Deck 3: Exploring Data: Central Tendency

Question 1

A distribution cannot have two means.

Answer 1

True

Question 2

A characteristic of the mean is that $\Sigma ( X - \bar { X } )$ is a minimum.

Answer 2

False

Question 3

For continuous data that are positively skewed, the mean is usually larger than the median

Answer 3

True

Question 4

The location of the median is found using the formula, $\frac { N + 1 } { 2 }$ .

Question 5

The mean is an appropriate measure of central tendency with open-ended distributions.

Question 6

If a distribution is skewed, the mean may be a misleading measure of central tendency.

Question 7

The mode is the midpoint between the largest score and the smallest score.

Question 8

The overall mean of 2 samples with different Ns is the sum of the two means divided by 2.

Question 9

Summing the scores and dividing by N produces the median.

Question 10

A distribution cannot have two medians.

Question 11

A characteristic of the mean is that $\Sigma ( X - \bar { X } )$ = 0.

Question 12

For continuous data that are positively skewed, the mean is usually smaller than the median.

Question 13

The location of the median is found using the formula, $\frac { N - 1 } { 2 }$ .

Question 14

The mean is an appropriate measure of central tendency for skewed distributions.

Question 15

The mode can be found for skewed distributions and open-ended distributions.

Question 16

The median is the midpoint between the two scores that establish the range.

Question 17

The overall mean of 2 samples with different Ns requires the formula for the weighted mean.

Question 18

For ordinal data, a median is an appropriate measure of central tendency.

Question 19

One way to find the median is to sum the scores and divide by N.

Question 20

A distribution cannot have two modes.

Question 21

A characteristic of the mean is that $\Sigma ( X - \bar { X } )$ is a minimum but greater than 0.

Question 22

For continuous data that are negatively skewed, the mean is usually smaller than the median.

Question 23

The location of the median is found using the formula, $\frac { N + 1 } { 4 }$ .

Question 24

The central tendency statistic that cannot be calculated on an open-ended distribution is the mean.

Question 25

The mean is appropriate for all four scales of measurement.

Question 26

A weighted mean is used when two samples have different Ns.

Question 27

Data Set 3-1 - CD A student was interested in the structure of the families in the U.S. He sampled 29 of his 330 classmates asking the question, "How many children are there in your family?" He compiled the answers into a simple frequency distribution:
$$\begin{array} { l r } X & f \\\hline 7 & 1 \\5 & 2 \\4 & 3 \\3 & 6 \\2 & 10 \\1 & 7\end{array}$$

-Refer to Data Set 3-1. The mean is

A) 3.67
B) 2.25
C) 2.35
D) none of the other alternatives are correct.

Question 28

Data Set 3-1 - CD A student was interested in the structure of the families in the U.S. He sampled 29 of his 330 classmates asking the question, "How many children are there in your family?" He compiled the answers into a simple frequency distribution:
$$\begin{array} { l r } X & f \\\hline 7 & 1 \\5 & 2 \\4 & 3 \\3 & 6 \\2 & 10 \\1 & 7\end{array}$$

-Refer to Data Set 3-1. A mean calculated for these data should be symbolized

A) $\mu$
B) $\overline { \mathrm { X } }$
C) either $\mu$ or $\overline { \mathrm { X } }$
D) neither $\mu$ nor $\overline { \mathrm { X } }$

Question 29

Data Set 3-1 - CD A student was interested in the structure of the families in the U.S. He sampled 29 of his 330 classmates asking the question, "How many children are there in your family?" He compiled the answers into a simple frequency distribution:
$$\begin{array} { l r } X & f \\\hline 7 & 1 \\5 & 2 \\4 & 3 \\3 & 6 \\2 & 10 \\1 & 7\end{array}$$

-Refer to Data Set 3-1. The median is

A) 5
B) 3.5
C) 3
D) 2.

Question 30

Data Set 3-1 - CD A student was interested in the structure of the families in the U.S. He sampled 29 of his 330 classmates asking the question, "How many children are there in your family?" He compiled the answers into a simple frequency distribution:
$$\begin{array} { l r } X & f \\\hline 7 & 1 \\5 & 2 \\4 & 3 \\3 & 6 \\2 & 10 \\1 & 7\end{array}$$

-Refer to Data Set 3-1. The mode is

A) 10
B) 8
C) 7
D) 2.

Question 31

Data Set 3-2: 5, 5, 1, 4, 4, 5

-The median of Data Set 3-2 is

A) 5
B) 4.5
C) 4
D) 24.

Question 32

Data Set 3-2: 5, 5, 1, 4, 4, 5

-The mean of Data Set 3-2 is

A) 5
B) 4.5
C) 4
D) 24.

Question 33

Data Set 3-2: 5, 5, 1, 4, 4, 5

-The mode of Data Set 3-2 is

A) 3
B) 4
C) 5
D) 6.

Question 34

Data Set 3-3: These data are representative of a freshman class at a Midwestern university.
$$\begin{array} { c c } \text { ACT Scores } & f \\\hline 35 & 1 \\33 & 1 \\32 & 1 \\28 & 3 \\27 & 3 \\26 & 5 \\22 & 2 \\20 & 1\end{array}$$

-The mean of Data Set 3-3 is

A) 26.0
B) 27.9
C) 57.4
D) 27.0

Question 35

Data Set 3-3: These data are representative of a freshman class at a Midwestern university.
$$\begin{array} { c c } \text { ACT Scores } & f \\\hline 35 & 1 \\33 & 1 \\32 & 1 \\28 & 3 \\27 & 3 \\26 & 5 \\22 & 2 \\20 & 1\end{array}$$

-The median of Data Set 3-3 is

A) 27.5
B) 27
C) 426
D) 8.5

Question 36

Data Set 3-3: These data are representative of a freshman class at a Midwestern university.
$$\begin{array} { c c } \text { ACT Scores } & f \\\hline 35 & 1 \\33 & 1 \\32 & 1 \\28 & 3 \\27 & 3 \\26 & 5 \\22 & 2 \\20 & 1\end{array}$$

-The mode of Data Set 3-3 is

A) 5
B) 16
C) 17
D) 26.

Question 37

Data Set 3-4
The descriptive statistics for these data are approximately the same as those of a freshman class at a small private college.
$$\begin{array} { c c } \text { ACT Scores } & f \\\hline 34 & 1 \\29 & 1 \\25 & 3 \\24 & 3 \\23 & 5 \\22 & 3 \\15 & 1\end{array}$$

-The mean of Data Set 3-4 is

A) 24.9
B) 58.0
C) 25.4
D) 23.9.

Question 38

Data Set 3-4
The descriptive statistics for these data are approximately the same as those of a freshman class at a small private college.
$$\begin{array} { c c } \text { ACT Scores } & f \\\hline 34 & 1 \\29 & 1 \\25 & 3 \\24 & 3 \\23 & 5 \\22 & 3 \\15 & 1\end{array}$$

-The median of Data Set 3-4 is

A) 8.5
B) 17
C) 23
D) 24.

Question 39

Data Set 3-4
The descriptive statistics for these data are approximately the same as those of a freshman class at a small private college.
$$\begin{array} { c c } \text { ACT Scores } & f \\\hline 34 & 1 \\29 & 1 \\25 & 3 \\24 & 3 \\23 & 5 \\22 & 3 \\15 & 1\end{array}$$

-The mode of Data Set 3-4 is

A) 3
B) 5
C) 22
D) 23.

Question 40

Data Set 3-5: 5, 1, 2, 1, 1, 5

-The median for Data Set 3-5 is

A) 1
B) 1.5
C) 2
D) 15.

Question 41

Data Set 3-5: 5, 1, 2, 1, 1, 5

-The mean of Data Set 3-5 is

A) 1.33
B) 2.33
C) 2.5
D) 15.

Question 42

Data Set 3-5: 5, 1, 2, 1, 1, 5

-The mode for Data Set 3-5 is

A) 1
B) 2
C) 3
D) 5.

Question 43

For a negatively skewed curve, the usual case with continuous data is that

A) high scores are more frequent than low scores and the mean is greater than the median
B) low scores are more frequent than high scores and the mean is greater than the median
C) high scores are more frequent than low scores and the median is greater than the mean
D) low scores are more frequent than high scores and the median is greater than the mean.

Question 44

Usually, a frequency distribution with a mean of 100 and a median of 90 is

A) positively skewed
B) negatively skewed
C) symmetrical
D) cannot be determined without knowing the mode.

Question 45

For a positively skewed curve, the usual case with continuous data is that

A) high scores are more frequent and the mean is larger than the median
B) low scores are more frequent and the mean is larger than the median
C) high scores are more frequent and the mean is smaller than the median
D) low scores are more frequent and the mean is smaller than the median.

Question 46

When the deviation scores, ( $X$ - $\overline { \mathrm { X } }$ ), are examined, your text noted two mathematical characteristics of the mean. These two characteristics involved

A) the maximum size of the mean and the minimum size of the mean
B) the size of the deviations when the mean is positive and the size when the mean is negative
C) the sum of the deviations and the size of the sum of the squared deviations
D) the maximum size of the deviations and their minimum size.

Question 47

Your text noted which of the following as a characteristic of the mean?

A) The sum of the results of squaring the difference between each score and the mean is zero.
B) The sum of the results of subtracting the mean from each score is a minimum.
C) Both of the descriptive alternatives.
D) Neither of the descriptive alternatives.

Question 48

Your text noted which of the following as a characteristic of the mean of a set of scores?

A) The sum is zero when the mean is subtracted from each score and these differences summed.
B) The sum of the results of scoring the difference between each score and the mean is a minimum.
C) Both of the descriptive alternatives.
D) Neither of the descriptive alternatives.

Question 49

Your text noted which of the following as a characteristic of the mean?

A) The sum of the results of squaring the difference between each score and the mean is a minimum.
B) The sum of the results of squaring the difference between each score and the mean is zero.
C) Both of the descriptive alternatives.
D) Neither of the descriptive alternatives.

Question 50

Your text noted which of the following as a characteristic of the mean of a set of scores?

A) If each score is squared, the sum will be greater than the mean.
B) If each score is squared, the sum will be less than the mean.
C) The sum of A's is zero, where A is the difference between each score and the mean.
D) None of the other alternatives are correct.

Question 51

Your text noted which of the following as a characteristic of the mean?

A) The sum of the results of subtracting the mean from each score is a minimum.
B) The sum of the results of subtracting the mean from each score is zero.
C) Both of the descriptive alternatives.
D) Neither of the descriptive alternatives.

Question 52

The median of 4, 3, 4, 2, 3, 4, 4, is

A) 3
B) 3.5
C) 4.5
D) 4

Question 53

The median of the numbers 7, 9, 8, 10, 11, 7, 8, is

A) 3.5
B) 8
C) 9
D) 22.5.

Question 54

The median of the numbers 3, 1, 2, 2, 3, 2, is

A) 2
B) 2.5
C) 3
D) 3.5.

Question 55

For scores of 8, 10, 8, 9, 8, 8, 9, 8, the median is

A) 8
B) 9
C) 4
D) 13.5.

Question 56

For scores of 6, 3, 7, 6, 6, 5, 6, 4, the median is

A) 4
B) 5
C) 6
D) 12.5.

Question 57

For scores of 6, 3, 5, 6, 4, 4, 6, 5, the median is

A) 9
B) 5
C) 4.5
D) 4.

Question 58

For scores of 4, 3, 1, 3, 2, 3, the median is

A) 5
B) 4
C) 3.5
D) 3.

Question 59

In an election Smith received 30 votes, Johnson 26, Williams 29, Jones 19, Brown 17, and Davis 31. (Smith is the most common name in the U.S., followed by Johnson, etc.) What is the mode of the distribution above?

A) 6
B) 31
C) Jones
D) none of the other alternatives are correct.

Question 60

The mean is the proper descriptive statistic when

A) you have nominal data
B) you have ordinal data
C) you have severely skewed data
D) none of the other alternatives are correct.

Question 61

In which situation would the mean be an appropriate measure of central tendency?

A) Most of the scores are near the minimum, a few are in the middle range, and there are almost none near the maximum
B) We have frequency data on cows, horses, mules, and goats
C) The data categories in the soil analysis are: 0-2 ppm, 3-5 ppm, 6-8 ppm, 9-11 ppm, and over 11 ppm
D) None of the other alternatives are correct.

Question 62

"For our study of driving habits, we recorded the speed of every fifth vehicle on Drury Lane. Nearly every car traveled right at the speed limit or a little over, but there were some that were 10 mph under, even fewer at 20 mph under, and one car that crept by at just 15 mph. On the basis of the central tendency calculation on our data, we drew conclusions about all drivers on this stretch of road." The proper central tendency value calculated from the data is the

A) population median
B) sample median
C) population mean ( $\mu$ )
D) sample mean ( $\overline { \mathrm { X } }$ ).

Question 63

Which of the following was not a consideration in deciding whether to use the mean as the appropriate measure of central tendency?

A) size and number of class intervals
B) degree of skew of the distribution
C) whether any class intervals have no upper limit or a lower limit
D) the scale of measurement used.

Question 64

The _______ is appropriate for skewed data with an open-ended category.

A) mean
B) median
C) mode
D) any of the other alternatives are correct.

Question 65

The U.S. Department of Agriculture reported the total number of bushels harvested of corn, soybeans, wheat, rice, and oats. This is a frequency distribution of a _______ variable; the proper measure of central tendency is a _______.

A) nominal mode
B) ordinal mode
C) nominal median
D) ordinal median.

Question 66

If trees in a forest were classified as pine, cedar, oak, hickory and other, the appropriate measure of central tendency would be

A) the mean
B) the median
C) the mode
D) any of the other alternatives are correct.

Question 67

Imagine a bar graph with the following categories and frequencies: almonds, 4; betel, 6; cashew, 3; donut, 7. The central tendency statistic that is appropriate and its value:

A) median, 4
B) median, 5
C) mode, 7
D) mode, donut.

Question 68

Imagine a bar graph with the following categories and frequencies: Alpha, 2; Beta, 4; Gamma, 1; Delta, 5. The central tendency statistic that is appropriate and its value:

A) median, 5
B) median, 3
C) mode, 5
D) mode, Delta.

Question 69

For which situation below is the mean the appropriate measure of central tendency?

A) the number of hours completed by college graduates, with categories of 120-129, 130-139, 140-149, 150-159, 160 and over.
B) the birds sighted on the annual Audubon bird count, with categories of blue jay, purple finch, scarlet tanager, crow, etc.
C) reaction time in stepping on the brake of a car when danger looms. This distribution is quite skewed
D) none of the other alternatives are correct.

Question 70

Suppose a distribution of scores had a mean of -6 and a median of +6. In the usual case for continuous data, you would conclude

A) the distribution is positively skewed
B) the distribution is negatively skewed
C) nothing about skewness unless additional information is given
D) that such scores are logically impossible.

Question 71

A distribution of scores had a mean of 30 and a median of 40. In the usual case of continuous data, the distribution is

A) positively skewed
B) negatively skewed
C) symmetrical
D) need to know the mode to make a decision.

Question 72

A frequency distribution had a mean of 3 and a median of -3. In the usual case of continuous data the distribution is

A) positively skewed
B) negatively skewed
C) symmetrical
D) you would have to know the mode in order to answer the question.

Question 73

In a negatively skewed curve the mean is usually

A) larger than the median
B) smaller than the median
C) exactly equal to the median
D) not https://d2lvgg3v3hfg70.cloudfront.net/TB9561/.

Question 74

If the mean of 7, 4, 4 is 5.0 and the mean of 14, 3, 7, 4 is 7.0, the weighted mean i

A) 6.0
B) 21.5
C) 4
D) none of the other alternatives are correct.

Question 75

The mean of 2, 3, and 4 is 3.0. The mean of 5, 6, 7, 8, and 9 is 7.0. The weighted mean is

A) 5.0
B) 4.5
C) 5.5

Question 76

The mean temperature for June was 70 $\degree$ F, for July it was 75 $\degree$ F, and for August it was 80 $\degree$ F. You should conclude that the overall mean for the three months is

A) 75 $\degree$ F
B) more than 75 $\degree$ F
C) less than 75 $\degree$ F.

Question 77

The mean temperature for January was 30 $\degree$ F. In February the mean was 25 $\degree$ F and for March the mean was 35 $\degree$ F. The weighted mean for these three months is

A) 30 $\degree$ F
B) greater than 30 $\degree$ F
C) less than 30 $\degree$ F.

Question 78

Suppose the mean ACT score for high school seniors in Big City was 21; for Small Town seniors was 20 and for Tiny Berg seniors was 19. The mean of the seniors in the three places is

A) 20
B) less than 20
C) more than 20.

Question 79

The mean salary for all those with a Bachelors degree was $40,000; for all those with Masters degrees, $60,000; and for all those with doctorates, $80,000. The weighted mean salary will be

A) $60,000
B) less than $60,000
C) more than $60,000.

Question 80

Two investigators tested their friends for memory span. The first tested five people and found a mean of 6.0. The second tested nine people and found a mean of 7.0. The weighted mean for the data is

A) 6.00
B) 6.50
C) 6.64
D) 7.00.