CH 2 HW STATs

A data set can have the same​ mean, median, and mode. The statement is true. The statement is false. A data set cannot have the same mean and mode. The statement is false. A data set cannot have the same mean and median. The statement is false. A data set cannot have the same median and mode.

The statement is true.

The second quartile is the median of an ordered data set. False. The third quartile is the median of an ordered data set. False. The first quartile is the median of an ordered data set. True.

True

It is impossible to have a​ z-score of 0. The statement is true. The statement is false. A​ z-score of 0 is a standardized value that is equal to the mean. The statement is false. A​ z-score of 0 is a standardized value that occurs when the test statistic is 0. The statement is false. A​ z-score of 0 is a standardized value that is equal to the standard deviation.

The statement is false. A​ z-score of 0 is a standardized value that is equal to the mean.

What is the difference between a frequency polygon and an​ ogive? A frequency polygon is a line graph while an ogive is a histogram. It is easier to find patterns in the data from a frequency polygon than an ogive. A frequency polygon displays class frequencies while an ogive displays cumulative frequencies. There is no difference between a frequency polygon and an ogive.

A frequency polygon displays class frequencies while an ogive displays cumulative frequencies.

In terms of displaying​ data, how is a​ stem-and-leaf plot similar to a dot​ plot? Both plots can be used to identify unusual data values. Both plots can be used to determine specific data entries. Both plots can be used to show large amounts of data. Both plots show how data are distributed.

Both plots can be used to identify unusual data values; Both plots can be used to determine specific data entries; Both plots show how data are distributed

In a frequency​ distribution, the class width is the distance between the lower and upper limits of a class. True. False. In a frequency​ distribution, the range is the distance between the lower and upper limits of a class. False. In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes.

False. In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes.

___________are special cases of ____________________. _____________ is the 25th​ percentile, ______________is the 50th ​percentile, and _____________ is the 75th percentile.

Quartiles;percentiles;Q1, Q2,Q3

What is the difference between relative frequency and cumulative​ frequency? Relative frequency of a class is the percentage of the data that falls in that​ class, while cumulative frequency of a class is the sum of the frequencies of that class and all previous classes. Relative frequency of a class is the number of observations in that​ class, while cumulative frequency of a class is the sum of all the frequencies. Relative frequency of a class is the proportion of the data in that​ class, while cumulative frequency of a class is the number of observations in that class. There is no difference between the two.

Relative frequency of a class is the percentage of the data that falls in that​ class, while cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.

Explain how to find the range of a data set. Choose the correct answer below. The range is found by adding the first and last data entries. The range is found by subtracting the first data entry from the last data entry. The range is found by subtracting the minimum data entry from the maximum data entry. The range is found by adding the minimum and maximum data entries.

The range is found by subtracting the minimum data entry from the maximum data entry

The 50th percentile is equivalent to Q1 The statement is false. The 50th percentile is equivalent to Q2. The statement is false. The 50th percentile is equivalent to the mean. The statement is false. The 50th percentile is equivalent to Q3. The statement is true.

The statement is false. The 50th percentile is equivalent to Q2.

A​ motorcycle's fuel efficiency represents the ninth decile of vehicles in its class. Make an observation about the​ motorcycle's fuel efficiency. The​ motorcycle's fuel efficiency is greater than the fuel efficiency for​ 100% of vehicles in its class. The​ motorcycle's fuel efficiency is greater than the fuel efficiency for​ 10% of vehicles in its class. The​ motorcycle's fuel efficiency is greater than the fuel efficiency for​ 9% of vehicles in its class. The​ motorcycle's fuel efficiency is greater than the fuel efficiency for​ 90% of vehicles in its class.

The​ motorcycle's fuel efficiency is greater than the fuel efficiency for​ 90% of vehicles in its class.

A frequency distribution is ____________ when a tail of the graph elongates more to the left than to the right.

skewed left

A frequency distribution is ______________ when its tail extends to the right instead of to the left

skewed right

A frequency distribution is _____________ when a vertical line can be drawn through the middle of a graph of the distribution and the resulting halves are approximately mirror images.

symmetric

A frequency distribution is ______________ when all​ entries, or​ classes, in the distribution have equal or approximately equal frequencies

uniform

What is a disadvantage of using the range as a measure of​ variation? It is hard to compute. It uses only two entries from the data set. It uses all entries from the data set.

It uses only two entries from the data set.

What is an advantage of using a​ stem-and-leaf plot instead of a​ histogram? -Stem-and-leaf plots contain original data values where histograms do not. ​-Stem-and-leaf plots show data clusters where histograms do not. ​-Stem-and-leaf plots easily organize data of all sizes where histograms do not. ​-Stem-and-leaf plots graph qualitative data where histograms do not. What is a disadvantage of using a​ stem-and-leaf plot instead of a​ histogram? -Histograms graph quantitative data where​ stem-and-leaf plots do not. -Histograms easily organize data of all sizes where​ stem-and-leaf plots do not. -Histograms contain original data values where​ stem-and-leaf plots do not. -Histograms show data clusters where​ stem-and-leaf plots do not.

Stem-and-leaf plots contain original data values where histograms do not; Histograms easily organize data of all sizes where​ stem-and-leaf plots do not.

What is an advantage of using the range as a measure of​ variation? It uses all entries from the data set. Your answer is correct. It uses only two entries from the data set.

It is easy to compute.

When each data class has the same​ frequency, the distribution is symmetric. The statement is true. The statement is false. When each data class has the same​ frequency, the distribution is bimodal. The statement is false. When each data class has the same​ frequency, the distribution is skewed right. The statement is false. When each data class has the same​ frequency, the distribution is skewed left.

The statement is true

Why should the number of classes in a frequency distribution be between 5 and​ 20? The number of classes in a frequency distribution should be between 5 and 20 so that the class width is between 5 and 20. The number of classes in a frequency distribution should be between 5 and 20 so that the classes do not overlap. The number of classes in a frequency distribution should be between 5 and 20 so that the class width is not too small. If the number of classes in a frequency distribution is not between 5 and​ 20, it may be difficult to detect any patterns. The number of classes in a frequency distribution should be between 5 and 20 so that the class width is not too large

If the number of classes in a frequency distribution is not between 5 and​ 20, it may be difficult to detect any patterns.

It is easier to determine the minimum and maximum values of a data set when it has been arranged into a frequency distribution. Organizing the data into a frequency distribution can make patterns within the data more evident. Organizing the data into a frequency distribution makes it possible to graph quantitative data. What are some benefits of representing data sets using frequency​ distributions? It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. It can be easier to determine the class boundaries by looking at a graph of the frequency distribution. Graphing a frequency distribution makes it possible to find the total number of observations. Graphing a frequency distribution makes it possible to determine the relative frequencies of each of the classes.

Organizing the data into a frequency distribution can make patterns within the data more evident; It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution.

A​ student's score on an actuarial exam is in the 78th percentile. What can you conclude about the​ student's exam​ score? The student scored higher than​ 78% of the students who took the actuarial exam. The student scored a​ 78% on the exam. About​ 78% of students achieved the same score as this particular student. ​78% of students scored higher than this particular student.

The student scored higher than​ 78% of the students who took the actuarial exam.

Why is the standard deviation used more frequently than the​ variance? The standard deviation requires less entries from the data set. The units of variance are squared. Its units are meaningless. The standard deviation is easier to compute.

The units of variance are squared. Its units are meaningless.

An outlier is any number above Q3 or below Q1. This statement is false. A true statement is​ "An outlier is any number above Q3+​1.5(IQR) or below Q1−​1.5(IQR) are considered​ outliers." This statement is false. A true statement is​ "An outlier is any number above Q1−​1.5(IQR) or below Q3+​1.5(IQR)." This statement is false. A true statement is​ "An outlier is any number above 2•Q3 or below 2•Q1​." This statement is true.

This statement is false. A true statement is​ "An outlier is any number above Q3+​1.5(IQR) or below Q1−​1.5(IQR) are considered​ outliers."

Class boundaries ensure that consecutive bars of a histogram touch. -False; class boundaries are the edges of each clustering of data. Sometimes they touch and sometimes they do not. ​-False; class boundaries are the descriptive​ (non-numerical) categories of data in a data set. -True ​-False; class boundaries are the width of bars and not the edges of bars in the histogram.

True

Given a data​ set, how do you know whether to calculate σ or​ s? If the given data set contains a large number of​ entries, then s is calculated. If the data set contains a small number of​ entries, then σ is calculated. When given a data​ set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a​ population, then σ is calculated. If the data are a​ sample, then s is calculated. When given a data​ set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a​ population, then s is calculated. If the data are a​ sample, then σ is calculated. If the given data set contains a large number of​ entries, then σ is calculated. If the data set contains a small number of​ entries, then s is calculated.

When given a data​ set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a​ population, then σ is calculated. If the data are a​ sample, then s is calculated.