\$ 355 \quad\$ 312$$
Compute the range.

A)$111
B)$154
C)$552
D)$557

Question 51

Solve the problem.

-When data are summarized in a frequency distribution, the median can be found by first identifying the median class (the class that contains the median). We then assume that the values in that class are evenly distributed and we can interpolate. This process can be described by $$\text { median } = ( \text { lower limit of median class } ) + ( \text { class width } ) \left( \frac { \frac { \mathrm { n } + 1 } { 2 } - ( \mathrm { m } + 1 ) } { \text { frequency of median class } } \right)$$ where n is the sum of all class frequencies and m is the sum of the class frequencies that precede the median class. Use this procedure to find the median of the frequency distribution below: $$\begin{array} { l | c } \text { Score } & \text { Frequency } \\\hline 50 - 59 & 21 \\60 - 69 & 24 \\70 - 79 & 22 \\80 - 89 & 16 \\90 - 99 & 17\end{array}$$

A)74.5
B)71.8
C)72.5
D)72.0

Question 52

Find the range for the given data.

-The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m)are listed below. $0.146\quad0.119\quad0528\quad0.346\quad0.616\quad0.245$
Compute the range.

A)0.119
B)0.497
C)0.099
D)0.528

Question 53

Solve the problem.
The mean salary of the female employees of one company is $29,525. The mean salary of the male employees of the same company is $33,470. Can the mean salary of all employees of the company be obtained by finding the mean of $29,525 and $33,470? Explain your thinking. Under what conditions would the mean of $29,525 and $33,470 yield the mean salary of all employees of the company?

Question 54

Solve the problem.

-The data below consists of the heights (in inches)of 20 randomly selected women. Find the 10% trimmed mean of the data set. The 10% trimmed mean is found by arranging the data in order, deleting the bottom 10% of the values and the top 10% of the values and then calculating the mean of the remaining values. $$\begin{array} { l l l l l } 62 & 64 & 67 & 61 & 63 \\68 & 70 & 67 & 62 & 63 \\61 & 64 & 75 & 68 & 60 \\59 & 64 & 68 & 65 & 71\end{array}$$

A)64.9 in
B)65.1 in
C)64.8 in
D)51.9 in

Question 55

Find the midrange for the given sample data.

-Fred, a local mechanic, gathered the following data regarding the price, in dollars, of an oil and filter change at twelve competing service stations: $$\begin{array} { l l l l } 32.95 & 24.95 & 26.95 & 28.95 \\18.95 & 28.95 & 30.95 & 22.95 \\24.95 & 26.95 & 29.95 & 28.95\end{array}$$
Compute the range.

A)$8
B)$14
C)$12
D)$10

Question 56

Solve the problem.
Elaine gets quiz grades of 60, 69, and 68. She gets a 65 on her final exam. Find the weighted mean if the quizzes each count for 10% and the final exam counts for 70% of the final grade.

A)65.3
B)62.2
C)65.5
D)65.2

Question 57

Find the range for the given data.

-The owner of a small manufacturing plant employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below: $$\begin{array} { c c c c c c } 2.6 & 5.4 & 1.6 & 4.9 & 6.7 & 3.8\end{array}$$
Compute the range.

A)5.4
B)5.1
C)1.6
D)1.2

Question 58

Find the range for the given data.

-A class of sixth grade students kept accurate records on the amount of time they spent playing video games during a one-week period. The times (in hours)are listed below:
$\begin{array} { c c c c c } 25.5 & 11.7 & 9.2 & 26.2 & 11.1 \\29.2 & 17.3 & 23.8 & 14.5 & 22.9\end{array}$
Compute the range.

A)11.1
B)20
C)9.2
D)13.8

Question 59

Find the midrange for the given sample data.
9, 5, -4, 9, and -2

A)39.7
B)29.8
C)37.3
D)37.2

Question 60

Find the midrange for the given sample data.

-Compute the variance. Jeanne is currently taking college zoology. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores: $$\begin{array} { l l l l l } 11 & 11 & 10 & 10 & 13\end{array}$$

A)26.7
B)1.5
C)1.2
D)1.4

Question 61

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

-The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m)are listed below. Compute the standard deviation s. $$\begin{array} { l l l l l l l } 0.189 & 0.518 & 0.665 & 0.568 & 0.149 & 0.573 & 0.202\end{array}$$

A)1.1718
B)0.568
C)0.2193
D)1.4602

Question 62

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

-Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores: $$\begin{array} { l l l l l l l } 50 & 12 & 38 & 25 & 16 & 48 & 58\end{array}$$ Compute the standard deviation s.

A)10,637
B)8715.6
C)38
D)17.9

Question 63

Find the variance for the given data. Round your answer to one more decimal place than the original data.
196, 205, 215, 185, 229, 278, 165

A)33.1
B)30.2
C)36.2
D)12.7

Question 64

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

-When investigating times required for drive-through service, the following results (in seconds)were obtained. $$\begin{array} { l | l | l | l | l | l | l | l | l } \text { Restaurant A } & 120 & 67 & 89 & 97 & 124 & 68 & 72 & 96 \\\hline \text { Restaurant B } & 115 & 126 & 49 & 56 & 98 & 76 & 78 & 95\end{array}$$

A)Restaurant A: 57; 493.98; 22.23
B)Restaurant A: 57; 493.98; 24.97 Restaurant B: 77; 727.98; 26.98 Restaurant B: 70; 722.53; 26.98
C)Restaurant A: 75; 493.98; 22.23
D)Restaurant A: 57; 493.98; 22.23 Restaurant B: 70; 727.98; 26.98 Restaurant B: 56; 727.98; 32.89

Question 65

Find the variance for the given data. Round your answer to one more decimal place than the original data.
22, 29, 21, 24, 27, 28, 25, 36

A)4.8
B)2.8
C)1.6
D)4.2

Question 66

Find the variance for the given data. Round your answer to one more decimal place than the original data.
496, 598, 503, 528, 565, 601, 576, 543

A)60.6
B)182.1
C)170.2
D)40.4

Question 67

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.

-When investigating times required for drive-through service, the following results (in seconds)were obtained. $$\begin{array} { l | l | l | l | l | l | l | l | l } \text { Restaurant A } & 120 & 123 & 153 & 128 & 124 & 118 & 154 & 110 \\\hline \text { Restaurant B } & 115 & 126 & 147 & 156 & 118 & 110 & 145 & 137\end{array}$$

A)Restaurant A: 44; 285.64; 16.15
B)Restaurant A: 46; 260.79; 16.15 Restaurant B: 46; 260.79; 16.90 Restaurant B: 44; 285.64; 16.90
C)Restaurant A: 44; 260.79; 16.15
D)Restaurant A: 46; 260.79; 16.90 Restaurant B: 46; 285.64; 16.90 Restaurant B: 44; 285.64; 16.15

Question 68

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

-To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below:
$\$ 293 \quad \$ 212 \quad \$ 440 \quad \$ 197 \quad \$ 446 \quad \$ 145 \quad \$ 342 \quad \$ 212$
Compute the standard deviation s.

A)$114.2
B)$329.0
C)$653,796.1
D)$745,051.0

Question 69

Find the midrange for the given sample data.

-Compute the variance. A class of sixth grade students kept accurate records on the amount of time they spent playing video games during a one-week period. The times (in hours)are listed below:
$\begin{array} { l l l l l } 19.8 & 21.6 & 13.4 & 26.7 & 25.6 \end{array}$
$\begin{array} { l l l l l } 19.2 & 17.0 & 12.9 & 26.8 & 15.2 \end{array}$

A)152.13
B)25.14
C)27.84
D)27.94

Question 70

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

-The manager of a small dry cleaner employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below:
$21.1\quad14.8\quad39.1\quad37.6\quad17.4\quad24.2$
Compute the standard deviation s.

A)38.4
B)3962.9
C)4495.2
D)10.32

Question 71

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.

-The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the standard deviation. Round your answer to one decimal place. $$\begin{array}{l}\text { Waiting tim\& Number of }\\\begin{array} { c | c } \text { (minutes } & \text { customer } \\\hline 0 - 3 & 12 \\4 - 7 & 14 \\8 - 11 & 10 \\12 - 15 & 13 \\16 - 19 & 0 \\20 - 23 & 1\end{array}\end{array}$$

A)4.9
B)5.2
C)7.0
D)4.7

Question 72

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.

-The test scores of 40 students are summarized in the frequency distribution below. Find the standard deviation. $$\begin{array} { r | r } \text { Score } & \text { Students } \\\hline 50 - 59 & 8 \\60 - 69 & 6 \\70 - 79 & 10 \\80 - 89 & 5 \\90 - 99 & 11\end{array}$$

A)s = 13.4
B)s = 14.9
C)s = 15.6
D)s = 14.2

Question 73

Find the variance for the given data. Round your answer to one more decimal place than the original data.
2, 6, 15, 9, 11, 22, 1, 4, 8, 19

A)2.1
B)6.3
C)6.8
D)7.1

Question 74

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

-The normal monthly precipitation (in inches)for August is listed for 12 different U.S. cities.
$\begin{array} { l l l l l l } 3.5 & 1.6 & 2.4 & 3.7 & 4.1 & 3.9 \end{array}$
$\begin{array} { l l l l l l } 1.0 & 3.6 & 4.2 & 3.4 & 3.7 & 2.2 \end{array}$
Compute the variance.

A)1.05
B)0.94
C)1.09
D)1.00

Question 75

Solve the problem.

-The heights in feet of people who work in an office are as follows. Use the range rule of thumb to find the standard deviation. Round results to the nearest tenth. $$\begin{array} { l l l l l l l l l l } 5.9 & 6.0 & 5.8 & 5.4 & 6.0 & 5.5 & 6.0 & 6.2 & 6.1 & 5.5\end{array}$$

A)0.1
B)0.2
C)0.5
D)1.2

Question 76

Find the midrange for the given sample data.

-Compute the variance. To get the best deal on a microwave oven, Jeremy called six appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $$\$ 476\quad \$ 477 \quad\$ 645 \quad\$ 334 \quad\$ 667 \quad\$ 237$$

A)40,214.5
B)28,452.3
C)23,710.2
D)28,452.2

Question 77

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.

-A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the standard deviation. $$\begin{array} { r | c } \text { Salary } & \text { Employees } \\\hline 5,001 - 10,000 & 11 \\10,001 - 15,000 & 15 \\15,001 - 20,000 & 19 \\20,001 - 25,000 & 10 \\25,001 - 30,000 & 25\end{array}$$

A)s = 7168.6
B)s = 7742.1
C)s = 7527.0
D)s = 7957.1

Question 78

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

-The normal monthly precipitation (in inches)for August is listed for 12 different U.S. cities.
$\begin{array}{llllll}3.5 & 1.6 & 2.4 & 3.7 & 4.1 & 3.9 \\1.0 & 3.6 & 4.2 & 3.4 & 3.7 & 2.2\end{array}$
Compute the standard deviation.

A)1.09
B)1.05
C)1.00
D)12.03

Question 79

Find the midrange for the given sample data.

-The weights (in ounces)of 10 cookies are shown. $$\begin{array} { l l l l l } 0.71 & 0.69 & 0.82 & 1.45 & 1.34 \\1.06 & 0.67 & 1.24 & 1.16 & 0.79\end{array}$$ Compute the variance.

A)0.064
B)0.077
C)0.086
D)0.07

Question 80

Find the variance for the given data. Round your answer to one more decimal place than the original data.
15, 42, 53, 7, 9, 12, 14, 28, 47

A)29.1
B)17.8
C)15.8
D)16.6