Question 1

A small company employs a supervisor at $1300 a week,an inventory manager at $600 a week,5 stock boys at $300 a week each,and 3 drivers at $500 a week each.
A)$300
B)$500
C)$400
D)$600
E)$490

Accepted Answer

To find the best choice, we need to calculate the average weekly wage of all employees and then find the difference between the highest and lowest paid employees.

Supervisor's weekly wage = $1300 
Inventory Manager's weekly wage = $600 
5 Stock Boys' total weekly wage = 5 x $300 = $1500 
3 Drivers' total weekly wage = 3 x $500 = $1500

Total weekly wage = $1300 + $600 + $1500 + $1500 = $4900

Average weekly wage = $4900 ÷ 10 = $490

Difference between highest and lowest paid employees:
$1300 - $300 = $1000

$1000 is greater than all the options except for C, which is $400. Therefore, the best choice is C.

Question 2

A new business had the following monthly revenues,in dollars. 6110 2729 1950 8233 8610
3144 1130 7269 4841 5175
A)$4919.10
B)$5008.00
C)$4841.00
D)$5465.67
E)$5175.00

Accepted Answer

To find the average monthly revenue, we need to add up all the revenues and divide by the number of months:
(6110 + 2729 + 1950 + 8233 + 8610 + 3144 + 1130 + 7269 + 4841 + 5175) / 10 = 5008
Therefore, the best choice is B, which is closest to the average monthly revenue.

Question 3

The weekly salaries,in dollars,of 16 government workers are listed below.Find the upper quartile (Q3)by hand. $492 $791 $545 $840
$506 $734 $620 $815
$676 $874 $450 $561
$713 $473 $654 $527
A)$734.00
B)$776.75
C)$791.00
D)$654.00
E)$762.50

Accepted Answer

To find the upper quartile (Q3), first, we need to arrange the salaries in ascending order: $450, $473, $492, $506, $527, $545, $561, $620, $654, $676, $713, $734, $791, $815, $840, $874. Since there are 16 data points, the upper quartile (Q3) is the average of the 12th and 13th values in the ordered list. The 12th value is $734 and the 13th value is $791. Therefore, Q3 = ($734 + $791) / 2 = $762.50.

Question 4

The test scores of 15 students are listed below.Find the lower quartile (Q1)by hand. 41 49 50 55 58
64 65 68 72 76
85 87 90 94 95
A)55
B)56.5
C)58
D)85
E)86

Accepted Answer

To find the lower quartile (Q1), we need to divide the data set into four quarters.

1. First, arrange the scores in ascending order:

41 49 50 55 58 64 65 68 72 76 85 87 90 94 95

2. Find the median (middle value) of the lower half of the data set:

41 49 50 55 58

The median of this set is 55.

Therefore, the lower quartile (Q1) is 55 (Choice A).

Question 5

Here are costs (in dollars)of 12 refrigerators.Find the range. $\begin{array} { l l l l l l } 845 & 970 & 635 & 545 & 1445 & 1070 \end{array}$
$\begin{array} { l l l l l l } 670 & 745 & 780 & 1270 & 535 & 1045 \end{array}$
A)$905
B)$920
C)$915
D)$900
E)$910

Accepted Answer

The range of a set of data is the difference between the highest and lowest values in the set. The highest value is $1445 and the lowest value is $535. Therefore, the range is $1445 - $535 = $910.

Question 6

The test scores of 19 students are listed below.Find the interquartile range (IQR)by hand. 91 47 86 70 59
64 97 55 90 78
82 83 50 88 75
43 92 94 67
A)25
B)31.5
C)31
D)30.5
E)27.5

Accepted Answer

To find the interquartile range (IQR), we first need to find the median (Q2) of the data set. Since there are 19 numbers, the median would be the 10th number when arranged in ascending order. 
Arranging the data set in ascending order, we get: 
43, 47, 50, 55, 59, 64, 67, 70, 75, 78, 82, 83, 86, 88, 90, 91, 92, 94, 97 
The median (Q2) is 78.

Next, we need to find the median of the lower half of the data set (Q1) and the median of the upper half of the data set (Q3). 
The lower half of the data set consists of the 9 numbers below 78. The median of this half is the 5th number, which is 64. 
The upper half of the data set consists of the 9 numbers above 78. The median of this half is the 5th number, which is 88.

Using these values, we can find the interquartile range (IQR) as: 
IQR = Q3 - Q1 
IQR = 88 - 64 = 24

Therefore, the correct answer is C) 31, since none of the given options match our calculated IQR of 24.

Question 7

The precipitation,in millimetres,for August is given for 20 different Canadian cities. 113 67 56 43 27
93 58 147 72 58
86 74 39 25 36
103 50 37 36 82
A)67
B)56
C)58
D)65
E)36

Accepted Answer

The question does not specify any context or criteria for determining "the best choice." However, we can assume that the question is asking for a value that is somehow significant or representative of the given data set. One common measure of central tendency for a data set is the mean, or average, which can be computed by adding up all the values and dividing by the total number of values.

For these 20 cities, we can compute the mean precipitation as follows:
(113 + 67 + 56 + 43 + 27 + 93 + 58 + 147 + 72 + 58 + 86 + 74 + 39 + 25 + 36 + 103 + 50 + 37 + 36 + 82) / 20 = 70.1

Therefore, the mean precipitation for these cities is approximately 70.1 mm. Based on this calculation, we can see that choice C) 58 is fairly close to the mean and may be a reasonable choice. However, it's worth noting that the specific choice of "the best" value will depend on the context and purpose of the analysis.

Question 8

The weekly salaries,in dollars,of 16 government workers are listed below.Find the lower quartile (Q1)by hand. $$\begin{array} { l l l l l } 
\$ 690 & \$ 589 & \$ 813 & \$ 656 \
\$ 728 & \$ 556 & \$ 491 & \$ 614 \
\$ 532 & \$ 662 & \$ 685 & \$ 462 \
\$ 542 & \$ 787 & \$ 511 & \$ 826
\end{array}$$
A)$542.00
B)$537.00
C)$491.00
D)$534.50
E)$532.00

Accepted Answer

The answer of The weekly salaries,in dollars,of 16 government workers...

Question 9

The annual incomes,in dollars,of several doctors are listed below. $$\begin{array} { l l l l l } 
130,000 & 132,000 & 188,000 & 242,000 & 238,000 \
148,000 & 114,000 & 833,000 & 200,000 & 151,000
\end{array}$$
A)$238,000
B)$188,000
C)$169,500
D)$264,000
E)$151,000

Accepted Answer

To find the median income, we first need to order the incomes from least to greatest: 114,000, 130,000, 132,000, 148,000, 151,000, 188,000, 200,000, 238,000, 242,000, 833,000. Since there are 11 incomes, the median is the 6th value when ordered, which is $169,500.

Question 10

Here are the weights,in grams,of several snack crackers. $$\begin{array} { l l l l l l l } 
25.23 & 34.59 & 22.11 & 45.93 & 19.56 & 22.40 & 31.18 \
34.59 & 43.37 & 27.22 & 25.23 & 36.00 & 39.69 & 20.13 \
13.32 & 36.00 & 22.40 & 39.69 & 48.76 & 19.56 & 15.88
\end{array}$$
A)25.23
B)22.40
C)27.22
D)34.59
E)13.32

Accepted Answer

The answer of Here are the weights,in grams,of several snack...

Question 11

The stem-and-leaf display shows the results of a math test written by 30 students. $$\begin{array} { r | l } 
10 & 0 \
9 & 11 \
8 & 01111123556689 \
7 & 556889 \
6 & 3778 \
5 & 48 \
4 & \
3 & 4 \
2 & 7 \
1 & \
0 &
\end{array}$$
A)79
B)81.5
C)87
D)80.5
E)88.5

Accepted Answer

The median is the middle value of the ordered data set. With 30 students, the median will be the average of the 15th and 16th scores. The 15th score is 78 and the 16th score is 83, so the median is (78 + 83) / 2 = 80.5.

Question 12

The weights,in kilograms,of 17 randomly selected adults are given below.Find the interquartile range (IQR)by hand. 65.3 74.8 84.8 64.9 54.0 59.9
57.6 70.8 81.2 72.1 81.6 91.6
51.7 66.2 68.5 76.2 78.5
A)21.3 kg
B)51.7 kg
C)17.5 kg
D)13.6 kg
E)39.9 kg

Accepted Answer

To find the IQR, we first need to find the median of the dataset.

Arranging the dataset in ascending order: 
51.7, 54.0, 57.6, 59.9, 64.9, 65.3, 66.2, 68.5, 70.8, 72.1, 74.8, 76.2, 78.5, 81.2, 81.6, 84.8, 91.6

The median is the middle value of the dataset, which is the average of the two middle values since there are an odd number of values:

Median = (72.1 + 74.8)/2 = 73.45

To find the quartiles, we need to find the medians of the two halves of the dataset:

Lower quartile (Q1) = median of the lower half of the dataset 
Q1 = (59.9 + 64.9)/2 = 62.4

Upper quartile (Q3) = median of the upper half of the dataset 
Q3 = (81.2 + 81.6)/2 = 81.4

Now, we can find the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 81.4 - 62.4 = 19

Therefore, the correct answer is (C) 17.5 kg.

Question 13

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 140 grams to 305 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 148,246,and 202 grams.Find the range and IQR of the weights.
A)Range: 41 grams; IQR: 53 grams
B)Range: 98 grams; IQR: 165 grams
C)Range: 445 grams; IQR: 98 grams
D)Range: 41 grams; IQR: 165 grams
E)Range: 165 grams; IQR: 98 grams

Accepted Answer

The range is the difference between the maximum and minimum values (305 - 140 = 165 grams). The Interquartile Range (IQR) is the difference between the third quartile and the first quartile (246 - 148 = 98 grams).

Question 14

The weights,in kilograms,of 18 randomly selected adults are given below.Find the range. 54.4 74.8 84.8 64.9 54.0 59.9
57.6 70.8 81.2 72.1 81.6 91.6
51.7 66.2 68.5 76.2 78.5 65.3
A)(51.7 kg,91.6 kg)
B)(54.4 kg,91.6 kg)
C)91.6 kg
D)37.2 kg
E)39.9 kg

Accepted Answer

The answer of The weights,in kilograms,of 18 randomly selected adults...

Question 15

The number of cars passing through a Tim Hortons "drive-thru" during each 15-minute period was recorded.The results are shown below. 20 22 20 23
23 20 25 22
30 26 26 24
19 26 20 15
10 22 22 22
A)20 cars
B)23 cars
C)22 cars
D)21.85 cars
E)26 cars

Accepted Answer

The mode, which is the value that appears most frequently in a data set, is 22 cars as it appears 6 times in the list provided.

Question 16

A substitute teacher traveled the following distances,in kilometres,to arrive at work. 10 15 19 21 27 32 55
A)21
B)24
C)26
D)20
E)55

Accepted Answer

The question asks for the distance traveled to arrive at work and from the given choices, only option A (21 km) is a plausible distance for a commute. Option E (55 km) could be a possibility, but it seems like an unusually long commute for a substitute teacher. The other options are either too low or too high to be likely.

Question 17

The test scores of 19 students are listed below.Find the range. 91 99 86 54 72
85 97 91 90 66
82 83 78 88 77
80 92 94 98
A)(54,99)
B)(66,99)
C)33
D)45
E)44

Accepted Answer

The answer of The test scores of 19 students are...

Question 18

The semester point totals of 16 students are listed below.Find the interquartile range (IQR)by hand. 787 640 820 677
475 611 527 667
574 687 875 512
592 460 542 490
A)297
B)165
C)162.5
D)592
E)611

Accepted Answer

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). First, we need to order the data from smallest to largest: 460, 475, 490, 512, 527, 542, 574, 592, 611, 640, 667, 677, 687, 787, 820, 875. With 16 data points, Q1 is the average of the 4th and 5th values (512 and 527), and Q3 is the average of the 12th and 13th values (677 and 687). Q1 = (512 + 527) / 2 = 519.5, Q3 = (677 + 687) / 2 = 682. So, IQR = Q3 - Q1 = 682 - 519.5 = 162.5.

Question 19

A store manager kept track of the number of newspapers sold each week.The results are shown below. $$\begin{array} { l l l l l l l } 
89 & 30 & 203 & 193 & 261 & 249 & 246
\end{array}$$
A)182 newspapers
B)203 newspapers
C)261 newspapers
D)193 newspapers
E)246 newspapers

Accepted Answer

The number 203 is present in the list of newspapers sold each week.

Question 20

The test scores of 19 students are listed below.Find the upper quartile (Q3)by hand. 36 45 49 53 55
56 59 61 62 65
67 71 75 79 82
88 90 92 97
A)55.5
B)82.0
C)65.0
D)79.0
E)80.5

Accepted Answer

To find the upper quartile, we need to first find the median (Q2) of the data set. 
The median is the middle value, so we need to find the average of the two middle values since we have an odd number of data points.
Median (Q2) = (65+67)/2 = 66
Next, we need to find the median of the upper half of the data set. 
There are 9 data points to the right of the median, so we need to find the average of the two middle values in that set. 
The upper half of the data set is: 
67 71 75 79 82 88 90 92 97
Median of Upper Half (Q3) = (82+88)/2 = 85
Therefore, the upper quartile (Q3) is 85. Answer choice B is correct.

Quiz 3: Displaying and Summarizing Quantitative Data

A small company employs a supervisor at $1300 a week,an inventory manager at $600 a week,5 stock boys at $300 a week each,and 3 drivers at $500 a week each.

A new business had the following monthly revenues,in dollars. 6110 2729 1950 8233 8610 3144 1130 7269 4841 5175

The weekly salaries,in dollars,of 16 government workers are listed below.Find the upper quartile (Q3) by hand. $492 $791 $545 $840 $506 $734 $620 $815 $676 $874 $450 $561 $713 $473 $654 $527

The test scores of 15 students are listed below.Find the lower quartile (Q1) by hand. 41 49 50 55 58 64 65 68 72 76 85 87 90 94 95

Here are costs (in dollars) of 12 refrigerators.Find the range. $\begin{array} { l l l l l l } 845 & 970 & 635 & 545 & 1445 & 1070 \end{array}$ $\begin{array} { l l l l l l } 670 & 745 & 780 & 1270 & 535 & 1045 \end{array}$

The test scores of 19 students are listed below.Find the interquartile range (IQR) by hand. 91 47 86 70 59 64 97 55 90 78 82 83 50 88 75 43 92 94 67

The precipitation,in millimetres,for August is given for 20 different Canadian cities. 113 67 56 43 27 93 58 147 72 58 86 74 39 25 36 103 50 37 36 82

The weekly salaries,in dollars,of 16 government workers are listed below.Find the lower quartile (Q1) by hand. $\begin{array} { l l l l l } \$ 690 & \$ 589 & \$ 813 & \$ 656 \\\$ 728 & \$ 556 & \$ 491 & \$ 614 \\\$ 532 & \$ 662 & \$ 685 & \$ 462 \\\$ 542 & \$ 787 & \$ 511 & \$ 826\end{array}$

The annual incomes,in dollars,of several doctors are listed below. $\begin{array} { l l l l l } 130,000 & 132,000 & 188,000 & 242,000 & 238,000 \\148,000 & 114,000 & 833,000 & 200,000 & 151,000\end{array}$

Here are the weights,in grams,of several snack crackers. $\begin{array} { l l l l l l l } 25.23 & 34.59 & 22.11 & 45.93 & 19.56 & 22.40 & 31.18 \\34.59 & 43.37 & 27.22 & 25.23 & 36.00 & 39.69 & 20.13 \\13.32 & 36.00 & 22.40 & 39.69 & 48.76 & 19.56 & 15.88\end{array}$

The stem-and-leaf display shows the results of a math test written by 30 students. $\begin{array} { r | l } 10 & 0 \\9 & 11 \\8 & 01111123556689 \\7 & 556889 \\6 & 3778 \\5 & 48 \\4 & \\3 & 4 \\2 & 7 \\1 & \\0 &\end{array}$

The weights,in kilograms,of 17 randomly selected adults are given below.Find the interquartile range (IQR) by hand. 65.3 74.8 84.8 64.9 54.0 59.9 57.6 70.8 81.2 72.1 81.6 91.6 51.7 66.2 68.5 76.2 78.5

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 140 grams to 305 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 148,246,and 202 grams.Find the range and IQR of the weights.

The weights,in kilograms,of 18 randomly selected adults are given below.Find the range. 54.4 74.8 84.8 64.9 54.0 59.9 57.6 70.8 81.2 72.1 81.6 91.6 51.7 66.2 68.5 76.2 78.5 65.3

The number of cars passing through a Tim Hortons "drive-thru" during each 15-minute period was recorded.The results are shown below. 20 22 20 23 23 20 25 22 30 26 26 24 19 26 20 15 10 22 22 22

A substitute teacher traveled the following distances,in kilometres,to arrive at work. 10 15 19 21 27 32 55

The test scores of 19 students are listed below.Find the range. 91 99 86 54 72 85 97 91 90 66 82 83 78 88 77 80 92 94 98

The semester point totals of 16 students are listed below.Find the interquartile range (IQR) by hand. 787 640 820 677 475 611 527 667 574 687 875 512 592 460 542 490

A store manager kept track of the number of newspapers sold each week.The results are shown below. $\begin{array} { l l l l l l l } 89 & 30 & 203 & 193 & 261 & 249 & 246\end{array}$

The test scores of 19 students are listed below.Find the upper quartile (Q3) by hand. 36 45 49 53 55 56 59 61 62 65 67 71 75 79 82 88 90 92 97