Deck 4: Measures of Central Tendency

Question 1

We are most likely to randomly pick which score from an actual data set?

A) the mode
B) the median
C) the highest score
D) the lowest score

Answer 1

the mode

Question 2

When the distribution is symmetric and unimodal, which of the following are always equal?

A) mean and mode
B) median and mode
C) mean and median
D) mean, median, and mode

Answer 2

mean, median, and mode

Question 3

Given the numbers 6 7 9 11 15 71 86, how many numbers fall below the median?

A) 3
B) 11
C) 6 to 86
D) 6, 7, 9, and 11

Answer 3

3

Question 4

The chief disadvantage of the median, when compared to the mean, is that

A) it is less stable than the mean from sample to sample.
B) its location cannot be calculated algebraically.
C) it is disproportionately affected by outliers.
D) it has no disadvantages.

Question 5

The median location is defined as

A)
B)
C) p(X_i =mode) > p(X_j =any other score)
D) the average score

Question 6

In which of the following situations would you be most likely to use the mean as a measure of central tendency?

A) You want to report data on family income so we know how families are doing.
B) You want to measure something that has a number of outliers.
C) You want to report the average weight of airline passengers so that the pilot can estimate the weight of the plane.
D) Your boss wants to know what size T-shirts to order for the next company picnic.

Question 7

The median has at least one advantage over the mean in that

A) it is not much affected by extreme scores.
B) it is easier to calculate than the mode.
C) it is usually closer to the population mean than the mode.
D) it varies less from sample to sample.

Question 8

The best measure of central tendency

A) is the mean.
B) is the median.
C) is the mode.
D) depends on the data and the question you want to ask.

Question 9

The measure of central tendency that is most useful in estimating population characteristics because it is less variable from sample to sample is the

A) mode
B) median
C) mean
D) All of the above are equally useful in estimating characteristics of the population.

Question 10

Which of the following is useful with data collected with nominal scales?

A) median
B) mode
C) mean
D) none of the above

Question 11

The most commonly used measure of central tendency is

A) the mode.
B) the median.
C) the mean.
D) all are equally common

Question 12

For the following set of data [5 9 5 5 2 4], the mean is

A) 4
B) 4.5
C) 5
D) 6

Question 13

When the distribution is symmetric, which of the following are always equal?

A) mean and mode
B) median and mode
C) mean and median
D) mean, median, and mode

Question 14

The mode of the numbers 1 3 4 5 6 6 7 8 9 9 9 is

A) 6
B) 6.5
C) 6.1
D) 9

Question 15

If we were interested in studying salaries in the National Basketball Association, the least useful measure of the typical salary would be

A) the median.
B) the mode.
C) the range.
D) the mean.

Question 16

The median location is

A) the number closest to the mean.
B) the number of scores that occur at the median.
C) the highest point on a frequency distribution.
D) the position, in an ordered series, occupied by the median.

Question 17

The chief advantage of the median is that

A) it represents a score actually occurring in the data set.
B) it is best used with nominal scales.
C) it is not disproportionately affected by extreme scores.
D) it is the most commonly occurring score.

Question 18

is the symbol commonly used for the

A) mean.
B) mode.
C) median.
D) none of the above

Question 19

Which of the following statements about the mode is false?

A) It must be an actual score that occurred in the data set.
B) It can consist of more than one number.
C) It can be calculated algebraically.
D) All of the above are false.

Question 20

In using ordinal data, which measure of central tendency is probably least useful?

A) mode
B) mean
C) median
D) You cannot use any measure of central tendency with ordinal data.

Question 21

If a physics professor gave her class the same exam every year, which of the following measures of exam scores would probably stay the most consistent in value from year to year?

A) mode
B) mean
C) median
D) none of the above

Question 22

For the following data set [1, 7, 9, 15, 33, 76, 103, 118], what is the median location?

A) 5
B) 4.5
C) 33
D) 24

Question 23

For the following data set [1, 9, 9, 9, 11, 28], which of the following is false?

A) The mode is 9.
B) The median is 9.
C) The mean is 9.
D) The median location is 3.5.

Question 24

Which of the following is true of the value "9" in the following data set [1, 1, 1, 7, 9, 12, 15, 65, 100]?

A) It is the mode.
B) It is the mean.
C) It is the 50^th percentile.
D) It is equal to (N+1)/2.

Question 25

Which of the following measures of central tendency is potentially misleading if the data are collected on an ordinal scale?

A) mean
B) median
C) mode
D) none of the above

Question 26

The median is typically more stable from sample to sample than the mean.

Question 27

The mean is more influenced by extreme scores than other measures of central tendency.

Question 28

If a store manager wanted to stock the men's clothing department with shirts fitting the most men, which measure of central tendency of men's shirt sizes should be employed?

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

Question 29

The mean is the number that corresponds to the point at or below which 50% of the scores fall when the data is arranged in numerical order.

Question 30

Which of the following is NOT a disadvantage of the mean?

A) It is unduly influenced by extreme scores.
B) Its value many not actually exist in the data.
C) It is least stable from sample to sample.
D) Its interpretation in terms of variables requires some faith in the interval properties of the data.

Question 31

Which of the following can be defined algebraically?

A) mean
B) median
C) median location
D) both a and c

Question 32

Measures of central tendency are used to describe the variability or spread of a distribution.

Question 33

For the data set [1, 3, 3, 5, 5, 5, 7, 7, 9], the value "5" is

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

Question 34

Alison received a score of 480 on the verbal portion of her SAT. If she scored at the 50^th percentile, her score represents the _______ of the distribution of all verbal SAT scores.

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

Question 35

Suppose a sample of children reported how many voices they heard in their heads on a particular day, and that hearing voices was a relatively uncommon experience. In this case the mode

A) will show that the most common number of voices heard is zero.
B) will tell us nothing about the children who do hear voices.
C) both a and b
D) none of the above

Question 36

When we make implicit assumptions about a scale having interval properties,

A) we are probably calculating a mode.
B) we are probably calculating a median.
C) we are assuming the distance between 4 and 6 is the same as the distance between 6 and 8.
D) we are always making unreasonable assumptions.

Question 37

The mode is the most common value in a series of numbers.

Question 38

On a histogram, which always refers to the highest point on the distribution?

A) mean
B) median
C) mode
D) none of the above

Question 39

Which of the following is probably most useful in studies in which extreme scores sometimes occur but have no real practical significance?

A) mean
B) median
C) average
D) none of the above

Question 40

Professor Neuberg found that the mean number of alcoholic drinks consumed at a party was much higher for males than for females. If the median and mode number of drinks consumed by males and females was both zero, how can the difference in means be explained?

A) The mean number of drinks consumed by females was disproportionately increased by outliers drinking lots of drinks.
B) The mean number of drinks consumed by males was disproportionately increased by outliers drinking lots of drinks.
C) The difference in means gives no information that is useful and should not be explained.
D) The difference most likely comes from an error in calculation.

Question 41

Given the following distributions, which measure of central tendency would be the largest value?
a. Negatively skewed
b. Positively skewed

Question 42

Algebraically, the mean = ( S X)²/N.

Question 43

When the median falls between two numbers, the lower number is used.

Question 44

A seasonal convenience store currently sells laundry detergent in three standard size containers. Due to limited shelf space, they want to offer only one size in the future. They have the sales record for each size over the previous year. Which measure of central tendency would best help them decide which size to stock in the future? Explain your answer.

Question 45

What is the relationship between the mean, median, and mode in a symmetrical distribution?

Question 46

A researcher recorded the gender of his participants as follows: 1=Male and 2=Female. Which measure of central tendency would be most useful to describe the gender of his sample? Explain your answer.

Question 47

Given the following data set, demonstrate that multiplying the mean by a constant of 2 is equivalent to multiplying each value by that constant (2) and then calculating the mean.
1               2               3               4

Question 48

A resident assistant was interested in the cigarette consumption in her dormitory. After conducting a survey with 700 residents, she reported that, on average, residents smoked 5 cigarettes a day. This statistic included the data from 400 students who claimed to smoke 0 cigarettes a day. What would be a more appropriate way to describe the cigarette consumption of smokers?

Question 49

A distribution can have more than one mode.

Question 50

The median may fall between two numbers when there is an even number of values.

Question 51

A sample of 20 families reported how many children they have. Answer the following questions based on the summary table below.

a. What is the mean?
b. What is the median?
c. What is the mode?

Question 52

Answer the following questions based on this set of numbers:
                1               2               2               3               3               3               4               5
 
a. What is the mean?
b. What is the median?
c. What is the mode?

Question 53

The following are test grades from the first statistics exam. Briefly describe the data, including each of the 3 measures of central tendency.
45            50            65            65            70            70            75            80            85            90            95            100

Question 54

In general, the sample mean is a better estimate of the population mean than are the median or mode.

Question 55

Answer the following questions based on this graph.

a. What is the median?
b. What is the mode?
c. What is a reasonable estimate of the mean? Explain your estimate.