Statistics Distribution Quiz
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Questions and Answers

Pick the statement that best describes the shape of the distribution for the states in the West.

  • The data appears to be right-skewed with a possible outlier. (correct)
  • The data appears to be normally distributed.
  • The data appears to be left-skewed.
  • The data appears to be evenly distributed.

    • Using the boxplot for the Midwest, determine which of the following statements about the distribution cannot be justified.

    There are fewer states with 3887.5 to 6887 prisoners than states with 6887 to 15,706 prisoners.

    Based on the boxplot for the West, which of the following is true?

    25% of the states sentenced more than 15,706 prisoners.

    The fastest 25% of women participants ran the marathon how quickly?

    <p>Less than 150 minutes.</p> Signup and view all the answers

    List ratings according to their median runtimes, from shortest to longest.

    <p>G, PG, R, PG-13</p> Signup and view all the answers

    What feature of a distribution can NOT be determined from a boxplot?

    <p>Number of observations.</p> Signup and view all the answers

    Calculate the five-number summary for the following dataset.

    <p>19.98, 41.19, 73.295, 83.88, 114.6</p> Signup and view all the answers

    How many pets do the ten households currently own based on the data provided?

    <p>3</p> Signup and view all the answers

    What is the number of bikes collected by the statistics student?

    <p>5</p> Signup and view all the answers

    What is the population of interest in the principal's poll about after-school activities?

    <p>All students who attend the school.</p> Signup and view all the answers

    The average gas mileage of the top selling mini-vans for each U.S. car manufacturer is an example of what type of variable?

    <p>Numerical variable</p> Signup and view all the answers

    The marital status of each member of a randomly selected group of adults is an example of what type of variable?

    <p>Categorical variable</p> Signup and view all the answers

    The ethnicity of the individual respondents in a political poll is an example of what type of variable?

    <p>Categorical variable</p> Signup and view all the answers

    The average number of hours spent on statistics homework is an example of what type of variable?

    <p>Numerical variable</p> Signup and view all the answers

    What types of variables summarize information in the table provided by the international relations professor?

    <p>Student number: categorical; area of interest: categorical; GPA: numerical</p> Signup and view all the answers

    Which variables are numerical and which are categorical from the given list?

    <p>Age and height are numerical variables. Gender, favorite candy, and eye color are categorical variables.</p> Signup and view all the answers

    The coded response '1' for yes and '0' for no in the children's survey is an example of?

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

    According to the data table, which variable(s) is(are) categorical?

    <p>Gender and ethnicity</p> Signup and view all the answers

    What method organizes the following data table showing men's and women's ages?

    <p>This is unstacked data because the ages are separated by groups (in this case, gender).</p> Signup and view all the answers

    What is the approximate percentage of men who prefer to rent a movie on DVD?

    <p>13.8%</p> Signup and view all the answers

    What percentage of study participants are women in the given data?

    <p>61.9%</p> Signup and view all the answers

    How many students check their Facebook page at least three times a day from a sample of 800 first-year college students who reported 72%?

    <p>576 students</p> Signup and view all the answers

    What percentage of the sample had texted at least once while driving in the past thirty days?

    <p>37.5%</p> Signup and view all the answers

    Of the adult males surveyed, what percentage had made a clothing purchase in the last thirty days?

    <p>50%</p> Signup and view all the answers

    What percentage of girls in the study of 1350 elementary school children want to be teachers when they grow up?

    <p>19.2%</p> Signup and view all the answers

    According to the two-way table, what percent of people in the sample prefer dogs?

    <p>65%</p> Signup and view all the answers

    Why are percentages more useful than counts in comparing the number of males and females who take naps?

    <p>There are more males than females in the sample.</p> Signup and view all the answers

    What pairs of variables could be used in a two-way table?

    <p>Gender and favorite class</p> Signup and view all the answers

    Is the study comparing obesity rates in urban versus rural children an observational study or a controlled experiment?

    <p>Observational study</p> Signup and view all the answers

    Is the study involving new chewable vitamins an observational study or a controlled experiment?

    <p>Controlled experiment</p> Signup and view all the answers

    Is the study comparing smoking rates among teens in urban versus rural areas an observational study or a controlled experiment?

    <p>Observational study</p> Signup and view all the answers

    Is the study involving cancer patients and a new drug a controlled experiment or observational study?

    <p>Controlled experiment</p> Signup and view all the answers

    Is the study comparing math test scores of students listening to music versus in silence an observational study or a controlled experiment?

    <p>Controlled experiment</p> Signup and view all the answers

    In the study of medication's impact on high blood pressure, is it an observational study or controlled experiment?

    <p>Controlled experiment</p> Signup and view all the answers

    In the study of medication reducing migraines, is it an observational study or controlled experiment?

    <p>Controlled experiment</p> Signup and view all the answers

    Is the study examining migraine frequency based on patients' medical records observational or controlled?

    <p>Observational study</p> Signup and view all the answers

    How many participants had a heart rate between 120 and 130 bpm in the yoga class?

    <p>3</p> Signup and view all the answers

    What percentage of participants had a heart rate greater than 130 bpm?

    <p>53%</p> Signup and view all the answers

    From the data set of a record store owner, which statements can be made?

    <p>All of these</p> Signup and view all the answers

    What is the typical pass rate for the swim test according to the distribution shown in the histogram?

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

    Based on the histogram, is it unusual to be on hold for 5 minutes or more at this call center?

    <p>Yes, it would be unusual.</p> Signup and view all the answers

    How many people were 23 years or older in the study?

    <p>8 people</p> Signup and view all the answers

    What can be concluded about the bin width from the histogram?

    <p>The bin width is too small. We are given too much detail.</p> Signup and view all the answers

    What can be concluded about the bin width from another histogram?

    <p>The bin width is too large. We are hiding details of the distribution.</p> Signup and view all the answers

    What is the typical value for a bimodal histogram?

    <p>Since the data are bimodal, there are two typical values - one is about 20 and the other is about 60.</p> Signup and view all the answers

    What is the typical movie runtime according to the distribution of 489 movies?

    <p>The typical value is about 100.</p> Signup and view all the answers

    What is the difference between a histogram and a relative frequency histogram?

    <p>A histogram uses counts to record how many observations are in a data set, and a relative histogram uses proportions.</p> Signup and view all the answers

    Which statement is true based on the histogram of Boy Scout troop heights?

    <p>All of these are true statements.</p> Signup and view all the answers

    What can be said about grip strength distribution based on the histogram?

    <p>The graph shows evidence that two different groups may have been combined into one collection.</p> Signup and view all the answers

    How is the distribution of the number of times individuals in the 18-24 age group log onto social media characterized?

    <p>Right skewed (tail on right side)</p> Signup and view all the answers

    How are individual observations recorded in the different statistical displays?

    <p>A dotplot displays a dot for every observation. A histogram uses bars to display intervals of observations. A stemplot displays the actual values of observations.</p> Signup and view all the answers

    How should the variability of income distribution in the United States be interpreted?

    <p>The median income is smaller than the mean income.</p> Signup and view all the answers

    What is the effect of a data entry error in accident reports for June 2013?

    <p>The mean will be higher than it should be, but the median will not be affected.</p> Signup and view all the answers

    What is the typical value calculated from the given sample data?

    <p>74.50</p> Signup and view all the answers

    What summarizes the meaning of the standard deviation for extreme 10K finish times?

    <p>The distribution of women's finish times is less varied than the distribution of men's finish times.</p> Signup and view all the answers

    Study Notes

    Statistics and Data Collection

    • Data collection from students can reveal trends, such as transportation preferences.
    • Population of interest in surveys typically encompasses the entire group being studied.

    Types of Variables

    • Numerical variables represent measurable quantities, such as average gas mileage or hours spent on homework.
    • Categorical variables classify data into categories, like marital status or ethnicity.

    Coded Data

    • Coded categorical data simplifies responses for analysis; for instance, recording "yes" as 1 and "no" as 0 helps in data processing.

    Observational Studies vs. Controlled Experiments

    • Observational studies compare existing conditions without intervention (e.g., smoking rates in urban vs. rural teens).
    • Controlled experiments assign participants to groups to test effects (e.g., medication for migraines).

    Descriptive Statistics

    • Measures of central tendency include mean, median, and mode, helping describe data distributions.
    • Variability in datasets can be assessed using standard deviation and interquartile ranges.

    Graphical Representations

    • Histograms and dotplots visually present data distributions and help identify typical values and variability.
    • Boxplots summarize data through five-number summaries, expressing minimum, quartiles, and maximum.

    Data Interpretation

    • Misleading graphs can distort perceptions; context (such as starting points on axes) is crucial for correct interpretations.
    • Right skewed distributions indicate that the mean exceeds the median, often seen in income data.

    Practical Applications

    • Surveys and studies are instrumental in understanding preferences and behaviors in populations, aiding policy decisions and service offerings.
    • Accurate statistical analysis is vital for drawing meaningful conclusions from collected data.

    Key Statistical Concepts

    • Understanding coded data and the distinction between observational studies and controlled experiments is fundamental for research integrity.
    • Familiarity with central tendency measures and variability indicators equips individuals to better interpret data outcomes.
    • Visual data interpretations should include evaluation of deceptive practices, like truncated axes in graphs, that hide true data insights.

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    Description

    Test your knowledge on the shape of distributions using data from various U.S. states. This quiz explores concepts like median, skewness, and interpreting boxplots. Challenge yourself to identify characteristics of distribution based on statistical visuals.

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