Deck 13: Finding Measures of Central Tendency for Prices and Heights

Question 1

Find the median.
8, 4, 28, 10, 29, 41, 35, 33

A)28.5
B)23.5
C)28
D)29

Answer 1

A

Question 2

Find the mean.
27, 39, 11, 35, 8, 39, 9

A)24
B)21
C)39
D)27

Answer 2

A

Question 3

Solve the problem.
The Wellspring Company has a fleet of seven trucks which get gas mileages of $19,8,16,14,18,8$ , and 25 miles per gallon, respectively. What is the mean gas mileage for the fleet? Round your answer to the nearest mpg.

A) $14 \mathrm { mpg }$
B) $18 \mathrm { mpg }$
C) $16 \mathrm { mpg }$
D) $15 \mathrm { mpg }$

Answer 3

D

Question 4

Find any modes that exist.
20, 21, 46, 21, 49, 21, 49

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

Question 5

Find the median.
13, 57, 275, 215, 378, 470

A)275
B)215
C)201.5
D)245

Question 6

Find any modes that exist.
$$\$ 83 , \$ 41 , \$ 32 , \$ 41 , \$ 29 , \$ 83$$

A) No mode exists.
B) $\$ 83 , \$ 41$
C) $\$ 83$
D) $\$ 41$

Question 7

Find the median.
67, 66, 222, 150, 251, 241, 232

A)222
B)150
C)176
D)232

Question 8

Solve the problem.
The five sales people at Southwest Appliances earned commissions last year of $\$ 20,000 , \$ 29,000 , \$ 48,000$ , $\$ 17,000$ , and $\$ 29,000$ . Find the mean commission.

A) $\$ 31,460$
B) $\$ 27,170$
C) $\$ 30,030$
D) $\$ 28,600$

Question 9

Find the median.
2, 3, 20, 21, 33, 33, 47

A)20
B)33
C)23
D)21

Question 10

Solve the problem.
Some players are thinking about quitting the company softball team. Their batting averages are $0.223,0.281$ , $0.223,0.331,0.206,0.339$ , and $0.271$ , respectively. What is the mean batting average of these players? Round your answer to the nearest thousandth.

A) $0.281$
B) $0.312$
C) $0.244$
D) $0.268$

Question 11

Find the mean.
8.4, 8.6, 6.8, 8.6, 6.6

A)8.6
B)6.5
C)8.4
D)7.8

Question 12

Find any modes that exist.
106, 150, 156, 106, 188, 199, 162

A)85
B)150
C)106
D)156

Question 13

Find the median.
$\$ 69.15 , \$ 52.55 , \$ 81.40 , \$ 74.35 , \$ 52.55$

A) $\$ 52.55$
B) $\$ 66.00$
C) $\$ 81.40$
D) $\$ 69.15$

Question 14

Find any modes that exist.
5, 9, 97, 3, 2, 8, 69, 1, 4, 16

A)No mode exists.
B)9
C)20.8
D)8

Question 15

Find any modes that exist.
93, 25, 93, 13, 25, 29, 56, 93

A)93
B)25
C)93, 25
D)53.4

Question 16

Find the mean.
33, 43, 19, 39, 16

A)30
B)25
C)43
D)33

Question 17

Find the median.
2.7, 4.7, 8.5, 3.5

A)3.5
B)4.7
C)4.1
D)8.5

Question 18

Find the mean.
$\$ 22.75 , \$ 51.00 , \$ 39.15 , \$ 44.35 , \$ 22.75$

A) $\$ 39.15$
B) $\$ 30.00$
C) $\$ 22.75$
D) $\$ 36.00$

Question 19

Find the median.
13, 16, 35, 52, 63, 63, 79

A)63
B)46
C)52
D)35

Question 20

Find any modes that exist.
7.2, 7.4, 5.6, 7.4, 5.4

A)7.2
B)7.4
C)5.5
D)6.6

Question 21

Evaluate.
$\left| \begin{array} { r r } 8 & - 9 \\ - 2 & 1 \end{array} \right|$
B) 26
C) $- 70$
D) $- 10$

A) 10
B) 26

Question 22

Evaluate.
$\left| \begin{array} { r r r } 5 & 8 & 9 \\ 3 & 8 & 5 \\ 6 & 5 & 2 \end{array} \right|$

A) $- 150$
B) $- 630$
C) 1060
D) 150

Question 23

Use synthetic division to divide.
$$\left( x ^ { 4 } - 625 \right) \div ( x + 5 )$$

A) $x ^ { 3 } + 5 x ^ { 2 } - 25 x + 125$
B) $x ^ { 3 } - 5 x ^ { 2 } + 25 x - 125$
C) $x ^ { 2 } + 5 x + 25$
D) $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125$

Question 24

Solve the problem.
The following is a list of heights, in inches, of six people:
$\begin{array} { l l } \text { Susan } & 66 \\ \text { Umar } & 74 \\ \text { Mark } & 75 \\ \text { Dorota } & 66 \\ \text { Mike } & 76 \\ \text { Gina } & 65 \end{array}$
What is the mode?

A) 70 inches
B) $70.5$ inches
C) 66 inches
D) 74 inches

Question 25

Use synthetic division to divide.
$$\left( 7 x ^ { 2 } + 12 x - 27 \right) \div ( x + 3 )$$

A) $x - 9$
B) $7 x - 9$
C) $- 7 x + 9$
D) $- 9 x + 3$

Question 26

Solve the problem.
Anthony wanted to buy a particular kind of cheese. He checked in five different stores and found the following I per pound:
$\$ 6.75 , \$ 5.25 , \$ 6.45 , \$ 5.75$ , and $\$ 5.65$ .
What was the mean price per pound?

A) $\$ 6.75$
B) $\$ 5.75$
C) $\$ 6.07$
D) $\$ 5.97$

Question 27

Use synthetic division to divide.
$$\left( 6 m ^ { 3 } + 10 m ^ { 2 } - 18 m + 18 \right) \div ( m + 3 )$$

A) $m ^ { 2 } + 8 m + 6$
B) $6 m ^ { 2 } + 8 m + 6$
C) $m ^ { 2 } + 9 m + 10$
D) $6 m ^ { 2 } - 8 m + 6$

Question 28

Solve the problem.
The following is a list of heights, in inches, of six people:
$\begin{array} { l l } \text { Susan } & 66 \\ \text { Umar } & 75 \\ \text { Mark } & 74 \\ \text { Dorota } & 66 \\ \text { Mike } & 76 \\ \text { Gina } & 64 \end{array}$
What is the median height?

A) $70.5$ inches
B) 70 inches
C) 66 inches
D) 74 inches

Question 29

Use synthetic division to divide.
$$\left( x ^ { 5 } - 243 \right) \div ( x - 3 )$$

A) $x ^ { 4 } + 3 x ^ { 3 } + 9 x ^ { 2 } + 27 x + 81$
B) $x ^ { 4 } + 3 x ^ { 3 } + 9 x ^ { 2 } + 27 x + 81 + \frac { - 243 } { x - 3 }$
C) $x ^ { 4 } - 3 x ^ { 3 } + 9 x ^ { 2 } - 27 x + 81$
D) $x ^ { 4 } + 3 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 3$

Question 30

Use synthetic division to divide.
$$\left( x ^ { 4 } + 625 \right) \div ( x - 5 )$$

A) $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125 + \frac { 625 } { x - 5 }$
B) $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125$
C) $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125 + \frac { 1250 } { x - 5 }$
D) $x ^ { 3 } - 5 x ^ { 2 } + 25 x - 125 + \frac { 1250 } { x - 5 }$

Question 31

Use synthetic division to divide.
$$\left( x ^ { 3 } - 2 x ^ { 2 } + 2 x - 7 \right) \div ( x + 4 )$$

A) $x ^ { 2 } - 6 x + 26 + \frac { - 111 } { x + 4 }$
B) $x ^ { 2 } - 6 x + 26 + \frac { - 111 } { \left( x ^ { 3 } - 2 x ^ { 2 } + 2 x - 7 \right) }$
C) $x ^ { 2 } - 6 x + 10 + \frac { - 47 } { x + 4 }$
D) $x ^ { 3 } - 2 x ^ { 2 } + 26 x - 111$

Question 32

Use synthetic division to divide.
$$\left( 8 r ^ { 3 } - 60 r ^ { 2 } - 27 r - 40 \right) \div ( r - 8 )$$

A) $r ^ { 2 } + 5 r + 4$
B) $8 r ^ { 2 } + 4 r + \frac { 5 } { r - 8 }$
C) $8 r ^ { 2 } + 4 r + 5$
D) $8 r ^ { 2 } - 4 r - 5$

Question 33

Solve the problem.
The following prices per pound of ocean perch were found at seven supermarkets:
$$\$ 7.59 , \$ 8.49 , \$ 8.39 , \$ 8.59 , \$ 7.59 , \$ 8.29 , \$ 7.39$$
What is the median price per pound?

A) $\$ 7.59$
B) $\$ 8.59$
C) $\$ 8.39$
D) $\$ 8.29$

Question 34

Solve the problem.
Jeremy's car gets 294 miles of highway driving on 7 gallons of gasoline. What is the mean number of miles expected per gallon -- that is, what is its gas mileage?

A) 43 mpg
B) $44 \mathrm { mpg }$
C) $42 \mathrm { mpg }$
D) $41 \mathrm { mpg }$

Question 35

Use synthetic division to divide.
$$\left( y ^ { 6 } + 3 \right) \div ( y - 1 )$$

A) $y ^ { 5 } + y ^ { 4 } + y ^ { 3 } + y ^ { 2 } + y + 1 + \frac { 4 } { y - 1 }$
B) $y ^ { 5 } + y ^ { 4 } + y ^ { 3 } + y ^ { 2 } + y + 1$
C) $y ^ { 5 } - y ^ { 4 } + y ^ { 3 } - y ^ { 2 } + y - 1$
D) $y ^ { 5 } - y ^ { 4 } + y ^ { 3 } - y ^ { 2 } + y - 1 + \frac { 4 } { y - 1 }$

Question 36

Solve the problem.
The following prices per pound of ocean perch were found at seven supermarkets:
$$\$ 6.59 , \$ 7.49 , \$ 7.39 , \$ 7.59 , \$ 6.59 , \$ 7.29 , \$ 6.39$$
What is the mode?

A) $\$ 7.59$
B) $\$ 6.59$
C) $\$ 7.39$
D) $\$ 7.29$

Question 37

Evaluate.
$\left| \begin{array} { r r r } 5 & - 4 & - 4 \\ 2 & - 3 & - 4 \\ - 2 & 4 & 3 \end{array} \right|$
B) 19
C) $- 237$
D) $- 19$

A) 83
B) 19
C) $- 237$
D) $- 19$

Question 38

Evaluate.
$\left| \begin{array} { l l } 6 & 8 \\ 9 & 5 \end{array} \right|$

A) 3
B) 102
C) $- 42$
D) 42

Question 39

Use synthetic division to divide.
$$\left( y ^ { 9 } + 1 \right) \div ( y + 1 )$$

A) $y ^ { 8 } + y ^ { 7 } + y ^ { 6 } + y ^ { 5 } + y ^ { 4 } + y ^ { 3 } + y ^ { 2 } + y + 1 + \frac { 2 } { y + 1 }$
B) $y ^ { 8 } + y ^ { 7 } + y ^ { 6 } + y ^ { 5 } + y ^ { 4 } + y ^ { 3 } + y ^ { 2 } + y + 1$
C) $y ^ { 8 } - y ^ { 7 } + y ^ { 6 } - y ^ { 5 } + y ^ { 4 } - y ^ { 3 } + y ^ { 2 } - y + 1$
D) $y ^ { 8 } - y ^ { 7 } + y ^ { 6 } - y ^ { 5 } + y ^ { 4 } - y ^ { 3 } + y ^ { 2 } - y + 1 + \frac { - 2 } { y + 1 }$

Question 40

Evaluate.
$\left| \begin{array} { r r } 1 & - 1 \\ 2 & 2 \end{array} \right|$

A) 4
B) $- 4$
C) $- 5$
D) 0

Question 41

Evaluate.
$$\left| \begin{array} { r r r } 7 & - 5 & 3 \\0 & 1 & 2 \\0 & 0 & - 9\end{array} \right|$$

A) $- 73$
B) 53
C) $- 63$
D) 63

Question 42

Solve using Cramer's rule.
$$\begin{array} { r } 3 x - 7 y - z = - 40 \\x - 4 y - 5 z = - 36 \\- 9 x + y + z = - 44\end{array}$$

A) $( 6 , - 8 , - 2 )$
B) $( 7,6,2 )$
C) $( 6,8,2 )$
D) $( 8,2,8 )$

Question 43

Solve using matrices.
$$\begin{array} { l } 2 x + y = 6 \\9 x + 2 y = 37\end{array}$$

A) $( - 4 , - 5 )$
В) $( 5 , - 5 )$
C) $( 5 , - 4 )$
D) $( - 4,5 )$

Question 44

Solve using Cramer's rule.
$$\begin{array} { l } 5 x + 5 y = 10 \\5 x + y = - 10\end{array}$$

A) $( 5 , - 3 )$
В) $( - 3,5 )$
C) $( 3 , - 5 )$
D) $( - 5 , - 3 )$

Question 45

Evaluate.
$$\left| \begin{array} { l l l } 3 & 5 & 1 \\3 & 4 & 3 \\2 & 2 & 4\end{array} \right|$$

A) $- 62$
B) $- 2$
C) 170
D) 2

Question 46

Solve using matrices.
$$\begin{array} { l } x - 5 y = - 4 \\x + 8 y = - 4\end{array}$$

A) $( 0 , - 4 )$
B) $( 4,0 )$
C) $( 0,4 )$
D) $( - 4,0 )$

Question 47

Solve using matrices.
$$\begin{array} { c } x + 6 y = 6 \\2 x - 5 y = - 5\end{array}$$

A) $( 0,0 )$
B) $( 0,1 )$
C) $( 1,0 )$
D) $( 1,1 )$

Question 48

Solve using Cramer's rule.
$$\begin{array} { l } 8 a \quad + 3 c = 69 \\5 a + 9 b - 9 c = 30 \\5 a - 9 b \quad = - 33\end{array}$$

A) $( 7,7,7 )$
В) $( 6 , - 7 , - 7 )$
C) $( 6,7,7 )$
D) $( 7,5,7 )$

Question 49

Solve using Cramer's rule.
$$\begin{array} { l } 2 x + 2 y = 22 \\2 x - 2 y = 2\end{array}$$

A) $( 5,6 )$
В) $( - 5,6 )$
C) $( 6,5 )$
D) $( - 6 , - 5 )$

Question 50

Solve using matrices.
$$\begin{array} { c } 5 x - 2 y = - 1 \\x + 4 y = 35\end{array}$$

A) $( 2,8 )$
B) $( 2,9 )$
C) $( 3,9 )$
D) $( 3,8 )$

Question 51

Solve using matrices.
$$\begin{array} { r } x + 7 y = - 2 \\3 x + y = 34\end{array}$$

A) $( 3,7 )$
B) $( 12 , - 2 )$
C) $( 7,12 )$
D) $( - 2,3 )$

Question 52

Solve using Cramer's rule.
$$\begin{array} { l } 3 x - 7 y - 5 z = - 58 \\2 x + 6 y - 7 z = 25 \\- 4 x - 6 y - 2 z = - 56\end{array}$$

A) $( 3,5,3 )$
B) $( 2 , - 7 , - 3 )$
C) $( 7,3,7 )$
D) $( 2,7,3 )$

Question 53

Evaluate.
$\left| \begin{array} { r r r } 7 & 0 & 0 \\ 9 & - 9 & 0 \\ - 9 & 3 & 5 \end{array} \right|$

A) $- 342$
B) 288
C) 315
D) $- 315$

Question 54

Solve using matrices.
$$\begin{array} { l } 5 x + 6 y = 20 \\2 x + 8 y = 36\end{array}$$

A) $( - 2,5 )$
B) $( 5,2 )$
C) $( - 2 , - 5 )$
D) $( 5 , - 2 )$

Question 55

Evaluate.
$\left| \begin{array} { l l l } 3 & 4 & 6 \\ 5 & 3 & 5 \\ 1 & 4 & 6 \end{array} \right|$
B) $- 44$
C) $- 4$
D) 4

A) 392

Question 56

Evaluate.
$$\left| \begin{array} { r r r } 0 & 0 & 9 \\6 & - 7 & 9 \\0 & 3 & 3\end{array} \right|$$

A) $- 162$
B) 162
C) 141
D) $- 183$

Question 57

Solve using Cramer's rule.
$$\begin{array} { l } 2 x - 2 y = 2 \\2 x + 3 y = 37\end{array}$$

A) $( - 7,8 )$
B) $( - 8 , - 7 )$
C) $( 7,8 )$
D) $( 8,7 )$