Deck 3: Describing Data

Question 1

Which of the following is not an important source of variability in data?

A) Calculation errors.
B) Differences between individuals.
C) Instrument error.
D) Measurement error.

Answer 1

A

Question 2

Which of the following accurately describes the numerator for the equation to calculate the variance?

A) The average of all the values.
B) The square root of the standard deviation.
C) The sum of the average deviations between the data values and the mean.
D) The sum of the squared deviations between the data values and the mean.

Answer 2

D

Question 3

Which of the following are a possible set of descriptive statistics for a data set?

A) Sum of squares of 18, variance of 6, standard deviation of 36
B) Sum of squares of 18, variance of 36, standard deviation of 6
C) Sum of squares of 180, variance of 6, standard deviation of 36
D) Sum of squares of 180, variance of 36, standard deviation of 6

Answer 3

D

Question 4

If a data set has a bell-shaped distribution, approximately what proportion of the values lie above the mean and within one standard deviation?

A) 25%
B) 33%
C) 38%
D) 48%

Question 5

If a data set has a bell-shaped distribution, approximately what proportion of the values lie above the mean and within two standard deviations?

A) 25%
B) 33%
C) 38%
D) 48%

Question 6

If a data set has a mean of 25 and a variance of 16, what is the coefficient of variation?

A) 16%
B) 64%
C) 80%
D) 156%

Question 7

Using the data set shown, what is the mean value for this data set?
Data set: 1, 4, 5, 9, 13, 24

A) 8.33
B) 8.66
C) 9.00
D) 9.33

Question 8

Using the data set shown, what is the sample variance for this data set?
Data set: 1, 4, 7, 9, 15, 24

A) 58.0
B) 69.6
C) 73.4
D) 78.4

Question 9

Using the data set shown, what are the correct mean and median values for this data set?
Data set: 3, 4, 5, 5, 8, 9, 11, 11

A) Mean = 6, median = 7.5
B) Mean = 6.5, median = 7
C) Mean = 7, median = 6.5
D) Mean = 7.5, median = 6

Question 10

Using the data set shown, what are the correct variance and interquartile range values for this data set?
Data set: 3, 4, 5, 5, 8, 9, 11, 11

A) Variance = 8.75, interquartile range = 5.5
B) Variance = 8.75, interquartile range = 6.5
C) Variance = 10, interquartile range = 5.5
D) Variance = 10, interquartile range = 6.5

Question 11

Using the data table shown, what is the mean number of galls found on a set of 30 leaves collected from a plant?
?
Number of galls found on 30 leaves collected from a plant.

$\begin{array}{cc}\begin{array}{l}\text { Number } \\\text { of galls }\end{array} & \text { Frequency } \\\hline 0 & 4 \\1 & 8 \\2 & 9 \\3 & 4 \\4 & 3 \\5 & 2 \\\hline\end{array}$ ?

A) 1.0
B) 1.33
C) 1.66
D) 2.0

Question 12

Using the data table shown, what is the standard deviation of the number of galls found on a set of 30 leaves collected from a plant?
?
Number of galls found on 30 leaves collected from a plant.

$\begin{array}{cc}\begin{array}{l}\text { Number } \\\text { of galls }\end{array} & \text { Frequency } \\\hline 0 & 4 \\1 & 8 \\2 & 9 \\3 & 4 \\4 & 3 \\5 & 2 \\\hline\end{array}$ ?

A) 1.0
B) 1.4
C) 2.0
D) 5.5

Question 13

Using the data table shown, what proportion of the leaves examined have four galls?
?
Number of galls found on 30 leaves collected from a plant.

$\begin{array}{cc}\begin{array}{l}\text { Number } \\\text { of galls }\end{array} & \text { Frequency } \\\hline 0 & 4 \\1 & 8 \\2 & 9 \\3 & 4 \\4 & 3 \\5 & 2 \\\hline\end{array}$ ?

A) 0.1
B) 0.3
C) 0.5
D) 0.7

Question 14

Using the data table shown, what proportion of the leaves examined have more than two galls?
?
Number of galls found on 30 leaves collected from a plant.

$\begin{array}{cc}\begin{array}{l}\text { Number } \\\text { of galls }\end{array} & \text { Frequency } \\\hline 0 & 4 \\1 & 8 \\2 & 9 \\3 & 4 \\4 & 3 \\5 & 2 \\\hline\end{array}$ ?

A) 0.1
B) 0.3
C) 0.5
D) 0.7

Question 15

Using the data table shown, what is the mean of the number of species' bones found in 40 sets of stomach contents collected from coyotes?
?
Number of species' bones found in 40 sets of stomach contents from coyotes.

$\begin{array}{l}\text { Number }\\\begin{array}{cc}\text { of bones } & \text { Frequency } \\\hline 0 & 3 \\1 & 7 \\2 & 10 \\3 & 5 \\4 & 12 \\5 & 6\end{array}\end{array}$ ?

A) 2.0
B) 3.0
C) 4.0
D) 5.0

Question 16

Using the data table shown, what is the standard deviation of the number of species' bones found in 40 sets of stomach contents collected from coyotes?
?
Number of species' bones found in 40 sets of stomach contents from coyotes.

$\begin{array}{l}\text { Number }\\\begin{array}{cc}\text { of bones } & \text { Frequency } \\\hline 0 & 3 \\1 & 7 \\2 & 10 \\3 & 5 \\4 & 12 \\5 & 6\end{array}\end{array}$ ?

A) 1.8
B) 2.0
C) 2.2
D) 2.4

Question 17

Using the data table shown, what proportion of the stomach contents examined have bones from three species?
?
Number of species' bones found in 40 sets of stomach contents from coyotes.

$\begin{array}{l}\text { Number }\\\begin{array}{cc}\text { of bones } & \text { Frequency } \\\hline 0 & 3 \\1 & 7 \\2 & 10 \\3 & 5 \\4 & 12 \\5 & 6\end{array}\end{array}$ ?

A) 0.125
B) 0.250
C) 0.375
D) 0.45

Question 18

Using the data table shown, what proportion of the stomach contents examined have bones from more than three species?
?
Number of species' bones found in 40 sets of stomach contents from coyotes.

$\begin{array}{l}\text { Number }\\\begin{array}{cc}\text { of bones } & \text { Frequency } \\\hline 0 & 3 \\1 & 7 \\2 & 10 \\3 & 5 \\4 & 12 \\5 & 6\end{array}\end{array}$ ?

A) 0.125
B) 0.250
C) 0.375
D) 0.45

Question 19

If we have a data set with a mean of 12 and a variance of 3, what are the new mean and variance if we multiply the values by 2 and then add 5?

A) Mean = 29, variance = 6
B) Mean = 29, variance = 12
C) Mean = 34, variance = 6
D) Mean = 34, variance = 12

Question 20

If we have a data set with a mean of 12 and a variance of 3, what are the new mean and variance if we add 5 to all the values, then multiply them by 2?

A) Mean = 29, variance = 6
B) Mean = 29, variance = 12
C) Mean = 34, variance = 6
D) Mean = 34, variance = 12

Question 21

If we have a data set with a mean of 25 and a variance of 16, what are the new mean and variance if we multiply the values by 3 and then add 4?

A) Mean = 79, variance = 48
B) Mean = 79, variance = 144
C) Mean = 87, variance = 48
D) Mean = 87, variance = 144

Question 22

If we have a data set with a mean of 25 and a variance of 16, what are the new mean and variance if we add 5 to all the values, then multiply them by 4?

A) Mean = 79, variance = 48
B) Mean = 79, variance = 144
C) Mean = 87, variance = 48
D) Mean = 87, variance = 144

Question 23

Imagine we have a symmetric data set for which we have calculated various statistics, but then a single very large outlier is added to it. When we recalculate the statistics, which of the following things is NOT true?

A) The mean increases.
B) The median increases.
C) The standard deviation increases.
D) The variance increases.

Question 24

What are the median and interquartile range for the set of data values shown?
Data: 2 4 6 8 10 12

A) Median = 6, interquartile range = 6
B) Median = 6, interquartile range = 7
C) Median = 7, interquartile range = 6
D) Median = 7, interquartile range = 7

Question 25

What are the median and interquartile range for the set of data values shown?
Data: -5 -1 0 1 3 6 13

A) Median = 0.5, interquartile range = 3
B) Median = 1, interquartile range = 4
C) Median = 1.5, interquartile range = 5
D) Median = 2.0, interquartile range = 6

Question 26

Which of the following must be true for a plot of a cumulative frequency distribution?

A) It is centered around the mean.
B) It is centered around the median.
C) The line has a shape like a bell curve.
D) The line moves upward from left to right.

Question 27

Consider a sample of foxes in which there are 20 adult females, 25 adult males, 35 juvenile females, and 20 juvenile males. What is the proportion of juvenile females?

A) 0.2
B) 0.25
C) 0.35
D) 0.55

Question 28

Consider a sample of foxes in which there are 20 adult females, 25 adult males, 35 juvenile females, and 20 juvenile males. What is the proportion of females?

A) 0.2
B) 0.25
C) 0.35
D) 0.55

Question 29

The location is always the most important statistic when considering a data set.

Question 30

If we do experiments correctly, the variability in the data values should be zero.

Question 31

The variance of a data set is always smaller than the sum of squares.

Question 32

The standard deviation has the same units as the data values, whereas the variance does not.

Question 33

The rounding of values should only be done for reported values; use extra digits when performing calculations.

Question 34

The interquartile range is larger than 50% of the data.

Question 35

The mean and the median will be the same for a symmetric distribution.

Question 36

A large outlier will tend to change the mean more than the median.

Question 37

A large outlier will tend to change the interquartile range more than the standard deviation.

Question 38

The mean is the most important descriptive statistic for a categorical variable.

Question 39

A percentile of a measurement specifies the number of values from the data set that are less than the measurement.

Question 40

The cumulative relative frequency at a given measurement is the proportion of values in the data set that have that measurement.

Question 41

A proportion must be between zero and one and can also be either zero or one.

Question 42

The proportion of values in a data set that are less than the median is 0.5.

Question 43

Calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the following data set: 5, 7, 10, 11, 14.

Question 44

Calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the following data set: -2, 0, 3, 4, 5.

Question 45

Calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the following data set: 9, 13, 14, 16, 17, 21.

Question 46

Calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the following data set: -2, 2, 4, 6, 8, 12.

Question 47

Sketch a boxplot showing data for the following two data sets.
Data set A: 2 3 5 7 9 11 12
Data set B: 3 5 6 8 9 11

Question 48

Consider a study of patients with heart problems that follows them for 5 years after treatment and measures the number of myocardial infarctions (i.e., heart attacks) they experience.
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Using the data shown in the table, calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the data values. Also, what proportion of patients experienced subsequent myocardial infarctions?

Question 49

Consider an ecological study of the insect populations in a region. Pit traps are set out overnight, and the number of insects in each trap is recorded the next day.
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Using the data shown in the table, calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the data values. Also, what proportion of traps failed to trap any insects?
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