Data Analysis Chapter 1-4 Flashcards
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Questions and Answers

What should axes be when creating a bar chart or histogram?

Clearly marked and labeled

Which of the following is a common graphical method that allows us to determine whether two numerical variables are related in some systematic way?

  • Bar chart
  • Histogram
  • Scatter plot (correct)
  • Line chart

    • How can a scatter plot incorporate a categorical variable?

    By using different colors or symbols

    What does the number 51 represent for Generation X in the table?

    <p>The number of Generation X employees who had personality types categorized as Analyst</p> Signup and view all the answers

    In a bubble plot, how is the third numerical variable represented?

    <p>Size of the bubble</p> Signup and view all the answers

    A ____ column chart is an advanced version of the column chart designed to visualize more than one categorical variable.

    <p>stacked</p> Signup and view all the answers

    Which of the following are true of line charts? (Select all that apply)

    <p>Useful for tracking changes or trends over time</p> Signup and view all the answers

    What does each point in a scatter plot represent?

    <p>A paired observation with one x-axis point and one y-axis point (x1, y1)</p> Signup and view all the answers

    A heat map uses ' ____ ' to display relationships between variables.

    <p>color</p> Signup and view all the answers

    A scatter plot with a ' ____ variable' includes a third categorical variable.

    <p>categorical</p> Signup and view all the answers

    A ___ plot shows the relationship between three numerical variables.

    <p>bubble</p> Signup and view all the answers

    A ___ chart displays a numerical variable as a series of data points connected by a line.

    <p>line</p> Signup and view all the answers

    Which of the following would be a good usage for a heat map? (Select all that apply)

    <p>Show inventory items needing replenishment and those with plenty on hand</p> Signup and view all the answers

    The difference between cross-sectional and time series data is whether the data is evaluated at a single point in time or multiple points in time.

    <p>True</p> Signup and view all the answers

    Data privacy evaluates moral problems related to data.

    <p>False</p> Signup and view all the answers

    Gender is an example of which measurement scale?

    <p>nominal</p> Signup and view all the answers

    Which of the following is true of structured data?

    <p>Most experts agree that only about 5% of all data used in business decisions are structured data.</p> Signup and view all the answers

    A good measure of dispersion should consider differences of all observations from the mean.

    <p>True</p> Signup and view all the answers

    If the covariance is negative, then x and y have a negative linear relationship.

    <p>True</p> Signup and view all the answers

    If the covariance is positive, then x and y have a positive linear relationship.

    <p>True</p> Signup and view all the answers

    If the covariance is zero, then x and y have no linear relationship.

    <p>True</p> Signup and view all the answers

    If the correlation coefficient equals -1, then x and y have a perfect negative linear relationship.

    <p>True</p> Signup and view all the answers

    If the correlation coefficient equals 0, then x and y are not linearly related.

    <p>True</p> Signup and view all the answers

    If the correlation coefficient equals 1, then x and y have a perfect positive linear relationship.

    <p>True</p> Signup and view all the answers

    When defining the 3 Vs of big data, 'velocity' refers to the immense amount of data compiled from a single source or a wide range of sources.

    <p>False</p> Signup and view all the answers

    Examples of categorical variables include: (Select all that apply!)

    <p>Course Grade</p> Signup and view all the answers

    We refer to the population mean as a ___ and the sample mean as a ___

    <p>parameter, statistic</p> Signup and view all the answers

    What type of data collection method involves collecting season records of baseball teams at the end of the season?

    <p>cross-sectional data</p> Signup and view all the answers

    A weakness of 'ordinal data' is that we cannot interpret the difference between the ranked value.

    <p>True</p> Signup and view all the answers

    What are the three most widely used measures of central location?

    <p>median, mean, mode</p> Signup and view all the answers

    Which of the measures of central location is defined as the middle value of a data set?

    <p>median</p> Signup and view all the answers

    The only thing that differs between a population mean and a sample mean is the notation. The population mean is referred to as:

    <p>μ, where μ is the Greek letter mu</p> Signup and view all the answers

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

    <p>unimodal, bimodal</p> Signup and view all the answers

    A percentile is technically a measure of location; how many students had scores lower than your score if you know that the raw score corresponds to the 75th percentile?

    <p>75%</p> Signup and view all the answers

    What is the primary measure of central location?

    <p>mean</p> Signup and view all the answers

    Which numerical descriptive measure shows whether two numerical variables have a linear relationship?

    <p>measures of association</p> Signup and view all the answers

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

    <p>central</p> Signup and view all the answers

    Select all of the measures below that are useful for measuring dispersion.

    <p>Range</p> Signup and view all the answers

    After arranging the data in ascending order, 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.

    <p>True</p> Signup and view all the answers

    Which is true of the use of the range as a measure of dispersion?

    <p>Ignores the middle observation of a variable, is not considered a good measure of dispersion, is the simplest measure of dispersion.</p> Signup and view all the answers

    Which of the measures of central location is defined as the observation that occurs most frequently?

    <p>mode</p> Signup and view all the answers

    What is true of the interquartile range (IQR)?

    <p>It is the range of the middle 50% of the variable.</p> Signup and view all the answers

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

    <p>first, second, third</p> Signup and view all the answers

    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?

    <p>6</p> Signup and view all the answers

    Measures of which type gauge the underlying variability of the data?

    <p>measures of dispersion</p> Signup and view all the answers

    Which of the following is true of the variance and standard deviation?

    <p>The standard deviation is the positive square root of the variance. The variance is an average of the squared differences between the observations and the mean.</p> Signup and view all the answers

    What measure equals zero if all observations are identical and increases as the observations become more diverse?

    <p>dispersion</p> Signup and view all the answers

    Which of the following are common measures of shape?

    <p>Skewness coefficient</p> Signup and view all the answers

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

    <p>range</p> Signup and view all the answers

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

    <p>interquartile</p> Signup and view all the answers

    Which of the following statements is true of the skewness coefficient? Select all that are true.

    <p>A symmetric distribution has a skewness coefficient of zero</p> Signup and view all the answers

    What does MAD stand for when used as a measure of dispersion?

    <p>mean absolute deviation</p> Signup and view all the answers

    The ____ coefficient is a summary measure that tells us whether the tails of the distribution are more or less extreme than the normal distribution.

    <p>kurtosis</p> Signup and view all the answers

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

    <p>population</p> Signup and view all the answers

    Which of the following is true of measures of association? Select all that are true.

    <p>These measures quantify the direction and strength of the linear relationship between two variables, x and y.</p> Signup and view all the answers

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

    <p>skewness</p> Signup and view all the answers

    Which of the following is true of the covariance? Select all that are true!

    <p>Covariance can be negative, positive, or zero.</p> Signup and view all the answers

    Which of the following statements is true regarding the kurtosis coefficient? Select all that are true.

    <p>A platykurtic distribution is one that has shorter tails.</p> Signup and view all the answers

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

    <p>association</p> Signup and view all the answers

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

    <p>correlation</p> Signup and view all the answers

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

    <p>covariance</p> Signup and view all the answers

    Which of the following is a true statement regarding outliers in data analysis? (Choose all that apply)

    <p>Outliers may indicate bad data due to incorrectly recorded observations.</p> Signup and view all the answers

    When constructing a box plot, what does the five-number summary contain?

    <p>Maximum value, Q1, Q2, Q3, Minimum value</p> Signup and view all the answers

    Which of the following is true of the correlation coefficient? Select all that are true!

    <p>If the correlation coefficient equals -1, then x and y have a perfect negative linear relationship.</p> Signup and view all the answers

    The Empirical Rule provides precise statements regarding the percentage of observations that fall within a specified number of standard deviations from the mean. Which of the following is a correct statement? Select all that apply!

    <p>Almost all observations fall within +/- 3 standard deviations of the mean.</p> Signup and view all the answers

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

    <p>outliers</p> Signup and view all the answers

    During boxplot construction, which of the following must be included? Rank these steps in the correct order.

    <p>Draw a dashed vertical line in the box at the median.</p> Signup and view all the answers

    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.

    <p>outlier</p> Signup and view all the answers

    Z-score measures the relative location of an observation and indicates whether it is an outlier.

    <p>True</p> Signup and view all the answers

    Which 'tool' depicts the frequency or the relative frequency for each category of the categorical variable as a series of horizontal or vertical bars?

    <p>bar chart</p> Signup and view all the answers

    In a survey with 1000 respondents, if the relative frequency of online teaching proponents was 0.252, how many respondents preferred online teaching?

    <p>252</p> Signup and view all the answers

    In a large lecture class of 280 students, if the professor announced that the mean score on an exam is 74 with a standard deviation of 8, how many standard deviations above the mean would a score of 90 be?

    <p>2</p> Signup and view all the answers

    If a bar chart depicts the relative frequency for categories of occupations, and the Doctor bar has a value of 0.4 with 10 employed individuals, how many Doctors were in the group?

    <p>4</p> Signup and view all the answers

    The mean and standard deviation of scores on an accounting exam are 74 and 8. If a student scores 90 in both classes, what are the z-scores?

    <p>Accounting class z-score: 2; Marketing class z-score: 1.2</p> Signup and view all the answers

    Which of the following are valid methods for visualizing a numerical variable?

    <p>Frequency distribution</p> Signup and view all the answers

    Converting raw data into a ' ___ ' distribution is often a first step in making the data more manageable.

    <p>frequency</p> Signup and view all the answers

    Which of the following examples violates the 'mutually exclusive' guideline for interval construction?

    <p>300 &lt; x ≤ 400 and 400 ≤ x ≤ 500</p> Signup and view all the answers

    A frequency distribution for a categorical variable records the number of observations that fall into each category. If 116 chose Audi out of 1000 respondents, what is the relative frequency of Audi respondents?

    <p>0.116</p> Signup and view all the answers

    Which of the following are valid shapes of a histogram?

    <p>Symmetric</p> Signup and view all the answers

    A vertical bar chart is often referred to as which of the following?

    <p>column chart</p> Signup and view all the answers

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

    <p>frequency</p> Signup and view all the answers

    When constructing a graph, the vertical axis SHOULD be stretched so that an increase or decrease appears more pronounced than warranted.

    <p>False</p> Signup and view all the answers

    For a numerical variable, what are some guidelines for developing intervals?

    <p>Interval limits are easy to recognize and interpret.</p> Signup and view all the answers

    Contingency tables and stacked column charts are methods that summarize the relationship between two categorical variables.

    <p>True</p> Signup and view all the answers

    When constructing a histogram, what does the height of each bar represent? Choose all that are correct responses.

    <p>Relative frequency</p> Signup and view all the answers

    When examining the relationship between two categorical variables, a ' ___ ' table proves very useful.

    <p>contingency</p> Signup and view all the answers

    Which of the following is true of a stacked column chart?

    <p>It is designed to visualize more than one categorical variable and allows for comparison of composition within each category.</p> Signup and view all the answers

    A scatter plot is a graphical tool that plots pairs of data. Once the data are plotted, what may the graph reveal? (Select all that apply)

    <p>A nonlinear relationship exists between the two variables.</p> Signup and view all the answers

    Select all that apply for the key guidelines for constructing or interpreting charts or graphs.

    <p>Use clear labeling and legends.</p> Signup and view all the answers

    Study Notes

    Data Types and Definitions

    • Cross-sectional data is evaluated at a single point in time, while time series data is evaluated across multiple time points.
    • Gender is classified as a nominal measurement scale.
    • Categorical variables can include marital status and course grade.

    Data Structure and Types

    • Structured data includes point-of-sale and financial data.
    • Unstructured data includes social media content, which does not conform to a predefined format.

    Measures of Dispersion and Central Tendency

    • A good measure of dispersion considers all observations' differences from the mean.
    • Common measures of central location are mean, median, and mode.
    • Median is defined as the middle value in a sorted data set.

    Covariance and Correlation

    • A negative covariance indicates a negative linear relationship between variables.
    • A positive covariance indicates a positive linear relationship.
    • A correlation coefficient of -1 signifies a perfect negative linear relationship, while 1 indicates a perfect positive linear relationship.

    Big Data Characteristics

    • The '3 Vs' of big data include Volume, Variety, and Velocity; 'velocity' refers to the speed at which data is generated and processed.

    Percentiles and Box Plots

    • A percentile measures relative position; the 75th percentile indicates that 75% of scores fall below that value.
    • The five-number summary for a box plot consists of minimum value, Q1, median (Q2), Q3, and maximum value.

    Measures of Variability

    • The interquartile range (IQR) is calculated as Q3 minus Q1, indicating the range of the middle 50% of the data.
    • The Mean Absolute Deviation (MAD) quantifies the average distance of observations from the mean.

    Graphical Representations

    • Histograms can show the frequency or relative frequency of data intervals.
    • A bar chart visually represents categorical data as bars of proportional length.
    • Scatter plots illustrate relationships between two numerical variables, with potential incorporation of a categorical variable through color or symbols.

    Outliers and Data Analysis

    • Outliers are extreme observations and can indicate data inaccuracies or natural anomalies.
    • The z-score helps detect outliers by measuring how many standard deviations an observation is from the mean.

    Statistical Interpretation

    • The range is the simplest measure of dispersion, calculated as maximum value minus minimum value.
    • The variance is a measure of the spread of data; the standard deviation is the square root of the variance.

    Graphical Presentation Guidelines

    • Effective graphs should have clearly marked axes, and similar bars/rectangles should be used for consistency.
    • Stacked column charts compare composition across categories and visualize multiple categorical variables.

    Bubble and Line Plots

    • In a bubble plot, the size of the bubble represents a third variable, adding depth to data interpretation.
    • Line charts represent data points connected by lines, suitable for showing trends over time.

    Summary Interpretation

    • Answers to questions about data types, measures, relationships between variables, and specific calculations can be derived from statistical principles and graphical analysis methods.### Graphical Tools in Data Visualization
    • Tracking changes or trends over time can be effectively represented using line charts.
    • Multiple lines can be plotted on a single chart to compare different data sets.

    Scatter Plots

    • Scatter plots are used to examine the relationship between two numerical variables.
    • Each point in a scatter plot represents a paired observation, defined by coordinates (x1, y1).

    Heat Maps

    • Heat maps utilize color to visually display relationships between variables.
    • They are effective in representing complex data that is difficult to analyze through raw data inspection.

    Categorical Variables in Scatter Plots

    • When incorporating a third variable that is categorical, the plot is referred to as a scatter plot with a categorical variable.

    Bubble Plots

    • Bubble plots illustrate the relationship between three numerical variables using circles (bubbles) to represent values and sizes.

    Line Charts

    • Line charts connect a series of data points with lines, effectively displaying trends in a numerical variable over time.

    Applications of Heat Maps

    • Heat maps can track the best and worst-selling products across different stores.
    • They can identify inventory items needing replenishment while monitoring abundant stock levels.
    • Usage includes analyzing frequently downloaded music genres across various streaming platforms, shedding light on consumer preferences.

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