Question 1

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 2

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 the data set. In this case, the value of $70 appears twice, which is more than any other value. Therefore, the mode of the prices is $70.

Question 3

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 find the semester grade point average, we need to first convert each grade to a numerical value using the standard 4.0 scale. A = 4.0, B = 3.0, C = 2.0, D = 1.0, F = 0.0.

Mathematics = 2.0 x 2 = 4.0 
English = 1.0 x 1 = 1.0 
History = 2.0 x 3 = 6.0 
Geography = 1.0 x 3 = 3.0 
Biology = 3.0 x 3 = 9.0

To find the total grade points, we add up all of the individual grade points:
4.0 + 1.0 + 6.0 + 3.0 + 9.0 = 23.0

To find the GPA, we divide the total grade points by the total number of credits:
23.0 / 12 = 1.92

Therefore, the student's semester GPA is 1.92, which is closest to choice C) 1.92.

Question 4

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

Question 5

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 6

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 order from least to greatest: 
0, 0, 0, 4, 4, 7, 7, 9 
The median is the middle value, and since there are an even number of values, we take the average of the two middle values, which are 4 and 4. Thus, the median is 4.

Question 7

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

The sample set for tossing three coins includes all possible outcomes, which are 2^3 = 8 in total. Each coin can land as either heads (H) or tails (T), leading to 8 combinations: HHH, HHT, HTH, THH, TTH, THT, HTT, TTT.

Question 8

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 on the quiz is (0*4 + 1*4 + 2*8 + 3*10 + 4*1) / (4 + 4 + 8 + 10 + 1) = 2.

Question 9

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, we need to add up all the numbers in the list and then divide by the total number of values. 
48 + 67 + 44 + 37 + 80 + 52 + 92 + 108 = 528
There are 8 values in the list, so we divide 528 by 8 to get the mean.
528/8 = 66
Therefore, the answer is D) 66.

Question 10

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 11

What is the event " getting at least one tails " for the experiment of tossing a coin twice?
A) E = { (T, T), (H, T), (T, H) }
B) E = { (H, H), (H, T), (T, H), (T, T) }
C) E = { (H, H), (H, T), (T, H) }
D) E = { (H, T), (T, H) }

Accepted Answer

The event "getting at least one tails" includes all outcomes where at least one of the tosses results in tails. This includes the combinations where both tosses are tails (T, T), one toss is heads and the other is tails (H, T), and one toss is tails and the other is heads (T, H).

Question 12

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

The set of numbers 0-9 includes all possible one-digit numbers. Choice A only includes numbers 1-9, while choice C only includes the number 10 which is not a one-digit number. Choice D represents an infinite sample space which is not applicable in this case.

Question 13

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

The answer of Find the mean of the list of...

Question 14

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 15

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 and his mean score is 84, all five scores must be 84. Therefore, the median and modal scores are both 84.

Question 16

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 answer of Find the median of the list of...

Question 17

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

The answer of Frank's algebra grade is based on the...

Question 18

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 19

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

To find the mean, we add up all the magnitudes and divide by the total number of earthquakes:
$$\frac{7+7.3+7.1+7.4+7.1+7.1+7.1+7.4+7.8+7.4+7.2}{11} \approx 7.3$$
Therefore, the mean magnitude is 7.3.

To find the median, we need to put the magnitudes in order from least to greatest:
$$7, 7.1, 7.1, 7.1, 7.2, 7.3, 7.4, 7.4, 7.8$$
The median is the middle number, which in this case is 7.2 (since there are an odd number of magnitudes).

To find the mode, we look for the magnitude that appears most frequently. In this case, both 7.1 and 7.4 appear twice, so there is no single mode. Therefore, we say that the data set is bimodal with modes 7.1 and 7.4.

Thus, the best choice is D with the calculated mean, median 7.2 and the modes 7.1 and 7.4.

Question 20

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

The answer of Several groceries reported differing prices for a...

Quiz 7: Graphs, Statistics, and Probability

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?

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

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

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

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

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

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

What is the event " getting at least one tails " for the experiment of tossing a coin twice?

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

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.

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

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.

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.

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.