Deck 3: Central Tendency and Variability

Question 1

A common shape in which data are found resembling a bell or hill is called a ______ distribution.

A) normal
B) skewed
C) robust
D) precise

Answer 1

A

Question 2

Given a distribution with a median of 0, if your data had a negative skew, you would expect to see ______.

A) the tail would point toward positive numbers
B) the tail would point toward negative numbers
C) the tails would point evenly in both directions
D) there would be no tail(s)

Answer 2

B

Question 3

How would you pronounce this symbol $\Sigma$ x?

A) mean of x
B) product of x
C) sum of x
D) none of these

Answer 3

sum of x

Question 4

Calculate $\Sigma$ x for the following production data: 10, 20, 30, 40

A) 25
B) 4
C) 100
D) none of these

Question 5

The mode is ______.

A) the most robust measure of central tendency
B) the most common value in a variable
C) appropriate for all scales of measurement
D) all of these

Question 6

Determine the mode for the following survey data: 2, 5, 2, 2, 5, 1, 4

A) 2
B) 3
C) 5
D) 7

Question 7

The middlemost value in a variable is the ______.

A) mode
B) median
C) mean
D) all of these

Question 8

Determine the median for the following survey data: 2, 4, 5, 5, 4, 4, 2, 2, 3, 3

A) 2.5
B) 3
C) 3.5
D) 4

Question 9

Determine the median for the following data on sales in Euros: 5426, 2681, 4200, 3766, 4437

A) 4200
B) 4437
C) 2681
D) 3766

Question 10

The least robust but most precise measure of central tendency is the ______.

A) mode
B) mean
C) median
D) All are equally robust.

Question 11

You should only use the mean when your data are ______.

A) nominal, ordinal, interval or ratio
B) ordinal, interval or ratio
C) interval or ratio
D) ratio only

Question 12

The correct formulaic notation for the mean is ______.

A) Ẍ
B) X ′
C) x̄̄
D) x̄

Question 13

Determine the mean for the following survey data: 3, 2, 5, 4, 2

A) 1.7
B) 3
C) 3.2
D) 16

Question 14

Determine x̄ for the following data on sales in British pounds: 369, 599, 381, 701, 694

A) 2744
B) 599
C) 163.75
D) 548.8

Question 15

You have measured annual salary in Euros for your current employees. Which measures of central tendency would be appropriate for this variable?

A) mode, median, and mean
B) mode only
C) mode or median, but not mean
D) median or mean, but not mode

Question 16

Identify the order of measures of central tendency from least precise to most precise.

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

Question 17

The general term for the degree to which scores within a single variable are different from one another is ______.

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

Question 18

If you wanted to find the difference between the smallest and largest score in a variable, you would calculate the ______.

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

Question 19

Determine the range for the following survey data: 4, 3, 4, 3, 3, 2, 4, 3, 4, 2

A) 2
B) 3.2
C) 0.62
D) 4

Question 20

The range is generally not a good way to assess variability because ______.

A) it is too robust
B) it is easily influenced by outliers
C) it does not measure variability
D) it is difficult to calculate

Question 21

A number that summarizes a population is a ______, whereas a number that summarizes a sample is a ______ .

A) statistic, statistic
B) statistic, parameter
C) parameter, statistic
D) parameter, parameter

Question 22

Which of the following symbols represents a parameter?

A) n
B) x̄
C) s²
D) $\sigma$

Question 23

The average deviation of a sample is always ______.

A) equal to 0
B) equal to 1
C) equal to the mean of the sample
D) equal to the standard deviation of the sample

Question 24

Determine the variance of the following sample of survey data: 2, 1, 3, 3, 4

A) 1.04
B) 1.02
C) 1.30
D) 1.14

Question 25

Determine the variance of the following population of survey data: 3, 4, 4, 1, 2

A) 1.17
B) 1.36
C) 1.70
D) 1.30

Question 26

Determine the standard deviation of the following sample of survey data: 3, 1, 5, 4, 5

A) 2.80
B) 2.24
C) 1.50
D) 1.67

Question 27

Determine the standard deviation of the following population of survey data: 1, 1, 1, 4, 3

A) 1.41
B) 1.26
C) 2.00
D) 1.60

Question 28

You should use the conceptual formula of variance instead of the computational formula when ______.

A) you're working with a population
B) you're working with a sample
C) you're working with discrete data
D) none of these

Question 29

If you're calculating $\sigma$ ², which of the following should you use for your mean?

A) m
B) $\mu$
C) x̄
D) none of these

Question 30

A systematic inaccuracy in a statistic in measuring what it is intended to measure is considered ______.

A) bias
B) variability
C) variance
D) skew

Question 31

A dataset where the tail leads to the right would have a positive skew.

Question 32

If you want to find the middle of a dataset, you are calculating variability.

Question 33

Conditions that must be true for a statistic to be meaningful are considered assumptions.

Question 34

For this survey dataset, the mode is equal to 4: 4, 5, 1, 4, 1, 2, 2, 3

Question 35

The median is more precise than the mode and less robust than the mean.

Question 36

You should not use the median for nominal data.

Question 37

The arithmetic average of values in a variable is the mode.

Question 38

For the following data, there is one outlier: 1, 1, 2, 2, 3, 50

Question 39

For the following data, the range is equal to 50: 1, 1, 2, 2, 3, 50

Question 40

s² is a sample statistic.

Question 41

The variance is the squared average distance between all scores in a variable and their mean.

Question 42

$\sigma$ is the symbol for the variance.

Question 43

The average distance between all scores in a variable and their mean is the standard deviation.

Question 44

If the variance is 16, the standard deviation is 8.

Question 45

The denominator of the variance formula for a population uses N - 1 in order to correct for bias.

Question 46

You need a bias correction for sample estimates of the variance because samples systematically overestimate population variance.

Question 47

For the following data, $\Sigma$ x² = 36: 1, 2, 3

Question 48

For the following data, $\Sigma$ x²) = 16: 1, 1, 2

Question 49

Describe the three common types of shapes of data discussed in Chapter 3. Draw an example of each.

Question 50

Define the three measures of central tendency described in this chapter. Explain how to determine each for a given dataset.

Question 51

For each of the three measures of central tendency, give an example of when it would be appropriate to use and when it would be inappropriate to use (up to six total examples). Explain why in each case.

Question 52

Explain why we need to square deviations before calculating the variance of a variable.

Question 53

The sales manager recently collected a dataset containing the number of days that it took each employees to make his/her first sale after being hired. This dataset appears below. Use it to respond to Questions . For all problems, show work.

-Calculate the mean of this sample.

Question 54

The sales manager recently collected a dataset containing the number of days that it took each employees to make his/her first sale after being hired. This dataset appears below. Use it to respond to Questions . For all problems, show work.

-Calculate the median of this sample.

Question 55

The sales manager recently collected a dataset containing the number of days that it took each employees to make his/her first sale after being hired. This dataset appears below. Use it to respond to Questions . For all problems, show work.

-Calculate the mode of this sample.

Question 56

The sales manager recently collected a dataset containing the number of days that it took each employees to make his/her first sale after being hired. This dataset appears below. Use it to respond to Questions . For all problems, show work.

-Calculate the range of this sample.

Question 57

The sales manager recently collected a dataset containing the number of days that it took each employees to make his/her first sale after being hired. This dataset appears below. Use it to respond to Questions . For all problems, show work.

-Calculate the variance of this sample.

Question 58

The sales manager recently collected a dataset containing the number of days that it took each employees to make his/her first sale after being hired. This dataset appears below. Use it to respond to Questions . For all problems, show work.

-Calculate the standard deviation of this sample.

Question 59

For the following problems, consider this frequency table of survey data:

-What is the mean of the sample described by this frequency table?

Question 60

For the following problems, consider this frequency table of survey data:

-What is the median of the sample described by this frequency table?

Question 61

For the following problems, consider this frequency table of survey data:

-What is the mode of the sample described by this frequency table?

Question 62

For the following problems, consider this frequency table of survey data:

-What is the standard deviation of the sample described by this frequency table?