Deck 4: Numerical Summary Measures

Question 1

Calculate for the following sample data set: ​ ​

A) 11.63
B) 15.1
C) 15.5
D) 9

Answer 1

11.63

Question 2

What is the smallest possible value for a sample standard deviation?

A) -10
B) 0
C) 1
D) There is no smallest value.

Answer 2

0

Question 3

The following is an abbreviated list of scores from a recent exam.Which exam score is the 15th percentile?

A) 98
B) 28
C) 51
D) 56

Answer 3

28

Question 4

The sample mean is:

A) the same for all distributions.
B) a random variable specific to each distribution (i.e., it varies from sample to sample).
C) an unknowable quantity.
D) a good indicator of the spread of a data set.

Question 5

Calculate s2 for the following sample data set: ​ ​

A) 4.57
B) 2.14
C) 4.17
D) 5

Question 6

A personnel manager believes that a particular employee produces more defective parts than his peers.The manager records the worker's production over the course of several weeks.Out of 315 parts produced, 11 are defective.Calculate (the sample proportion) if we define a defective part as a "success."

A) 0.035
B) 11
C) 28.64
D) Need more information

Question 7

The mode of a symmetric, bell-shaped distribution should:

A) be roughly the same as the mean.
B) be roughly the same as the median.
C) be unique.
D) All of the above.

Question 8

What is the largest possible value of the sample standard deviation?

A) 100
B) 1000
C) 1,000,000
D) There is no largest possible value.

Question 9

Marine was a black Labrador retriever that was trained to detect colorectal cancer by smelling the breath of patients with cancer.In one test to determine how well this dog could detect colorectal cancer, Marine correctly identified a bag containing the breath of a patient with colorectal cancer (from about five bags, with four containing the breath of healthy subjects) in 30 out of 33 trials.What is (the sample proportion) in this situation?

A) 30
B) 33
C) 0.91
D) 0.33

Question 10

The lengths of the reigns of 50 British monarchs (in years) are summarized with the following five-number summary: ​
Xmin = 0, Q1 = 6, = 15.5, Q3 = 24, xmax = 63, = 18.92 = 18.92
​
Based on the five-number summary, the overall shape of the lengths of these reigns appears to be:

A) right-skewed.
B) symmetric.
C) left-skewed.
D) Data shape can be discerned only from visual methods.

Question 11

The median of the lower half of the observations when arranged in ascending order is the:

A) low median.
B) lower arithmetic mean.
C) first (lower) quartile.
D) third (upper) quartile.

Question 12

The symbol represents the:

A) population mean.
B) sample mean.
C) geometric mean.
D) sample median.

Question 13

Calculate for the following sample data set: ​ ​

A) 5
B) 11.5
C) 9
D) 15.1

Question 14

If we have a distribution with ith deviation from the mean equal to 0, then we know that:

A) the distribution is symmetric.
B) the ith observation is the same as the mean.
C) the variance must be 0.
D) the median would be a more accurate representation of central tendency.

Question 15

It is known that the body mass index (BMI) of healthy American males follows a normal distribution, with a mean of 24.5 and a standard deviation of 3.0.Approximately what proportion of male BMI values fall below 18.5?

A) 0.0003
B) 0.025
C) 0.05
D) 0.16

Question 16

The smallest numeric value in a data set subtracted from the largest gives the:

A) standard deviation.
B) variance.
C) mean squared error.
D) range.

Question 17

The __________ of a data set, if any, is the value that occurs most often, or with the greatest frequency.

A) mean
B) median
C) mode
D) relative frequency

Question 18

The _________ of a data set is the middle number when the observations are arranged in order from smallest to largest.

A) weighted mean
B) mode
C) median
D) arithmetic mean

Question 19

If a set of data contains an odd number of values and the data are ordered from smallest to largest, then:

A) the mean is the single middle value.
B) the mean is the same as the median.
C) the median is the single middle value.
D) the median is the average of the two middle values.

Question 20

For any set of n numbers, the sum of all n deviations about the arithmetic mean will always be:

A) greater than 0.
B) less than 0.
C) equal to 0.
D) greater than n.

Question 21

The IQ curve is normal, with a mean of 100 and a standard deviation of 15.If "normal" IQ is defined as a score within 1 standard deviation of the mean, what range of scores is considered "normal"?

A) 85-115
B) 75-125
C) 100-115
D) 85-100

Question 22

A continuous population has a mean of 210.51 and a standard deviation of 10.31.Suppose we know that the population is normally distributed.Compute the smallest interval centered on the mean that will contain 95% of the observations.

A) (200.20, 220.82)
B) (164.40, 256.62)
C) (179.58, 241.44)
D) (189.89, 231.13)

Question 23

If , then:

A) the sample is negatively skewed.
B) the population must be negatively skewed.
C) the sample is positively skewed.
D) the population must be positively skewed.

Question 24

σ is the symbol for the:

A) sample standard deviation.
B) population standard deviation.
C) population variance.
D) squared sample standard deviation.

Question 25

Which measure of central tendency is equivalent to the 50th percentile?

A) Mean
B) Median
C) Mode
D) Arithmetic average

Question 26

In general, a data set that has a very large gap between its minimum/maximum values and a very large gap between its first/third quartiles will also have:

A) a large amount of variability.
B) a completely positive set of values.
C) a completely negative set of values.
D) values that are both positive and negative.

Question 27

Calculate the mean for the following sample data set:

A) 5
B) 151
C) 9
D) 15.1

Question 28

It is known that the body mass index (BMI) of healthy American females follows a normal distribution, with a mean of 22.5 and a standard deviation pf 3.0.Approximately what percentage of female BMI values fall between 16.5 and 28.5?

A) 99.7%
B) 95%
C) 81.5%
D) 68%

Question 29

If the sample mean is greater than the sample median, the sample is:

A) positively skewed.
B) negatively skewed.
C) symmetric.
D) not valid for inference.

Question 30

A conservationist measures the diameters, in centimeters, of 200 white pine trees in the Allegheny National Forest in Northwest Pennsylvania.The data are summarized with the following five-number summary: ​
Xmin = 18.23, Q1 = 24.29, = 30.35, Q3 = 36.41, xmax = 42.47
​
Based on the five-number summary, the overall shape of the tree diameters appears to be:

A) heavily right-skewed.
B) symmetric.
C) heavily left-skewed.
D) Data shape can be discerned only from visual methods.

Question 31

The lengths of the reigns of 50 British monarchs (in years) are summarized with the following five-number summary: xmin = 0, Q1 = 6, = 15.5, Q3 = 24, xmax = 63, = 18.92
If the maximum of 63 years is accidentally recorded as 630 years, how will this affect the mean?

A) The mean will increase.
B) The mean will decrease.
C) The mean will be unchanged.
D) It is impossible to determine without having the complete data set.

Question 32

What is the mode of the following sample data set?

A) 15.1
B) 9
C) 5
D) 22

Question 33

The lengths of the reigns of 50 British monarchs (in years) are summarized with the following five-number summary: xmin = 0, Q1 = 6, = 15.5, Q3 = 24, xmax = 63
If the maximum of 63 years is accidentally recorded as 630 years, how will this affect the median?

A) The median will increase.
B) The median will decrease.
C) The median will be unchanged.
D) It is impossible to determine without having the complete data set.

Question 34

The Roller Coaster Database maintains a website (www.rcdb.com) with data on roller coasters around the world.Some of the data recorded include whether the coaster is made of wood or steel and the maximum speed achieved by the coaster, in miles per hour.The box plots display the distributions of speed by type of coaster for 145 roller coasters in the United States as downloaded from the site in November 2003. Are there more wooden or steel roller coasters displayed in this plot?

A) Wooden
B) Steel
C) There are an equal number of both types of roller coasters.
D) We cannot tell the sample sizes from a box plot.