Question 1

Which of the following statements correctly describes the five-number summary of a set of data?

Accepted Answer

The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum, which can all be determined from a stemplot.

Question 2

A study of freely forming groups in bars throughout Europe examined the number of individuals found in groups that were laughing together. A summary of the 501 groups examined is shown here:
 $$\begin{array} { | l | l | } 
\hline \text { Group size } & \text { Number of groups } \
\hline 2 & 254 \
\hline 3 & 168 \
\hline 4 & 52 \
\hline 5 & 21 \
\hline 6 & 6 \
\hline
\end{array}$$ What is the median group size?

Accepted Answer

The answer of A study of freely forming groups in...

Question 3

A maze experiment uses 24 lab rats of various ages, as summarized here:
$$\begin{array} { | l | l | } 
\hline \text { Age (in months) } & \text { Number of rats } \
\hline 2 & 4 \
\hline 3 & 6 \
\hline 4 & 6 \
\hline 5 & 4 \
\hline 7 & 3 \
\hline 9 & 1 \
\hline
\end{array}$$ What is the median rat age (in months) for this maze experiment?

Accepted Answer

The median is the middle value when the data is ordered. With 24 rats, the median will be the average of the 12th and 13th values. Ordering the ages, the 12th and 13th rats both fall into the age group of 4 months, making the median 4 months.

Question 4

Researchers measured the length of the central retrix (R1), a flight-involved tail feather, in 21 female long-tailed finches. A boxplot of the length, in millimeters (mm), is given here:
 Based on this boxplot, to which value is the interquartile range closest?

Accepted Answer

The answer of Researchers measured the length of the central...

Question 5

Researchers measured the length of the central retrix (R1), a flight-involved tail feather, in 21 female long-tailed finches. A boxplot of the length, in millimeters (mm), is given here:
 Based on this boxplot, which of the following statements is TRUE?

Accepted Answer

The boxplot shows that there is one outlier on the high end, with a value above 90 mm. Therefore, statement B is true. Choice A is incorrect because there is only one peak in the distribution of lengths. Choice C is incorrect because the upper quartile is around 80 mm, meaning that only 25% of the birds had an R1 length above 80 mm, not 70 mm. Choice D cannot be determined from the boxplot, as it does not display the mean length.

Question 6

If the graph of a distribution of data is skewed, which measure of central tendency is most appropriate?

Accepted Answer

The median is the most appropriate measure of central tendency for a skewed distribution because the mean may be influenced by extreme values and the mode may not accurately represent the center of the distribution. The median is a robust measure that is not affected by outliers or extreme values, and it reflects the central value of the data.

Question 7

Geckos are lizards with specialized toe pads that enable them to easily climb all sorts of surfaces. A research team examined the adhesive properties of 7 Tokay geckos. Following are the toe-pad areas (in square centimeters, cm²) for this sample: 5.6 4.9 6.0 5.1 5.5 5.1 7.5 Rounded to two decimal places, what is the mean toe-pad area in this sample of geckos?

Accepted Answer

The answer of Geckos are lizards with specialized toe pads...

Question 8

Geckos are lizards with specialized toe pads that enable them to easily climb all sorts of surfaces. A research team examined the adhesive properties of 7 Tokay geckos. Following are the toe-pad areas (in square centimeters, cm²) for this sample: 5.6 4.9 6.0 5.1 5.5 5.1 7.5 Using the correct units, what is the value of the sample variance of toe-pad areas?

Accepted Answer

The sample variance is calculated using the formula for variance, which involves squaring the difference between each data point and the mean, then dividing by the number of data points minus one (n-1). The units of variance are the square of the units of the original data, so since the original data is in cm^2, the variance will be in cm^4. The correct numerical value is not provided, but the focus here is on understanding the correct units for the answer.

Question 9

Geckos are lizards with specialized toe pads that enable them to easily climb all sorts of surfaces. A research team examined the adhesive properties of 7 Tokay geckos. Following are the toe-pad areas (in square centimeters, cm²) of this sample: 5.6 4.9 6.0 5.1 5.5 5.1 7.5 What is the first quartile for these data?

Accepted Answer

The answer of Geckos are lizards with specialized toe pads...

Question 10

Geckos are lizards with specialized toe pads that enable them to easily climb all sorts of surfaces. A research team examined the adhesive properties of 7 Tokay geckos. Following are the toe-pad areas (in square centimeters, cm²) for this sample: 5.6 4.9 6.0 5.1 5.5 5.1 7.5 What is the value of the interquartile range for these data?

Accepted Answer

The answer of Geckos are lizards with specialized toe pads...

Question 11

Geckos are lizards with specialized toe pads that enable them to easily climb all sorts of surfaces. A research team examined the adhesive properties of 7 Tokay geckos. Following are the toe-pad areas (in square centimeters, cm²) for this sample: 5.6 4.9 6.0 5.1 5.5 5.1 7.5 Which of the following ranges must a value fall outside of to be considered an outlier according to the 1.5 × IQR rule?

Accepted Answer

To find the outlier range using the 1.5 × IQR rule, we need to first calculate the IQR (interquartile range). 
1. Arrange the data in ascending order: 
4.9, 5.1, 5.1, 5.5, 5.6, 6.0, 7.5 
2. Find the median (Q2): 
Since there are 7 data points, the median is the 4th value, which is 5.5. 
3. Divide the data into two halves: 
First half: 4.9, 5.1, 5.1, 5.5 
Second half: 5.6, 6.0, 7.5 
4. Find the median of the first half (Q1): 
Since there are 4 data points, the median is the average of the 2nd and 3rd values, which is 5.1. 
5. Find the median of the second half (Q3): 
Since there are 3 data points, the median is the 2nd value, which is 6.0. 
6. Calculate the IQR: 
IQR = Q3 - Q1 = 6.0 - 5.1 = 0.9 
7. Multiply the IQR by 1.5: 
1.5 × IQR = 1.5 × 0.9 = 1.35 
8. Determine the outlier range: 
Lower outlier limit = Q1 - 1.5 × IQR = 5.1 - 1.35 = 3.75 
Upper outlier limit = Q3 + 1.5 × IQR = 6.0 + 1.35 = 7.35

Therefore, any value that falls outside the range of 3.75 to 7.35 would be considered an outlier according to the 1.5 × IQR rule. 
So, the best choice is D.

Question 12

The distribution of ages of people in a class (to the nearest year) is as follows:
$$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline \text { Age } & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25 & 32 \
\hline \text { Number of students } & 14 & 120 & 200 & 200 & 90 & 30 & 10 & 2 & 1 \
\hline
\end{array}$$ What is TRUE about the median age (to the nearest year) of this distribution?

Accepted Answer

The median is the middle value in a data set. With 667 students, the median is the 334th value, which falls in the age group of 20.

Question 13

Which of the following data are likely to have a mean that is smaller than the median?

Accepted Answer

In left-skewed data, the mean is typically smaller than the median because the long tail on the left pulls the mean downwards.

Question 14

By inspection, which of the following sets of numbers has the smallest standard deviation?

Accepted Answer

The standard deviation measures how spread out the data is from the average. In set B, all of the numbers are the same, which means they have a deviation of zero from the mean. Therefore, the standard deviation for set B is also zero, making it the smallest.

Question 15

Brown tree snakes are an invasive species causing huge environmental and financial damage in Guam. In June 2000, researchers captured 504 brown tree snakes on Guam's Andersen Air Force Base. On average, the snakes weighed 121 g, and their weights ranged from 23 to 663 g at capture. From this information, what can we conclude about the shape of the distribution of brown tree snake masses?

Accepted Answer

The wide range from 23 to 663 g, with an average of 121 g, suggests the distribution is right-skewed or has high outliers, as the mean is pulled towards the higher values.

Question 16

The following histogram shows the yearly number of unprovoked attacks by alligators on people in Florida over a 33-year period.
 What must be the median yearly counts of alligator attacks?

Accepted Answer

The answer of The following histogram shows the yearly number...

Question 17

The following histogram shows the yearly number of unprovoked attacks by alligators on people in Florida over a 33-year period.
 What must be the third quartile of yearly counts of alligator attacks?

Accepted Answer

The answer of The following histogram shows the yearly number...

Question 18

In a study of the function of pectoral fins in fish, a graduate student examined 7 fish with the following lengths (in centimeters, cm):
30 28 29 27 31 25 29
What is the mean length of these 7 fish?

Accepted Answer

The mean length is calculated by adding all the lengths together and then dividing by the number of fish. The sum of the lengths is 199 cm (30+28+29+27+31+25+29=199), and there are 7 fish. Dividing 199 cm by 7 gives a mean length of 28.4 cm.

Question 19

In a study of the function of pectoral fins in fish, a graduate student examined 7 fish with the following lengths (in centimeters, cm):
30 28 29 27 31 25 29
What is the variance of these 7 fish lengths?

Accepted Answer

To calculate the variance, first find the mean of the fish lengths: $ \frac{30 + 28 + 29 + 27 + 31 + 25 + 29}{7} = 28.43 $ cm. Then, calculate the squared differences from the mean, sum them, and divide by the number of observations minus one (for sample variance): $ \frac{(30-28.43)^2 + (28-28.43)^2 + (29-28.43)^2 + (27-28.43)^2 + (31-28.43)^2 + (25-28.43)^2 + (29-28.43)^2}{7-1} = 3.95 $ cm².

Question 20

In a study of the function of pectoral fins in fish, a graduate student examined 7 fish with the following lengths (in centimeters, cm):
30 28 29 27 31 25 29
What is the first quartile for these data?

Accepted Answer

The first quartile is the median of the lower half of the data. The data can be ordered as: 25, 27, 28, 29, 29, 30, 31. The median of the lower half is 27, so the first quartile is 27 cm.

Quiz 2: Describing Quantitative Distributions With Numbers

Which of the following statements correctly describes the five-number summary of a set of data?

Researchers measured the length of the central retrix (R1) , a flight-involved tail feather, in 21 female long-tailed finches. A boxplot of the length, in millimeters (mm) , is given here: Based on this boxplot, to which value is the interquartile range closest?

Researchers measured the length of the central retrix (R1) , a flight-involved tail feather, in 21 female long-tailed finches. A boxplot of the length, in millimeters (mm) , is given here: Based on this boxplot, which of the following statements is TRUE?

If the graph of a distribution of data is skewed, which measure of central tendency is most appropriate?

Which of the following data are likely to have a mean that is smaller than the median?

By inspection, which of the following sets of numbers has the smallest standard deviation?

The following histogram shows the yearly number of unprovoked attacks by alligators on people in Florida over a 33-year period. What must be the median yearly counts of alligator attacks?

The following histogram shows the yearly number of unprovoked attacks by alligators on people in Florida over a 33-year period. What must be the third quartile of yearly counts of alligator attacks?

In a study of the function of pectoral fins in fish, a graduate student examined 7 fish with the following lengths (in centimeters, cm) : 30 28 29 27 31 25 29 What is the mean length of these 7 fish?

In a study of the function of pectoral fins in fish, a graduate student examined 7 fish with the following lengths (in centimeters, cm) : 30 28 29 27 31 25 29 What is the variance of these 7 fish lengths?

In a study of the function of pectoral fins in fish, a graduate student examined 7 fish with the following lengths (in centimeters, cm) : 30 28 29 27 31 25 29 What is the first quartile for these data?