Deck 3: Measures of Central Tendency

Question 1

Which of the following measures of central tendency can be used when examining gender distribution?

A) mode
B) median
C) mean
D) all of the above

Answer 1

mode

Question 2

Which of the following measures of central tendency can be used when working with ordinal variables?

A) mode
B) median
C) mean
D) both a and b

Answer 2

both a and b

Question 3

Which of the following measures of central tendency can be used when working with interval/ratio variables?

A) mode
B) median
C) mean
D) all of the above

Answer 3

all of the above

Question 4

Which of the following measures of central tendency can be used when examining the age distribution of your classmates?

A) mode
B) median
C) mean
D) all of the above

Question 5

In the following table, which race represents the mode?
$\begin{array}{ l }\text { } \text { \(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)RACE OF RESPONDENT } & \\\begin{array}{|l|l|l|l|ll|} \hline \text { } & \text { Frequency } & \text { percent } & \text { Valid percent } & \text { Cumulatieve Percent } \\\hline \text { Valid \(~~ ~~~\) 1 WHITE } & 3284 & 72.8 & 72.8 & 72.8 \\ \text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) 2 BLACK } & 634 & 14.1 & 14.1 & 86.9 & \\\text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) 3 OTHER } & 592 & 13.1 & 13.1 & 100.0 & \\\text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) Total } & 4510 & 100.0 & 100.0 & \\\hline\end{array}\end{array}$

A) white
B) black
C) other

Question 6

Use the following table to answer questions
HAPPINESS OF MARRIAGE
$\begin{array}{ l }\text { } \text { \(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\) } & \\\begin{array}{|l|l|l|lll|} \hline \text { } & \text { Frequency } & \text { percent } & \text { Cumulatieve Percent } \\\hline \text { Valid \(~~ ~~~\) 1 VERY HAPPY } & 861 & 61.1 & 61.1 & \\ \text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) 2 PRETTY HAPPY } & 512 & 36.3 & 97.4 & \\\text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) 3 NOT TOO HAPPY } & 37 & 2.6 & 100.0 & \\\text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) Total } & 1410 & 100.0 & & \\\hline\end{array}\end{array}$

-What is the mode?

A) very happy
B) pretty happy
C) not too happy
D) 512

Question 7

Use the following table to answer questions
HAPPINESS OF MARRIAGE
$\begin{array}{ l }\text { } \text { \(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\) } & \\\begin{array}{|l|l|l|lll|} \hline \text { } & \text { Frequency } & \text { percent } & \text { Cumulatieve Percent } \\\hline \text { Valid \(~~ ~~~\) 1 VERY HAPPY } & 861 & 61.1 & 61.1 & \\ \text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) 2 PRETTY HAPPY } & 512 & 36.3 & 97.4 & \\\text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) 3 NOT TOO HAPPY } & 37 & 2.6 & 100.0 & \\\text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) Total } & 1410 & 100.0 & & \\\hline\end{array}\end{array}$

-What is the median?

A) very happy
B) pretty happy
C) not too happy
D) 512

Question 8

Use the following table to answer questions
HAPPINESS OF MARRIAGE
$\begin{array}{ l }\text { } \text { \(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\)\(~~~~\) } & \\\begin{array}{|l|l|l|lll|} \hline \text { } & \text { Frequency } & \text { percent } & \text { Cumulatieve Percent } \\\hline \text { Valid \(~~ ~~~\) 1 VERY HAPPY } & 861 & 61.1 & 61.1 & \\ \text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) 2 PRETTY HAPPY } & 512 & 36.3 & 97.4 & \\\text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) 3 NOT TOO HAPPY } & 37 & 2.6 & 100.0 & \\\text { \(~~ ~~~\) \(~~ ~~\) \(~~~~\) Total } & 1410 & 100.0 & & \\\hline\end{array}\end{array}$

-What is the mean?

A) 470
B) 861
C) 512
D) mean cannot be calculated

Question 9

What is the mode of the following numbers? 28, 5, 17, 14, 17, 30, 51, 5, 17, 22

A) 5
B) 14
C) 17
D) 20.6

Question 10

What is the median of the following numbers? 28, 5, 17, 14, 17, 30, 51, 5, 17, 22

A) 5
B) 14
C) 17
D) 20.6

Question 11

What is the mean of the following numbers? 28, 5, 17, 14, 17, 30, 51, 5, 17, 22

A) 5
B) 14
C) 17
D) 20.6

Question 12

What is the median age of the following students?
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { Student } & \text { Age } \\\hline 1 & 18 \\\hline 2 & 22 \\\hline 3 & 19 \\\hline 4 & 21 \\\hline 5 & 24 \\\hline 6 & 26 \\\hline\end{array}\end{array}$

A) 19
B) 20
C) 21
D) 21.5

Question 13

What is the median age of the following students?
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { Student } & \text { Age } \\\hline 1 & 18 \\\hline 2 & 22 \\\hline 3 & 19 \\\hline 4 & 21 \\\hline 5 & 24 \\\hline 6 & 26 \\\hline 7 & 19 \\\hline\end{array}\end{array}$

A) 19
B) 20
C) 21
D) 21.5

Question 14

What is the mean age of the following students?

$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { Student } & \text { Age } \\\hline 1 & 18 \\\hline 2 & 22 \\\hline 3 & 19 \\\hline 4 & 21 \\\hline 5 & 24 \\\hline 6 & 26 \\\hline 7 & 19 \\\hline\end{array}\end{array}$

A) 19
B) 20
C) 21.3
D) 24.9

Question 15

What is the mode in the following age distribution of students?
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { Student } & \text { Age } \\\hline 1 & 18 \\\hline 2 & 22 \\\hline 3 & 19 \\\hline 4 & 21 \\\hline 5 & 24 \\\hline 6 & 26 \\ \hline\end{array}\end{array}$

A) 18
B) 21.5
C) 26
D) none of the above, there is no single mode

Question 16

Use the following table to answer questions :
NUMBER OF CHILDREN
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { } & \text { Frequency } \\\hline \text {Valid \(~~ ~~~\) \(~~ ~~~\) } 1 & 710 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 2 & 1147 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 3 & 738 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 4 & 386 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 5 & 139 \\ \hline\end{array}\end{array}$

-What is the mode?

A) 1 child
B) 2 children
C) 3 children
D) 4 children

Question 17

Use the following table to answer questions :
NUMBER OF CHILDREN
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { } & \text { Frequency } \\\hline \text {Valid \(~~ ~~~\) \(~~ ~~~\) } 1 & 710 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 2 & 1147 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 3 & 738 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 4 & 386 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 5 & 139 \\ \hline\end{array}\end{array}$

-What is the median?

A) 1 child
B) 2 children
C) 3 children
D) 4 children

Question 18

Use the following table to answer questions :
NUMBER OF CHILDREN
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { } & \text { Frequency } \\\hline \text {Valid \(~~ ~~~\) \(~~ ~~~\) } 1 & 710 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 2 & 1147 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 3 & 738 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 4 & 386 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 5 & 139 \\ \hline\end{array}\end{array}$

-What is the mean number of children?

A) 1.5
B) 2.4
C) 624
D) 1147

Question 19

Histograms should be used to present what type of variables?

A) nominal
B) ordinal
C) interval/ratio
D) none of the above

Question 20

If the mean of a distribution is greater than the mode, the distribution is .

A) negatively skewed
B) positively skewed
C) normal
D) symmetrical

Question 21

If the mode of a distribution is greater than the mean, the distribution is .

A) negatively skewed
B) positively skewed
C) normal
D) symmetrical

Question 22

Measures of central tendency indicate the range of all cases.

Question 23

Measures of central tendency indicate what is typical, or where cases tend to cluster, in a distribution.

Question 24

The value of the middle case in a rank-ordered distribution is the average.

Question 25

Outliers are only the cases with the highest values.

Question 26

The mean is calculated by summing all cases and dividing by N+1.

Question 27

The median is the measure of central tendency most affected by outliers.

Question 28

If the mean is greater than the mode we know that more cases with higher values exist in the data.

Question 29

Use the following data to answer questions:
15
29
20
14
20
30
49
20
63
-What is the mode for the distribution?

Question 30

Use the following data to answer questions:
15
29
20
14
20
30
49
20
63
-What is the median of the above distribution?

Question 31

Use the following data to answer questions:
15
29
20
14
20
30
49
20
63
-What is the mean of the above distribution?

Question 32

Use the following data to answer questions:
15
29
20
14
20
30
49
20
63

-Is this distribution symmetrical, negatively skewed, or positively skewed? How did you determine this?

Question 33

Use the following table to answer questions :
AGE OF RESPONDENT
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { } & \text { Frequency } \\\hline \text {Valid \(~~ ~~~\) \(~~ ~~~\) } 18 & 19 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 19 & 47 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 20 & 50 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 21 & 52 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 22 & 72 \\ \hline \text { Total } & 240 \\ \hline\end{array}\end{array}$

-What is the mode?

Question 34

Use the following table to answer questions :
AGE OF RESPONDENT
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { } & \text { Frequency } \\\hline \text {Valid \(~~ ~~~\) \(~~ ~~~\) } 18 & 19 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 19 & 47 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 20 & 50 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 21 & 52 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 22 & 72 \\ \hline \text { Total } & 240 \\ \hline\end{array}\end{array}$

-What is the median?

Question 35

Use the following table to answer questions :
AGE OF RESPONDENT
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { } & \text { Frequency } \\\hline \text {Valid \(~~ ~~~\) \(~~ ~~~\) } 18 & 19 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 19 & 47 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 20 & 50 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 21 & 52 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 22 & 72 \\ \hline \text { Total } & 240 \\ \hline\end{array}\end{array}$

-What is the mean age?

Question 36

Use the following table to answer questions :
AGE OF RESPONDENT
$\begin{array}{l}\text { } \\\begin{array}{|l|l|}\hline \text { } & \text { Frequency } \\\hline \text {Valid \(~~ ~~~\) \(~~ ~~~\) } 18 & 19 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 19 & 47 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 20 & 50 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 21 & 52 \\\hline \text { \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } 22 & 72 \\ \hline \text { Total } & 240 \\ \hline\end{array}\end{array}$

-Is this distribution normal, negatively skewed, or positively skewed? How did you determine this?

Question 37

Below is a ranking of the ten highest state-level unemployment rates at the end of 2010. Use this information to answer questions :
$\begin{array}{l}\text { } \\\begin{array}{|ll|}\hline \text { Michigan\(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 9.6 \\ \text {Rhode island \(~~ ~~~\) \(~~ ~~~\) } & 9.3 \\ \text {Califoline \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8.4 \\ \text {South Caroline\(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8.4 \\ \text {Orgon \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8.1 \\ \text {District of Columbia \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8 \\ \text {North Caroline \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 7.9 \\ \text {Georgia \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 7.5 \\ \text {A;aska \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 7.3 \\\hline\end{array}\end{array}$


-What is the mode?

Question 38

Below is a ranking of the ten highest state-level unemployment rates at the end of 2010. Use this information to answer questions :
$\begin{array}{l}\text { } \\\begin{array}{|ll|}\hline \text { Michigan\(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 9.6 \\ \text {Rhode island \(~~ ~~~\) \(~~ ~~~\) } & 9.3 \\ \text {Califoline \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8.4 \\ \text {South Caroline\(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8.4 \\ \text {Orgon \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8.1 \\ \text {District of Columbia \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8 \\ \text {North Caroline \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 7.9 \\ \text {Georgia \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 7.5 \\ \text {A;aska \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 7.3 \\\hline\end{array}\end{array}$


-What is the median unemployment rate?

Question 39

Below is a ranking of the ten highest state-level unemployment rates at the end of 2010. Use this information to answer questions :
$\begin{array}{l}\text { } \\\begin{array}{|ll|}\hline \text { Michigan\(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 9.6 \\ \text {Rhode island \(~~ ~~~\) \(~~ ~~~\) } & 9.3 \\ \text {Califoline \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8.4 \\ \text {South Caroline\(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8.4 \\ \text {Orgon \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8.1 \\ \text {District of Columbia \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 8 \\ \text {North Caroline \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 7.9 \\ \text {Georgia \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 7.5 \\ \text {A;aska \(~~ ~~~\) \(~~ ~~~\)\(~~ ~\) \(~~ ~~~\) } & 7.3 \\\hline\end{array}\end{array}$


-What is the mean?