Question 1

Find the mean of the list of data.
46, 62, 42, 32, 85, 57, 96, 104
A) 64.5
B) 68.5
C) 66.5
D) 65.5
E) 67.5

Accepted Answer

Mean is the sum of all values divided by the number of values in a dataset. In this case, the mean can be calculated as (46 + 62 + 42 + 32 + 85 + 57 + 96 + 104) / 8 = 532 / 8 = 66.5. Therefore, the correct answer is D.

Question 2

Assume that the probability that an airplane engine will fail a test is $\frac { 1 } { 2 }$ and that the aircraft in question has 4 engines. What is the sample space for the problem? Use N for not fail and F for fail.

Accepted Answer

The answer of Assume that the probability that an airplane...

Question 3

Find the mode (if any) of the list of data.
16, 16, 18, 18, 16, 17, 18, 16
A) 16
B) 17
C) 16.5
D) 18
E) 15

Accepted Answer

The mode is the most frequent value in the list. In this case, the number 16 appears 4 times, which is more than any other number in the list. Therefore, the mode is 16.

Question 4

Which of the following is the sample set for an experiment which involves tossing three coins?
A) HHH, TTT
B) HHH, HHT, HTT, TTT
C) HHH, HHT, HTH, THH, TTT
D) HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

Accepted Answer

Each outcome in the sample set represents a possible result of tossing three coins, where 'H' stands for heads and 'T' for tails. With three coins, there are 2^3 = 8 possible outcomes, all of which are listed in option D.

Question 5

List the sample set for an experiment which involves picking a one-digit number.
A) 1, 2, 3, 4, 5, 6, 7, 8, 9
B) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
C) 10
D) $\infty$

Accepted Answer

One-digit numbers include 0 through 9, making option B the correct sample set for this experiment.

Question 6

Find the semester grade point average for a student that received the following grades. Round to the nearest hundredth.
$\begin{array} { | c | c | c | } 
\hline \text { Course } & \text { Grade } & \text { Credits } \
\hline \text { Mathematics } & \text { C } & 2 \
\hline \text { English } & \text { D } & 1 \
\hline \text { History } & \text { C } & 3 \
\hline \text { Geography } & \text { D } & 3 \
\hline \text { Biology } & \text { B } & 3 \
\hline
\end{array}$
A) 2
B) 2.4
C) 1.92
D) 0.4

Accepted Answer

To calculate the semester grade point average, we need to first assign each letter grade a point value:
A = 4.0
B = 3.0
C = 2.0
D = 1.0
F = 0

Then, we multiply the point value by the number of credits for each course and add the results. 
Mathematics contributes $2 	imes 2 = 4$ points, English contributes $1 	imes 1 = 1$ point, History contributes $3 	imes 2 = 6$ points, Geography contributes $3 	imes 1 = 3$ points, and Biology contributes $3 	imes 3 = 9$ points.

So the total number of grade points is $4+1+6+3+9=23$. The total number of credits is $2+1+3+3+3=12$.

The semester grade point average is $\dfrac{23}{12} \approx 1.92$. Therefore, the best answer choice is C.

Question 7

Find the mean of the list of data.
12, 14, 16, 16, 14, 12
A) 15
B) 13
C) 16
D) 17
E) 14

Accepted Answer

To find the mean, we need to add up all the numbers and divide by the total number of numbers.

12 + 14 + 16 + 16 + 14 + 12 = 84

There are six numbers in the list, so we divide by 6 to get:

84/6 = 14

Therefore the mean of the list is 14, so the best choice is E.

Question 8

Several groceries reported differing prices for a bread. The prices are as follows: 2.3, 2.6, 3.2, 2.8, 3.1, 3, 2.2, 2, 2.8. Find the mean, median, and mode of the prices for a bread. Then find the range of the prices.
A) mean: $3.67, median: $3.8, mode: $1.8, range: $2.2
B) mean: $2.67, median: $2.8, mode: $2.8, range: $1.2
C) mean: $1.67, median: $4.8, mode: $3.8, range: $3.2
D) mean: $4.67, median: $1.8, mode: $4.8, range: $0.5
E) mean: $0.67, median: $5.8, mode: $0.8, range: $4.2

Accepted Answer

To find the mean, we add all the prices and divide by the total number of prices:
(2.3 + 2.6 + 3.2 + 2.8 + 3.1 + 3 + 2.2 + 2 + 2.8) / 9 = 24 / 9 = $2.67
To find the median, we need to arrange the prices in numerical order:
2, 2.2, 2.3, 2.6, 2.8, 2.8, 3, 3.1, 3.2
The median is the middle number, which is 2.8.
To find the mode, we look for the number that appears most frequently. In this case, 2.8 appears twice, while no other number appears more than once. So the mode is also 2.8.
To find the range, we subtract the lowest price from the highest price:
3.2 - 2 = $1.2
Therefore, the best choice is B, which matches all of the calculations we just did.

Question 9

Several computer stores reported differing prices for a toner cartridge for a laser printer. The prices are as follows: 59, 50, 77, 70, 71, 73, 54, 56, 70. Find the mode of the prices for a toner cartridge.
A) $69
B) $70
C) $71
D) $72
E) $68

Accepted Answer

The mode is the value that appears most frequently in a set of data. In this case, the price that appears most frequently is $70, which is the answer choice B. Therefore, B is the best choice.

Question 10

Find the mode of these values:
4, 4, 8, 8, 4, 7, 8, 4
A) 4
B) 7
C) 5.5
D) 8
E) 3

Accepted Answer

The mode is the number that appears most frequently in a data set. In this case, the number 4 appears four times, which is more frequent than any other number.

Question 11

The scores on the first exam of the students in a history class were 52, 57, 63, 62, 62, 62, 84, 82, 98, 91, and 100. Kia got a score of 85 and claims that "85 is better than average." Which of the three measures of central tendency is she better than: the mean, the median, or the mode?
A) better than the mean
B) worse than the mean
C) better than the mode
D) worse than the median
E) better than the median
F) worse than the mode

Accepted Answer

The answer of The scores on the first exam of...

Question 12

Find the weighted mean of a set of values. Round to the nearest tenth. $$\begin{array} { | c | c | } 
\hline \text { Value of } x & \begin{array} { c } 
\text { The weights to } \
\text { the } x \text { values }
\end{array} \
\hline 3 & 20 \
\hline 4 & 34 \
\hline 2 & 47 \
\hline 1 & 54 \
\hline
\end{array}$$
A) 2.2
B) 38.8
C) 15.5
D) 2.5

Accepted Answer

Weighted mean = (3 * 20 + 4 * 34 + 2 * 47 + 1 * 54) / (20 + 34 + 47 + 54) = 2.2

Question 13

Use the following bar graph to find the average number of therms of natural gas used per month.

Accepted Answer

The answer of Use the following bar graph to find...

Question 14

Frank's algebra grade is based on the average of four exams, which will count equally. His grades are 85, 70, 70 and 85. Find his average.
A) 72.5
B) 77.5
C) 82.5
D) 92.5
E) 87.5

Accepted Answer

To find the average, add all the grades together and divide by the number of exams: (85 + 70 + 70 + 85) / 4 = 310 / 4 = 77.5.

Question 15

Find the median of the list of data.
15, 18, 20, 29, 34, 44
A) 22.5
B) 29
C) 20
D) 24.5
E) 26.7

Accepted Answer

The median is the middle value of a data set. For an even number of data points, it is the average of the two middle numbers. Here, the middle numbers are 20 and 29, so the median is (20 + 29) / 2 = 24.5.

Question 16

Roberto received the same score on each of five exams, and his mean score is 84. Find his median score and his modal score.
A) median 79, mode 74
B) median 89, mode 89
C) median 84, mode 84
D) median 74, mode 74
E) median 89, mode 79

Accepted Answer

Since Roberto received the same score on each of the five exams, his median score would also be 84. And since all the scores are the same, the mode would also be 84. Therefore, the correct answer is choice C.

Question 17

Find the mean of the list of data.
48, 67, 44, 37, 80, 52, 92, 108
A) 65
B) 64
C) 67
D) 66
E) 68

Accepted Answer

To find the mean, add up all the numbers and divide by the total number of numbers. 
48 + 67 + 44 + 37 + 80 + 52 + 92 + 108 = 528 
528/8 = 66

Question 18

The class results on a mathematical quiz are shown in the table below. Find the average number of incorrect answers on the quiz.
$\begin{array} { | c | c | } 
\hline \begin{array} { c } 
\text { Total number } \
\text { of incorrect } \
\text { answers on } \
\text { the quiz }
\end{array} & \begin{array} { c } 
\text { Number } \
\text { of students }
\end{array} \
\hline 0 & 4 \
\hline 1 & 4 \
\hline 2 & 8 \
\hline 3 & 10 \
\hline 4 & 1 \
\hline
\end{array}$
A) 2
B) 5.4
C) 9
D) 1.8

Accepted Answer

The average number of incorrect answers is calculated by multiplying each number of incorrect answers by the number of students, summing these products, and then dividing by the total number of students: $(0*4 + 1*4 + 2*8 + 3*10 + 4*1) / (4+4+8+10+1) = 2$.

Question 19

Find the median of the list of data.
0, 0, 4, 7, 0 , 0, 4, 7, 9
A) 0
B) 7
C) 3
D) 4
E) 9

Accepted Answer

To find the median, we need to arrange the data in ascending order: 0, 0, 0, 4, 4, 7, 7, 9. The median is the middle value, so in this case it is 4. Therefore, the answer is D.

Question 20

The magnitudes of the major earthquakes in 1999 are listed below.
$\begin{array} { l l l } 
\text { 1/19/99 } & \text { New Ireland, Papua New Guinea } & 7 \
2 / 6 / 99 & \text { Santa Cruz Islands, S.Pacific Sea } & 7.3 \
3 / 4 / 99 & \text { Celebes Sea, Indonesia } & 7.1 \
4 / 5 / 99 & \text { New Britain, Papua New Guinea } & 7.4 \
4 / 8 / 99 & \text { E.Russia/N.E.China border } & 7.1 \
5 / 10 / 99 & \text { New Britain, Papua New Guinea } & 7.1 \
5 / 16 / 99 & \text { New Britain, Papua New Guinea } & 7.1 \
8 / 17 / 99 & \text { Izmit region, western Turkey } & 7.4 \
9 / 21 / 99 & \text { Taiwan } & 7.8 \
9 / 30 / 99 & \text { Oaxaca, Mexico } & 7.4 \
11 / 12 / 99 & \text { Bolu Province, northwest Turkey } & 7.2
\end{array}$
Find the mean, median, and mode of the magnitudes. Round to the nearest tenth.
A) mean 7.2; mode 7; median 7.3
B) mean 7.3; mode 7.2; median 7.2
C) mean 7.4; mode 7.2; median 7.2
D) mean 7.3; mode 7.1; median 7.2
E) mean 7.2; mode 7.1; median 7.2

Accepted Answer

The answer of The magnitudes of the major earthquakes in...

Quiz 7: Graphs, Statistics, and Probability

Find the mean of the list of data. 46, 62, 42, 32, 85, 57, 96, 104

Assume that the probability that an airplane engine will fail a test is 12\frac { 1 } { 2 }21​ and that the aircraft in question has 4 engines. What is the sample space for the problem? Use N for not fail and F for fail.

Find the mode (if any) of the list of data. 16, 16, 18, 18, 16, 17, 18, 16

Which of the following is the sample set for an experiment which involves tossing three coins?

List the sample set for an experiment which involves picking a one-digit number.

Find the mean of the list of data. 12, 14, 16, 16, 14, 12

Several groceries reported differing prices for a bread. The prices are as follows: 2.3, 2.6, 3.2, 2.8, 3.1, 3, 2.2, 2, 2.8. Find the mean, median, and mode of the prices for a bread. Then find the range of the prices.

Several computer stores reported differing prices for a toner cartridge for a laser printer. The prices are as follows: 59, 50, 77, 70, 71, 73, 54, 56, 70. Find the mode of the prices for a toner cartridge.

Find the mode of these values: 4, 4, 8, 8, 4, 7, 8, 4

The scores on the first exam of the students in a history class were 52, 57, 63, 62, 62, 62, 84, 82, 98, 91, and 100. Kia got a score of 85 and claims that "85 is better than average." Which of the three measures of central tendency is she better than: the mean, the median, or the mode?

Use the following bar graph to find the average number of therms of natural gas used per month.

Frank's algebra grade is based on the average of four exams, which will count equally. His grades are 85, 70, 70 and 85. Find his average.

Find the median of the list of data. 15, 18, 20, 29, 34, 44

Roberto received the same score on each of five exams, and his mean score is 84. Find his median score and his modal score.

Find the mean of the list of data. 48, 67, 44, 37, 80, 52, 92, 108

Find the median of the list of data. 0, 0, 4, 7, 0 , 0, 4, 7, 9

Assume that the probability that an airplane engine will fail a test is $\frac { 1 } { 2 }$ and that the aircraft in question has 4 engines. What is the sample space for the problem? Use N for not fail and F for fail.