Statistics Homework 3.2 Flashcards
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Questions and Answers

What is the measure of dispersion that requires the least amount of steps to calculate?

Range

Explain how to find the range of a data set.

The range of a data set is the difference between the maximum and minimum data entries in the set.

What is an advantage of using the range as a measure of variation?

  • It accurately reflects variation in the data.
  • It uses all entries in the data set.
  • It is always non-negative.
  • It is easy to compute. (correct)

    • What is a disadvantage of using the range as a measure of variation?

    <p>It only uses two entries from the data set.</p> Signup and view all the answers

    Find the range of the data set from a leaf stem histogram where the lowest number is 23 and the highest number is 97.

    <p>74</p> Signup and view all the answers

    What does the symbol sigma represent?

    <p>Population standard deviation</p> Signup and view all the answers

    What is the range of the April precipitation amounts if the highest is 4 inches and the lowest is 0.8 inches?

    <p>3.2 inches</p> Signup and view all the answers

    Explain the relationship between variance and standard deviation.

    <p>Standard deviation is the positive square root of the variance.</p> Signup and view all the answers

    Can either variance or standard deviation be negative?

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

    What can be said about a set of data with a standard deviation of zero?

    <p>All the observations are the same value.</p> Signup and view all the answers

    Can a standard deviation be negative?

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

    To which distributions does the empirical rule apply?

    <p>Any normal distribution</p> Signup and view all the answers

    In a normal distribution, approximately what percentage of the area under the normal curve is within two standard deviations of the mean?

    <p>95%</p> Signup and view all the answers

    According to the empirical rule, what percent of the area under the normal curve is between the mean and one standard deviation above the mean?

    <p>34%</p> Signup and view all the answers

    What percentage of the area under the normal curve is more than one standard deviation from the mean?

    <p>32%</p> Signup and view all the answers

    Use the empirical rule to determine what percentage of people has an IQ score between 52 and 148, if the mean is 100 and the standard deviation is 16.

    <p>99.7%</p> Signup and view all the answers

    What percentage of people has an IQ score less than 84 or greater than 116?

    <p>32%</p> Signup and view all the answers

    What percentage of people has an IQ score greater than 116?

    <p>16%</p> Signup and view all the answers

    Study Notes

    Range

    • The range is the measure of dispersion that requires the least steps to calculate.
    • To find the range, subtract the minimum value from the maximum value in a dataset.

    Advantages and Disadvantages of Range

    • Advantage: Simple to compute.
    • Disadvantage: Only considers two entries (maximum and minimum) and may not accurately reflect the data's overall variation.

    Example Calculation of Range

    • For a dataset ranging from 23 to 97, the calculated range is 74 (97 - 23).

    Symbols and Definitions

    • Sigma (σ) represents the population standard deviation.

    Calculating Range Example

    • Given highest precipitation of 4 inches and lowest of 0.8 inches, the range is 3.2 inches.

    Variance and Standard Deviation

    • Standard deviation is the positive square root of variance.
    • Both variance and standard deviation cannot be negative since squared deviations are always non-negative.

    Population vs. Sample

    • Determine whether to use σ (population) or S (sample) based on the context of the dataset.

    Zero Standard Deviation

    • A standard deviation of zero indicates all observations in the dataset are the same value, resulting in no variation.

    Standard Deviation Properties

    • Standard deviation cannot be negative as it measures data spread from the mean.

    Empirical Rule

    • The empirical rule applies to normal distributions and estimates percentages within specific standard deviations.
    • Approximately 95% of data falls within two standard deviations from the mean.

    Normal Distribution and Standard Deviations

    • About 68% of data lies within one standard deviation from the mean.
    • 34% of the area under the curve is between the mean and one standard deviation above the mean.

    Area Beyond One Standard Deviation

    • 32% of data lies more than one standard deviation away from the mean, calculated as 100% - 68%.

    IQ Test Scores Analysis

    • IQ scores have a mean of 100 and a standard deviation of 16.
    • Approximately 99.7% of individuals have IQ scores between 52 and 148, which encompasses three standard deviations.
    • 32% of individuals score less than 84 or greater than 116 (outside one standard deviation).
    • 16% of individuals have scores greater than 116 (half of the 32% beyond one standard deviation).

    Additional Note

    • No content provided for Card 16 to summarize.

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    Description

    This quiz focuses on key concepts related to the range in statistics. It includes definitions and an explanation of how to calculate the range of a data set. Ideal for students working on their statistics homework.

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