Deck 4: Central Tendency and Dispersion

Question 1

A variable that has a bimodal distribution

A) has no mode
B) has two modes
C) is negatively skewed
D) is positively skewed

Answer 1

has two modes

Question 2

What is the lowest level of measurement for which it is permissible to calculate a median?

A) nominal
B) ordinal
C) interval/ratio

Answer 2

ordinal

Question 3

You want to know the approximate average distance of cases from the mean on a particular variable. What statistic would you calculate?

A) median
B) range
C) standard deviation
D) variance

Answer 3

standard deviation

Question 4

It is customary when describing the scores on an interval/ratio variable to report the values of which four statistics?

A) mean, median, mode, and variance
B) mean, standard deviation, minimum, and maximum
C) range, standard deviation, variance, and percent distribution
D) mode, standard deviation, minimum, and interquartile range

Question 5

Which of the following is a univariate statistic?

A) mean
B) range
C) variance
D) all of the above are univariate statistics

Question 6

It is customary when describing the scores on an ordinal variable to report the values of which three statistics?

A) mean, median, and mode
B) median, minimum, and maximum
C) median, standard deviation, and variance
D) mode, minimum, and maximum

Question 7

If the standard deviation in commuting time to work is 9 minutes, the variance is

A) 3 minutes
B) 9 minutes
C) 18 minutes
D) 81 minutes

Question 8

Which of the following is correct?

A) Nominal measures of central tendency can be used on ordinal variables.
B) Ordinal measures of central tendency can be used on nominal variables.
C) Interval/ratio measures of central tendency can be used on nominal variables.
D) Interval/ratio measures of central tendency can be used on ordinal variables.

Question 9

Which of the following is a measure of dispersion?

A) mean
B) median
C) mode
D) percentiles

Question 10

For interval/ratio data that is very positively skewed (that is, there are a few cases with extremely high values), the value of the mean will be _____ the value of the median.

A) greater than
B) less than
C) the same as

Question 11

The scores on an interval/ratio variable are very positively skewed. Most of the cases on the variable have values _____ the mean. If you are reporting just one measure of central tendency, it should be the _____.

A) above … mean
B) above … median
C) below … mean
D) below … median

Question 12

When the scores on an interval/ratio variable are very negatively skewed, there are

A) a few extremely low scores
B) a few extremely high scores
C) a few extremely low scores and a few extremely high scores
D) no extreme scores in either direction

Question 13

What is the lowest level of measurement for which it is permissible to calculate a mode?

A) nominal
B) ordinal
C) interval/ratio

Question 14

If everyone in a class of 35 students got an exam score of 75, the value of the variance would be

A) 0
B) 35
C) 75
D) 100

Question 15

What is the lowest level of measurement for which it is permissible to calculate a variance?

A) nominal
B) ordinal
C) interval/ratio

Question 16

A standard deviation is

A) a multivariate descriptive statistic
B) a multivariate inferential statistic
C) a univariate descriptive statistic
D) a univariate inferential statistic

Question 17

At Company A employees commute an average of 25 miles and the standard deviation is 10 miles. At Company B employees commute an average of 50 miles and the standard deviation is 5 miles. At which company is there more dispersion in commuting distances?

A) Company A
B) Company B
C) Company A and Company B are exactly equal
D) there is insufficient information

Question 18

What do measures of central tendency communicate about the scores on a variable?

A) The difference in scores
B) The diversity of scores
C) The typical score
D) The variability of scores

Question 19

A researcher has a nominal level variable. Which of the following would be an acceptable way to discuss its dispersion?

A) standard deviation
B) minimum and maximum
C) percentage distribution
D) range

Question 20

To locate the range in which the middle 80% of the class scored on an exam, you would want to see which percentiles?

A) the 0^th and 80^th percentiles
B) the 10^th and 90^th percentiles
C) the 20^th and 80^th percentiles
D) the 25^th and 75^th percentiles

Question 21

Which of the following variables has the greatest dispersion?

A) variable A with a standard deviation of 3
B) variable B with a variance of 25
C) variable C with a variance of 1
D) variable D with a standard deviation of 6

Question 22

Which of the following is a measure of central tendency?

A) mode
B) range
C) standard deviation
D) variance

Question 23

If an ordinal variable has nine attributes, is the fifth attribute always the median? Explain your answer.

Question 24

Scores on an exam had a mean of 75 and a standard deviation of 5. Which of the following statements is most likely to be true about the distribution of scores on the exam?

A) all the students scored within 5 points of the mean
B) all the students scored more than 5 points below or more than 5 points above the mean
C) all the students scored exactly 5 points below or above the mean
D) students scored an average of 5 points from the mean but some students were closer than that to the mean and some were further than that from the mean

Question 25

You want a measure of dispersion for an interval/ratio level variable. You want the measure that makes use of the fact that the attributes are not only different and have rank order but also represent a numeric scale. What statistic would you calculate?

A) mean
B) mode
C) percent distribution
D) standard deviation

Question 26

You have an interval/ratio variable. It is very negatively skewed. You want to report just one measure of central tendency. Which of the following is correct?

A) there are a few cases with very high values; report the mean
B) there are a few cases with very high values; report the median
C) there are a few cases with very low values; report the mean
D) there are a few cases with very low values; report the median

Question 27

Name five different univariate descriptive statistics.

Question 28

If the mean on an exam was 75 and the standard deviation was 5, what do you know about the distribution of exam grades around the mean?

Question 29

What is the lowest level of measurement for which it is permissible to calculate a mean?

A) nominal
B) ordinal
C) interval/ratio

Question 30

Exactly half the class got a 70 on an exam and exactly half got a 90 on the exam. The median is

A) 71
B) 80
C) 89
D) 70 and 90

Question 31

The admissions office has ordinal-level data on parental income levels of enrolled students. What would an appropriate measure of central tendency be to report?

A) mean
B) median
C) percent distribution
D) standard deviation
(Note: * indicates

Question 32

What is the lowest level of measurement for which it is permissible to calculate a minimum?

A) nominal
B) ordinal
C) interval/ratio

Question 33

What is the difference between central tendency and dispersion?

Question 34

What measures of central tendency and dispersion only become available at the interval/ratio level of measurement?

Question 35

A mean is

A) a multivariate descriptive statistic
B) a multivariate inferential statistic
C) a univariate descriptive statistic
D) a univariate inferential statistic

Question 36

The registrar has nominal-level data on students' racial classification. What would be an appropriate measure of central tendency to report?

A) mean
B) median
C) mode
D) percent distribution

Question 37

What are three measures of central tendency? What are three measures of dispersion? Make it clear which are which.

Question 38

You want a measure of central tendency for an ordinal level variable. You want the measure that makes use of the fact that the attributes are not only different but also have rank order. What statistic would you calculate?

A) mean
B) median
C) range
D) standard deviation

Question 39

You want to see the mean, standard deviation, minimum, and maximum for a variable. Which SPSS procedure would be most appropriate?

A) Display Data File Information
B) Edit Options
C) Frequencies
D) Select Cases

Question 40

You want to see the mode and percent distribution for a variable. Which SPSS procedure would be most appropriate?

A) Descriptives
B) Display Data File Information
C) Explore
D) Frequencies

Question 41

Answer the questions that follow this SPSS output:

ABORTOK is an interval/ratio variable that measures a person's willingness to allow abortion to be legal. High scores indicate greater willingness; low scores indicate less willingness. The following figure describes the scores on ABORTOK for the baby boom twentysomethings and for the genXY twentysomethings.

A) In which group was there more disagreement on the subject of abortion: the baby boom twentysomethings, the genXY twentysomethings, or was the amount of disagreement within the two groups exactly the same? ____________________
B) Justify your answer in no more than two sentences. Name the statistic(s) that backs up your conclusion and indicate its value(s).

Question 42

You want to see the mean, standard deviation, minimum, and maximum for a variable. Name one SPSS procedure that would give you this.

Question 43

You want to see the median, minimum, and maximum for a variable. Name one SPSS procedure that would give you this.

Question 44

What univariate statistics are usually used to describe the distribution of cases on an ordinal variable?

Question 45

You want to see the mode and percent distribution for a variable. Name one SPSS procedure that would give you this.

Question 46

Answer the question that follows this SPSS output:

What is the mode? _______________

Question 47

A researcher takes a sample of three students from a large class and asks each of them how many times they ate at a fast food restaurant so far this week. The three students' answers are 0, 4, 8. What is the variance for this data? It might help you to know that the standard deviation is 4.
variance: __________

Question 48

Answer the questions that follow this SPSS output:

EDUC is an interval/ratio variable that measures number of years of formal schooling completed. This figure describes the scores on EDUC for a group of World War I fiftysomethings and a group of baby boomer fiftysomethings.

A) In which group was there more variability in years of schooling completed: the World War I fiftysomethings, the baby boom fiftysomethings, or was the amount of variability within the two groups exactly the same? ____________________
B) Justify your answer in no more than two sentences. Name the statistic(s) that backs up your conclusion and indicate its value(s).

Question 49

Five college students have the following number of TV shows they watch regularly: 0, 0, 3, 4, 8. Compute the following statistics based on these values:mean: _____ median: _____ mode: _____
range: _____ minimum: _____ 50^th percentile: _____

Question 50

Answer the questions that follow this SPSS output:

A) What is the value of the mode for this variable? __________
B) What is the value of the median for this variable? __________
C) What is the value of the minimum for this variable? __________
D) What is the value of the 25^th percentile for this variable? __________

Question 51

A variable has a standard deviation of 4. What is the value of its variance?
variance: __________

Question 52

What univariate statistics are usually used to describe the distribution of cases on a nominal variable?

Question 53

Answer the question that follows this SPSS output:

What is the mode? _______________

Question 54

An interval/ratio variable has a variance of 100. What is the value of the standard deviation?
standard deviation = __________

Question 55

A researcher takes a sample of three students from a playground and asks each of them what grade they are in. The students' answers are 3, 3, and 3. What is the variance for this data?
variance: __________

Question 56

Answer the questions that follow this SPSS output:

A) What is the value of the mode for this variable? __________
B) What is the value of the median for this variable? __________
C) What is the value of the range for this variable? __________
D) What is the value of the 80^th percentile for this variable? __________

Question 57

Six college students have the following number of TV shows they watch regularly: 0, 1, 3, 3, 5, 6. Compute the following statistics based on these values:mean: _____ median: _____ mode: _____
range: _____ minimum: _____ maximum: _____

Question 58

What univariate statistics are usually used to describe the distribution of cases on an interval/ratio variable that is not badly skewed?