McGraw Hill ch. 3

unimodal; bimodal

If a variable has one mode, then we say it is '' If it has two modes, then it is common to call it ''.

central

The term ______ location relates to the way numerical data tend to cluster around some middle or central value.

parameter; statistic

We refer to the population mean as a ____ and the sample mean as a ____.

range mean absolute deviation interquartile range

There are several measures of dispersion that gauge the variability of a data set. Select all of the measures below that are useful for measuring dispersion. Multiple select question. range mean absolute deviation Use the mean interquartile range

median

Which of the measures of central location is defined as the middle value of a data set; that is, an equal number of observations lie above and below it? Multiple choice question. Median Range Mean Mode

Measures of association

Which numerical descriptive measure shows whether two numerical variables have a linear relationship? Multiple choice question. Measures of dispersion Measures of central location Measures of shape Measures of association

Skewness coefficient Kurtosis coefficient

Which of the following are common measures of shape? Multiple select question. Skewness coefficient Kurtosis coefficient MAD or the Mean absolute deviation Range

scatter plot

Which of the following is a common graphical method that allows us to determine whether two numerical variables are related in some systematic way? Multiple choice question. Scatter plot Pie chart Contingency table Stacked column chart

Outliers

Extremely large or small observations for a variable are referred to as ''.

When creating a bar chart or a histogram, each bar/rectangle should be of the same width Axes should be clearly marked and labeled

Select all that apply Which of the basic guidelines should you follow when constructing or interpreting charts or graphs? Choose all that apply! Multiple select question. When creating a bar chart or a histogram, each bar/rectangle should be of the same width Give high values for upper limits on a graph The prettiest graph should be used for a given set of data Axes should be clearly marked and labeled

Blank 1: Correlation

The '' coefficient describes both the direction and the strength of the linear relationship between x and y

kurtosis

The '' coefficient is a summary measure that tells us whether the tails of the distribution are more or less extreme than the normal distribution. Listen to the complete question

true

True or false: After arranging the data in ascending order (smallest to largest), we calculate the median as (1) the middle value if the number of observations is odd or (2) the average of the two middle values if the number of observations is even.

Mode Mean Median

What are the three most widely used measures of central location? Multiple select question. Mode Mean Range Median

Mean Absolute Deviation

What does MAD stand for, when used as a measure of dispersion? Multiple choice question. Main Absolute Description Mean Absolute Data Middle Absolute Deviation Mean Absolute Deviation

Outlier

Because almost all observations fall within three standard deviations of the mean, it is common to treat an observation as an '' if its z-score is more than 3 or less than −3

2

A large lecture class has 280 students. The professor has announced that the mean score on an exam is 74 with a standard deviation of 8. The distribution of scores is bell-shaped. How many standard deviations above the mean would a score of 90 be? Multiple choice question. 1.5 2 3 1

6 Reason: =abs((31-40)+(40-40) +(49-40))/3 = 6

Calculate the Mean Absolute Deviation for the following data: We have observed the age of 3 individuals in a study, where the mean age is 40. The observed ages were 31, 40, and 49. What is the MAD? Multiple choice question. -6 6 9 Not enough data

1. Intervals are exhaustive 2. The total number of intervals in a frequency distribution usually ranges from 5 to 20 3. Interval limits are easy to recognize and interpret

Select all that apply For a numerical variable, instead of categories, we construct a series of intervals (sometimes called classes). We must make certain decisions about the number of intervals, as well as the width of each interval. Which of the following is a guideline for developing the intervals? Multiple select question. Intervals are exhaustive The total number of intervals in a frequency distribution usually ranges from 5 to 20 Intervals are NOT mutually exclusive Interval limits are easy to recognize and interpret

true

True or false: Contingency tables and stacked column charts are two common tabular and graphical methods that help us summarize the relationship between two categorical variables.

Dispersion

'Each measure is a numerical value that equals zero if all observations are identical and increases as the observations become more diverse'. What measure does this describe? Multiple choice question. Central Location Dispersion Shape Mode

stacked

A ______ column chart is an advanced version of the column chart that we discussed. It is designed to visualize more than one categorical variable, plus it allows for the comparison of composition within each category.

Association

A measure of '' quantifies the direction and strength of the linear relationship between two variables, x and y.

75%

A percentile is technically a measure of location; however, it is also used as a measure of relative position because it is so easy to interpret. if you know that the raw score corresponds to the 75th percentile, then you know that approximately how many students had scores lower than your score? Multiple choice question. 25% We have no way of knowing 74% 75%

75%

A percentile is technically a measure of location; however, it is also used as a measure of relative position because it is so easy to interpret. if you know that the raw score corresponds to the 75th percentile, then you know that approximately how many students had scores lower than your score? Multiple choice question. 74% We have no way of knowing 25% 75%

column chart

A vertical bar chart is often referred to as which of the following? Multiple choice question. Column chart Line chart Pie chart Horizontal chart

covariance

An objective numerical measure that reveals the direction of the linear relationship between two variables is called the ''.

4

If a bar chart depicts the relative frequency for type of occupations (with options as Doctor, Professor, Athlete, or Actor) as the categorical variable as a series of vertical bars, and the Doctor vertical bar has a value of .4, and there are 10 employeed individuals responding, how many Doctors were in the group of 10? Multiple choice question. 6 10 40 4

mode

Which of the measures of central location is defined as the observation that occurs most frequently? Multiple choice question. Median Mean Range Mode

.116

A frequency distribution for a categorical variable groups the data into categories and records the number of observations that fall into each category. In a survey, we asked 1000 respondents which car they would purchase if they had a choice between an Audi, a Mazda, a Toyota, or a Subaru. Of the 1000 respondents, 116 chose the Audi. What is the relative frequency of Audi respondents?

A linear relationship exists between the two variables No relationship exists between the two variables A nonlinear relationship exists between the two variables

A scatter plot is a simple, yet useful, graphical tool. We plot each pairing: (x1, y1), (x2, y2), and so on. Once the data are plotted, according to the textbook, the graph may reveal which of the following? (Select all that apply) Multiple select question. A linear relationship exists between the two variables No relationship exists between the two variables A bar chart would have been a better choice A nonlinear relationship exists between the two variables

frequency

For a numerical variable, a _________ distribution groups data into intervals and records the number of observations that falls into each interval.

Approximately 95% of all observations fall in the interval ̄x±2 Almost all observations fall in the interval ̄x±3 Approximately 68% of all observations fall in the interval ̄x±s

Given a sample mean ̄x, a sample standard deviation s, and a relatively symmetric and bell-shaped distribution, the empirical rule states that: (Select all the apply) Multiple select question. Approximately 90% of all observations fall in the interval ̄x±2 Approximately 95% of all observations fall in the interval ̄x±2 Almost all observations fall in the interval ̄x±3 Approximately 68% of all observations fall in the interval ̄x±s

Relative Frequency Frequency of each interval

Select all that apply When constructing a histogram, we typically mark off the interval limits along the horizontal axis. What does the height of each bar represent? Choose all that are correct responses. Multiple select question. Number of intervals Relative Frequency Frequency of each interval The type of response

Histogram Frequency distribution

Select all that apply Which of the following are described as valid methods for visualizing a numerical variable? Multiple select question. Tree diagram Histogram Frequency distribution Decision tree

Positively skewed Negatively skewed Symmetric

Select all that apply Which of the following are valid shapes of a histogram? Multiple select question. Positively skewed Negatively skewed Correlated Symmetric

Skewness

The '' coefficient measures the degree to which a distribution is not symmetric about its mean.

range

The '' is the simplest measure of dispersion; it is the difference between the maximum and the minimum observations of a variable.

First; Second; Third

The 25th percentile is also referred to as the '' quartile, the 50th percentile is referred to as the '' quartile, and the 75th percentile is referred to as the '' quartile.

population

The formula for the variance differs depending on whether we have a sample or a ''.

It is the range of the middle 50% of the variable

The interquartile range (IQR) is the difference between the third quartile and the first quartile, or, equivalently, IQR = Q3 − Q1.Which of the following is true of the interquartile range? Multiple choice question. the average of the squared differences from the mean It is the range of the middle 50% of the variable it is the difference between the maximum and the minimum observations of a variable Is an average of the absolute differences between the observations and the mean.

z-score in the marketing class is z=(90−78)/10=1.2 z-score in the accounting class is z=(90-74)/8 =2

The mean and the standard deviation of scores on an accounting exam are 74 and 8, respectively. The mean and the standard deviation of scores on a marketing exam are 78 and 10, respectively. Find the z-scores for a student who scores 90 in both classes. Multiple select question. z-score in the accounting class is z=(90-74)/10 =1.6 z-score in the marketing class is z=(90−78)/10=1.2 z-score in the marketing class is z=(90−78)/8=1.5 z-score in the accounting class is z=(90-74)/8 =2

Show the most-or least-frequently downloaded music genres across various music streaming platforms Show the inventory items which need to be replenished, which items have plenty on hand inventory, and which items should be evaluated to order Show which products are the best-or worst-selling products at various stores

There are a number of ways to display a heat map, but they all share one thing in common—they use color to communicate the relationships between the variables that would be harder to understand by simply inspecting the raw data. Choose all the examples below that would be a good usage for a heat map. Multiple select question. Show the most-or least-frequently downloaded music genres across various music streaming platforms Show the trend of product sales over time, such as sales in one period and then the next Show the inventory items which need to be replenished, which items have plenty on hand inventory, and which items should be evaluated to order Show which products are the best-or worst-selling products at various stores

false

True or false: When constructing a graph, the vertical axis SHOULD be stretched so that an increase (or decrease) of the data appears more pronounced than warranted. This will help prove your point more graphically.

true

True or false: z-score measures the relative location of an observation and indicates whether it is an outlier.

252

We asked 1000 respondents whether they preferred Online teaching, hybrid teaching, or attending class in person. The relative frequency of the Online teaching proponents was point 252 or (.252). How many respondents preferred online teaching? Multiple choice question. 748 There is no way to know 252 We can identify the relative frequency, but not the frequency

Measures of dispersion

We can use numerical descriptive measures to extract meaningful information from data. Which measure gauges the underlying variability of the data? Multiple choice question. Measures of shape Measures of central location Measures of association Measures of dispersion

Maximum value Minimum value Q1, Q2, Q3

When constructing a box plot, the first step is to use a five-number summary. What does the five-number summary contain? Multiple select question. Maximum value Minimum value Q1, Q2, Q3, Q4 Q1, Q2, Q3

Contingency

When examining the relationship between two categorical variables, a _____ table proves very useful

A paired observation with one x-axis point and one y-axis point. (x1, y1)

When examining the relationship between two numerical variables, a scatter plot is a simple, yet useful, graphical tool. What does each point in a scatter plot represent? Multiple choice question. A paired observation with one x-axis point and one y-axis point. (x1, y1) Two x-axis comparisons Multiple paired observations such as (x1, x2), (y2, y3) An unpaired observation but two y-axis comparisons

Bar Chart

Which 'tool' depicts the frequency or the relative frequency for each category of the categorical variable as a series of horizontal or vertical bars, the lengths of which are proportional to the values that are to be depicted. Multiple choice question. Pie chart Frequency distribution Hypothesis test Bar chart

These measures quantify the direction and strength of the linear relationship between two variables, x and y. These measures are not appropriate when the underlying relationship between the variables is nonlinear

Which of the following is true of measures of association? Select all that are true. Multiple select question. These measures quantify the direction and strength of the linear relationship between two variables, x and y. These measures are not appropriate when the underlying relationship between the variables is nonlinear Measures the degree to which a distribution is not symmetric about its mean. These measures reflect the typical or central value of a variable

If the correlation coefficient equals 0, then x and y are not linearly related The correlation coefficient is unit free If the correlation coefficient equals −1, then x and y have a perfect negative linear relationship

Which of the following is true of the correlation coefficient? Select all that are true! Multiple select question. If the correlation coefficient equals 0, then x and y are not linearly related The correlation coefficient is unit free If the correlation coefficient equals −1, then x and y have a perfect negative linear relationship The value of the correlation coefficient falls between zero and 1

If the covariance is negative, then x and y have a negative linear relationship. The covariance is sensitive to the units of measurement Covariance can be negative, positive, or zero

Which of the following is true of the covariance? Select all that are true! Multiple select question. We can comment on the strength of the relationships using the covariance If the covariance is negative, then x and y have a negative linear relationship. The covariance is sensitive to the units of measurement Covariance can be negative, positive, or zero

The variance is an average of the squared differences between the observations and the mean The standard deviation is the positive square root of the variance.

Which of the following is true of the variance and standard deviation? Multiple select question. The difference between the third quartile and the first quartile An average of the absolute differences between the observations and the mean. The variance is an average of the squared differences between the observations and the mean The standard deviation is the positive square root of the variance.

color

A heat map is an important visualization tool that uses _______ to display relationships between variables. (Please enter one word for one blank.)

300 < x ≤ 400 and 400 < x ≤ 500

Which of the following examples violates the 'mutually exclusive' guideline for interval construction? Multiple choice question. 300 < x ≤ 400 and 400 < x ≤ 500 200 < x ≤ 300 and 301 < x ≤ 500 100 < x ≤ 200 and 201 < x ≤ 300 300 < x ≤ 400 and 401 < x ≤ 500

interquartile

The '' range is the difference between the third quartile and the first quartile.

μ, where μ is the Greek letter mu

The only thing that differs between a population mean and a sample mean is the notation. The population mean is referred to as: Multiple choice question. There are many differences the number of observations in a population x (pronounced x-bar) μ, where μ is the Greek letter mu

Is the simplest measure of dispersion Ignores the middle observation of a variable Is not considered a good measure of dispersion

Which is true of the use of the range as a measure of dispersion? Multiple select question. Focuses solely on the middle observations Is the simplest measure of dispersion Ignores the middle observation of a variable Is not considered a good measure of dispersion

Outliers may just be due to random variations There are no universally agreed upon methods for treating outliers Outliers may indicate bad data due to incorrectly recorded observations

Which of the following is a true statement regarding outliers in data analysis? (Choose all that apply) Multiple select question. Outliers will not unduly affect the mean of a sample Outliers may just be due to random variations There are no universally agreed upon methods for treating outliers Outliers may indicate bad data due to incorrectly recorded observations

A positively skewed distribution has a positive skewness coefficient A symmetric distribution has a skewness coefficient of zero

Which of the following statements is true of the skewness coefficient? Select all that are true. Multiple select question. A positively skewed distribution has a positive skewness coefficient A negatively skewed distribution has a zero skewness coefficient The normal distribution has a skewness coefficient of 1 A symmetric distribution has a skewness coefficient of zero

A platykurtic distribution is one that has shorter tails A distribution that has tails that are more extreme than the normal distribution is leptokurtic Excess kurtosis is calculated as the kurtosis coefficient minus 3

Which of the following statements is true regarding the kurtosis coefficient? Select all that are true. Multiple select question. A platykurtic distribution is one that has shorter tails A distribution that has tails that are more extreme than the normal distribution is leptokurtic The kurtosis coefficient of a normal distribution is zero Excess kurtosis is calculated as the kurtosis coefficient minus 3