statistics

b

Can the variance of a data set ever be​ negative? Explain. Can the variance ever be smaller than the standard​ deviation? Explain. Choose the correct answer below. A. The variance of a data set can be negative if the mean is negative. Variance can be smaller than the standard deviation if the variance is less than 0. B. The variance of a data set cannot be negative because it is the sum of the squared deviations divided by a positive value. Variance can be smaller than the standard deviation if the variance is less than 1. C. The variance of a data set cannot be negative because deviation from the mean is always a positive value. Variance cannot be smaller than the standard deviation because the variance is the square of the standard deviation. D. The variance of a data set can be negative if all of the data values are negative. Variance cannot be smaller than the standard deviation because the standard deviation is the square root of the variance.

A

Define a bivariate relationship. Choose the correct answer below. A. A bivariate relationship is the relationship between two quantitative variables. B. A bivariate relationship is the relationship between more than two qualitative variables. C. A bivariate relationship is the relationship between two qualitative variables. D. A bivariate relationship is the relationship between more than two quantitative variables.

a

Define an outlier. Choose the correct answer below. A. An outlier is a point whose residual is more than 3 standard deviations from 0. B. An outlier is a point whose residual is within 1 standard deviation of 0. C. An outlier is a point that the experimenter thinks should be ignored. D. An outlier is a point that is a good example of the model equation.

d

Define statistical thinking. Choose the correct answer below. A. Statistical thinking is a series of actions or operations that transforms inputs to outputs. B. Statistical thinking is a statement about the degree of uncertainty associated with a statistical inference. C. Statistical thinking utilizes sample data to make​ estimates, decisions,​ predictions, or other generalizations about a larger set of data. D. Statistical thinking involves applying rational thought and the science of statistics to critically assess data and inferences.

b

Describe the sample variance using words rather than a formula. Do the same with the population variance. Choose the correct answer below. A. The sample variance is the sum of the deviations from the mean divided by the number of measurements. The population variance is the sum of the deviations from the mean divided by the number of measurements minus one. B. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one. The population variance is the average of the squared distances of the measurements on all units in the population from the mean. C. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements. The population variance is the sum of the squared deviations from the mean divided by the number of measurements minus one. D. The sample variance is the sum of the deviations from the mean divided by the number of measurements minus one. The population variance is the average of the distances of the measurements on all units in the population from the mean.

b

Explain how populations and samples differ. Choose the correct answer below. A. A sample is a set of measurements that are recorded on a naturally occurring numerical scale. A population is a set of measurements that cannot be measured on a natural numerical​ scale; they can only be classified into one of a group of categories. B. A population is a set of units of interest to a study. A sample is a subset of the units of a population. Your answer is correct.C. A population is an object upon which data is collected. A sample is a characteristic or property of an individual experimental unit. D. A sample is a set of units of interest to a study. A population is a subset of the units of a sample.

b

Explain how populations and variables differ. Choose the correct answer below. A. A population is a set of units of interest to a study. A variable is an object upon which data is collected. B. A population is a set of units of interest to a study. A variable is a characteristic or property of the units being studied. C. A population is a set of units of interest to a study. A variable is a subset of the units of a population. D. A variable is a set of units of interest to a study. A population is a characteristic or property of the units being studied.

d

Explain how the relationship between the mean and median provides information about the symmetry or skewness of the​ data's distribution. Select the correct answer below. A. The mean is affected by extreme​ values, while the median is not. If the data set is skewed to the​ right, then the median is greater than the mean. If the data set is​ symmetric, the mean equals the median. If the data set is skewed to the​ left, the mean is greater than the median. B. The median is affected by extreme​ values, while the mean is not. If the data set is skewed to the​ right, then the median is less than the mean. If the data set is​ symmetric, the mean equals the median. If the data set is skewed to the​ left, the mean is less than the median. C. The median is affected by extreme​ values, while the mean is not. If the data set is skewed to the​ right, then the median is greater than the mean. If the data set is​ symmetric, the mean equals the median. If the data set is skewed to the​ left, the mean is greater than the median. D. The mean is affected by extreme​ values, while the median is not. If the data set is skewed to the​ right, then the median is less than the mean. If the data set is​ symmetric, the mean equals the median. If the data set is skewed to the​ left, the mean is less than the median.

B, C

Explain the difference between a bar graph and a Pareto diagram. What is a bar​ graph? A. A bar graph represents the frequencies of values either from​ left-to-right or​ right-to-left. The different segments of the bar are used to indicate the different frequencies of each category. B. A bar graph is a horizontal or vertical representation of the frequency or relative frequency of the categories. The height of each rectangle represents the​ category's frequency or relative frequency. C. A bar graph is a circular graph that uses bars to divide it into segments corresponding to each category. The segments are proportional to the frequency of its category. What is a Pareto​ diagram? A. A Pareto diagram is a combination of a pie chart and a bar graph. B. A Pareto diagram is a display of two data sets side by side where the height of each rectangle represents the​ category's frequency or relative frequency. Your answer is not correct. C. A Pareto diagram is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency.

A

Explain the difference between a bar graph and a histogram. Choose the correct answer below. A. A bar graph is used for displaying categories​ (or classes) of qualitative variables while histograms are used to display groupings of similar data values for quantitative data. B. A bar graph is used for displaying condensed data by grouping all values with the same stem while a histogram is used for displaying condensed data by grouping similar data values into the same class. C. A bar graph is used for displaying condensed data by grouping similar data values into the same class while a histogram is used for displaying condensed data by grouping all values that are the same. D. A bar graph is used to display groupings of similar data values for quantitative data while histograms are used for displaying categories​ (or classes) of qualitative variables.

c

Name and describe the three most important measures of central tendency. Choose the correct answer below. A. The​ mean, sample​ size, and mode are the most important measures of central tendency. The mean of a data set is the sum of the observations divided by the middle value in its ordered list. The sample size of a data set is the number of observations. The mode of a data set is its highest value in its ordered list. B. The​ mean, median, and mode are the most important measures of central tendency. The mean of a data set is the product of the observations divided by the number of observations. The median of a data set is the lowest value in its ordered list. The mode of a data set is its least frequently occurring value. C. The​ mean, median, and mode are the most important measures of central tendency. The mean of a data set is its arithmetic average. The median of a data set is the middle value in its ordered list. The mode of a data set is its most frequently occurring value. D. The sample​ size, median, and mode are the most important measures of central tendency. The sample size of a data set is the difference between the highest value and lowest value in its ordered list. The median of a data set is its most frequently occurring value. The mode of a data set is sum of the observations divided by the number of observations.

C, A

Suppose​ you're given a data set that classifies each sample unit into one of four​ categories: A,​ B, C, or D. You plan to create a computer database consisting of these​ data, and you decide to code the data as Aequals=​1, Bequals=​2, Cequals=​3, and Dequals=4. Are the data consisting of the classifications​ A, B,​ C, and D qualitiative or​ quantitative? After the data are input as​ 1, 2,​ 3, or​ 4, are they qualitative or​ quantitative? Are the data consisting of the classifications​ A, B,​ C, and D qualitiative or​ quantitative? A. ​Qualitative, because they are measured on a naturally occuring numerical scale. B. ​Quantitative, because they are measured on a naturally occuring numerical scale. C. ​Qualitative, because they can only be classified into categories. Your answer is correct.D. ​Quantitative, because they can only be classified into categories. After the data are input as​ 1, 2,​ 3, or​ 4, are they qualitative or​ quantitative? A. ​Qualitative, because they cannot be meaningfully​ added, subtracted,​ multiplied, or divided. This is the correct answer.B. ​Quantitative, because they are measured on a naturally occurring numerical scale. C. ​Qualitative, because they are measured on a naturally occurring numerical scale. D. ​Quantitative, because they cannot be meaningfully​ added, subtracted,​ multiplied, or divided.

symmetric and unimodal.

The Empirical Rule applies to distributions that are

iqr

The length of the box in a boxplot is proportional to which of the​ following? Choose the correct answer below. Median IQR Standard deviation

C

Explain the difference between a bar graph and a pie chart. Choose the correct answer below. A. In a bar​ graph, a slice of a rectangle is shaded for each class of the qualitative variable with its width corresponding to the class frequency or class relative frequency. In a pie​ chart, each slice of the pie corresponds to the frequency of a class of the qualitative variable. B. In a bar​ graph, each bar or rectangle corresponds to the relative frequency of a class of the qualitative variable. In a pie​ chart, a slice is drawn above each class of the qualitative variable corresponding to the class frequency or class relative frequency. C. In a bar​ graph, a bar or rectangle is drawn above each class of the qualitative variable corresponding to the class frequency or class relative frequency. In a pie​ chart, each slice of the pie corresponds to the relative frequency of a class of the qualitative variable. D. In a bar​ graph, a bar or rectangle is drawn for each class of the qualitative variable with its width corresponding to the class frequency or class relative frequency. In a pie​ chart, each class is represented by a pie​ (or circle) that is proportional to its relative frequency.

c

Explain the difference between descriptive and inferential statistics. Choose the correct answer below. A. Descriptive statistics is a characteristic or property of an individual experimental unit. Inferential statistics is the process used to assign numbers to variables of individual population units. B. Descriptive statistics draws conclusions about the sets of data based on sampling. Inferential statistics summarizes the information revealed in data sets. C. Descriptive statistics describes sets of data. Inferential statistics draws conclusions about the sets of data based on sampling. D. Descriptive statistics are measurements that are recorded on a naturally occurring numerical scale. Inferential statistics are measurements that cannot be measured on a natural number​ scale; they can only be classified into one of a group of categories.

A, B

Explain the difference between each pair of concepts. a. Frequency and relative frequency b. Percentage and relative frequency a. Select the correct choice below. A. Frequency is the number of times a particular distinct value occurs. Relative frequency is the ratio of the frequency of a value to the total number of observations. B. Frequency is the total number of observations in a data set. Relative frequency is the ratio of the number of times a particular distinct value occurs to the frequency. C. Frequency is the total number of observations in a data set. Relative frequency is the number of times a particular distinct value occurs. D. Frequency is the number of times a particular distinct value occurs. Relative frequency is the ratio of the frequency of two different values. b. Select the correct choice below. A. A relative frequency is the ratio of two percentages. Your answer is not correct. B. A relative frequency is the same as a percentage expressed as a decimal. C. A relative frequency expressed as a decimal is the same as a percentage. D. There is no difference between a relative frequency and a percentage.

c

Explain the difference between qualitative and quantitative data. Choose the correct answer below. A. Quantitative data are collected from a designed​ experiment, while qualitative data are from an observational study. B. Quantitative data are data from a​ population, while qualitative data are data from a sample. C. Quantitative data are numerical in​ nature, while qualitative data are categorical in nature. D. Quantitative data are categorical in​ nature, while qualitative data are numerical in nature. E. Quantitative data are data from a​ sample, while qualitative data are data from a population. F. Quantitative data are collected from an observational​ study, while qualitative data are from a designed experiment.

A,B, D

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

d

What is a representative​ sample? What is its​ value? Choose the correct answer below. A. A representative sample is a sample that exhibits characteristics typical of those possessed by the population of interest. It is valuable because these characteristics allow descriptive statistics to be applied. B. A representative sample is a sample that is selected at random from the population of interest. It is valuable because its unbiased nature allows descriptive statistics to be applied. C. A representative sample is a sample that is selected at random from the population of interest. It is valuable because its unbiased nature allows inferential statistics to be applied. D. A representative sample is a sample that exhibits characteristics typical of those possessed by the population of interest. It is valuable because these characteristics allow inferential statistics to be applied.

A

What is the difference between positive association and negative association as it pertains to the relationship between two​ variables? Choose the correct answer below. A. A positive association occurs when an increase in one variable is generally associated with an increase in the second​ variable, and a negative association occurs when one variable has a tendency to decrease as the other increases. B. A positive association occurs when one variable has a tendency to decrease as the other​ increases, and a negative association occurs when an increase in one variable is generally associated with an increase in the second variable. C. A positive association occurs when one variable has a tendency to decrease as the other​ increases, and a negative association occurs when one variable does not change as the other increases. D. A positive association occurs when an increase in one variable is generally associated with an increase in the second​ variable, and a negative association occurs when one variable does not change as the other increases.

b

What is the primary disadvantage of using the range to compare the variability of data​ sets? Choose the correct answer below. A. It does not have any units. B. It is a rather insensitive measure of data variation. C. It is hard to compute. D. It is a sensitive measure of data variation.

d

What is​ statistics? A. It is an estimate or prediction or some other generalization about a population based on information contained in a sample. B. It is a characteristic or property of an individual experimental unit. C.It is the process used to assign numbers to variables of individual population units. D.It is the science that deals with​ collection, classification,​ analysis, and interpretation of information or data.

d

Why would a statistician consider an inference incomplete without an accompanying measure of its​ reliability? Choose the correct answer below. A. The measure of reliability is a value​ (probability) assigned by the individual making the inference to indicate the accuracy of their​ inference; it is based on what they believe the strength of their research was and the quality of the sample. Without this​ value, there is no way to differentiate the validity of the inference from pure guessing. B. The measure of reliability is a strength rating based on the quality of the sample used to make the​ inference; it is a measure of the validity of the inference. C. The measure of reliability is a strength rating based on the sources providing the inference. The better the​ sources, the stronger the​ rating, and the more likely that the inference is true. D. The measure of reliability separates the science of statistics from the art of​ fortune-telling; it provides a bound on the estimation error.

class relative frequency

class frequency/n