Question 1

Use the range rule of thumb to approximate the standard deviation. 22, 29, 21, 24, 27, 28, 25, 38

Accepted Answer

The range is 38 - 21 = 17. The range rule of thumb states that the standard deviation is approximately 1/4 of the range. Therefore, the standard deviation is approximately 17/4 = 4.25.

Question 2

Which of the distributions has the greatest variation?

Accepted Answer

The answer of Which of the distributions has the greatest...

Question 3

The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score 533 drops the seminar and is replaced by a student with a score of 585. What will happen to the mean and the median scores of the class?

Accepted Answer

The mean will increase because the sum of the scores increases when 533 is replaced by 585. The median remains unchanged at 586, as it is still the middle value in the ordered list.

Question 4

The following data set is the GPAs of the students in a statistics class.  
What percentile is a GPA of 2.34?

Accepted Answer

The answer of The following data set is the GPAs...

Question 5

A softball player has a batting average of exactly .300 and no more than 60 times at bat. Suppose this player gets 5 hits in her next 6 times at bat. What is the highest possible average she could now have?

Accepted Answer

The answer of A softball player has a batting average...

Question 6

The batting averages of the first three batters in the Eureka College women's softball team lineup are .310, .301, and .277. If the first three batters are considered as the "lead-off group", What is the batting average of the group?

Accepted Answer

The answer of The batting averages of the first three...

Question 7

The grocery expenses for six families were $80.86, $47.74, $57.92, $81.08, $75.18, and $88.08. Compute the mean grocery bill. Round your answer to the nearest cent.

Accepted Answer

The answer of The grocery expenses for six families were...

Question 8

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpg's for four of the five models of a manufacturer are 19, 22, 28, and 26, and the manufacturer just meets the government standard of 31 mpg. Find the mileage for the fifth model.

Accepted Answer

To meet the average of 31 mpg over 5 models, the total mpg must be 31 * 5 = 155. The sum of the given mpgs is 19 + 22 + 28 + 26 = 95. Therefore, the fifth model must have 155 - 95 = 60 mpg.

Question 9

Find the standard deviation 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

Accepted Answer

To find the standard deviation, first calculate the mean of the data set, then find the squared differences from the mean, average those squared differences, and finally take the square root. The calculated standard deviation for this data set is approximately 17.8.

Question 10

Al and Joe are two county sheriff's deputies assigned to watch for traffic violations. Their
arrest and conviction records for May and June are shown below.

$$\begin{array} {c}
  \quad \quad \quad { \text { May } }    \quad \quad\quad \quad \quad{ \text { June } } \
\begin{array} { | l | l | l | l | l | }

\hline & \text { Arrests } & \text { Convictions } & \text { Arrests } & \text { Convictions } \
\hline \mathrm{Al} & 90 & 30 & 20 & 12 \
\hline \text { Joe } & 10 & 2 & 80 & 40 \
\hline
\end{array}\end{array}$$ Who had the best conviction percentage in May?
Who had the best conviction percentage in June?
Who had the best conviction percentage overall?

Accepted Answer

The answer of Al and Joe are two county sheriff's...

Question 11

The table shows the country represented by the winner of the 10,000 meter run in the Summer Olympic Games in various years. 
$$\begin{array} { l l | l l } 
\text { Year } & \text { Country } & \text { Year } & \text { Country } \
\hline 1912 & \text { Finland } & 1968 & \text { Kenya } \
1920 & \text { Finland } & 1972 & \text { Finland } \
1924 & \text { Finland } & 1976 & \text { Finland } \
1928 & \text { Finland } & 1980 & \text { Ethiopia } \
1932 & \text { Poland } & 1984 & \text { Italy } \
1936 & \text { Finland } & 1988 & \text { Morocco } \
1948 & \text { Czechoslovakia } & 1992 & \text { Morocco } \
1952 & \text { Czechoslovakia } & 1996 & \text { Ethiopia } \
1956 & \text { USSR } & 2000 & \text { Ethiopia } \
1960 & \text { USSR } & 2004 & \text { Ethiopia } \
1964 & \text { United States } & 2008 & \text { Ethiopia } \
& & 2012 & \text { Britain }
\end{array}$$ Find the mode of the country data.

Accepted Answer

The answer of The table shows the country represented by...

Question 12

The test scores of 32 students are listed below. Construct a boxplot for the data set. 
$ \begin{array}{llllllll}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\end{array} $

Accepted Answer

The answer of The test scores of 32 students are...

Question 13

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the average mpg for the four models manufactured is 24 mpg and the government standard is 31 mpg. The manufacturer will add a model. What mileage must the new model get so that the manufacturer meets the government
Requirement?

Accepted Answer

To meet the government requirement of 31 mpg, the average mpg of all five models must be 31. The current total mpg for four models is 4 * 24 = 96. For five models, the total must be 5 * 31 = 155. Therefore, the new model must have 155 - 96 = 59 mpg.

Question 14

Which of the distributions is skewed to the right?

Accepted Answer

The answer of Which of the distributions is skewed to...

Question 15

Consider the distribution of heights of all the players in the national Basketball Association. What would you expect the shape of the distribution to be?

Accepted Answer

The answer of Consider the distribution of heights of all...

Question 16

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

Accepted Answer

The answer of The normal monthly precipitation (in inches) for...

Question 17

The mathematics SAT scores of the seven students in a mathematics seminar are 538, 550, 570, 593, 610, 622, and 634. Suppose the student with the score 634 drops the seminar and is replaced by a student with a score of 600. What will happen to the mean and the median scores of the class?

Accepted Answer

The mean will decrease because the sum of the scores will decrease when 634 is replaced by 600. The median will not change because the middle score (593) remains the same.

Question 18

Find the mode(s) for the given sample data.
66, 25, 66, 13, 25, 29, 56, 66

Accepted Answer

The answer of Find the mode(s) for the given sample...

Question 19

The host of a dinner party purchases wine based on the weighted average of clarity (10%), bouquet (5%), friendliness to the palate (5%), storage ability of opened bottles (40%), and price (40%). Suppose that Bone Ranch Wave has scores in these categories of 4, 5, 3, 8, and 9, respectively. What is its rating?

Accepted Answer

The weighted average is calculated as follows:(0.10 * 4) + (0.05 * 5) + (0.05 * 3) + (0.40 * 8) + (0.40 * 9) = 7.60

Question 20

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.
88, 84, 209, 151, 271, 242, 234
Find the median number of newspapers sold.

Accepted Answer

The answer of A store manager kept track of the...

Quiz 4: Describing Data

Use the range rule of thumb to approximate the standard deviation. 22, 29, 21, 24, 27, 28, 25, 38

Which of the distributions has the greatest variation?

The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score 533 drops the seminar and is replaced by a student with a score of 585. What will happen to the mean and the median scores of the class?

The following data set is the GPAs of the students in a statistics class. What percentile is a GPA of 2.34?

A softball player has a batting average of exactly .300 and no more than 60 times at bat. Suppose this player gets 5 hits in her next 6 times at bat. What is the highest possible average she could now have?

The batting averages of the first three batters in the Eureka College women's softball team lineup are .310, .301, and .277. If the first three batters are considered as the "lead-off group", What is the batting average of the group?

The grocery expenses for six families were $80.86, $47.74, $57.92, $81.08, $75.18, and $88.08. Compute the mean grocery bill. Round your answer to the nearest cent.

Find the standard deviation 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

The test scores of 32 students are listed below. Construct a boxplot for the data set. $\begin{array}{llllllll}32 & 37 & 41 & 44 & 46 & 48 & 53 & 55 \\ 57 & 57 & 59 & 63 & 65 & 66 & 68 & 69 \\ 70 & 71 & 74 & 74 & 75 & 77 & 78 & 79 \\ 81 & 82 & 83 & 86 & 89 & 92 & 95 & 99\end{array}$

Which of the distributions is skewed to the right?

Consider the distribution of heights of all the players in the national Basketball Association. What would you expect the shape of the distribution to be?

The mathematics SAT scores of the seven students in a mathematics seminar are 538, 550, 570, 593, 610, 622, and 634. Suppose the student with the score 634 drops the seminar and is replaced by a student with a score of 600. What will happen to the mean and the median scores of the class?

Find the mode(s) for the given sample data. 66, 25, 66, 13, 25, 29, 56, 66

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below. 88, 84, 209, 151, 271, 242, 234 Find the median number of newspapers sold.