Distribution Shapes and Characteristics
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Questions and Answers

What characterizes a positively skewed distribution?

  • Mean < median < mode
  • Scores concentrated at the low end of the distribution
  • More high scores than low
  • Mean > median > mode (correct)

    • Which of the following indicates a negatively skewed distribution?

  • Scores concentrated at the low end
  • Mean < median < mode (correct)
  • Longer tail to the right
  • Mean = median = mode

    • If a distribution is described as leptokurtic, what does this imply about its peakedness?

  • It has no peak.
  • It has a flat and spread out shape
  • It is high and thin (correct)
  • It is normal in shape

    • What is true regarding the skewness of a symmetric distribution?

    <p>Skewness = 0</p> Signup and view all the answers

    When using Pearson’s Coefficient of Skewness, what is the condition for a negatively skewed distribution?

    <p>Mean - median &lt; 0</p> Signup and view all the answers

    How is kurtosis classified when K > 3?

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

    Which statement is false about scores in a positively skewed distribution?

    <p>There are more high scores than low</p> Signup and view all the answers

    What does a negative skew indicate about the scores relative to the mean?

    <p>Majority of scores fall above the mean</p> Signup and view all the answers

    What characterizes a symmetrical distribution?

    <p>The mean, median, and mode are equal.</p> Signup and view all the answers

    Which of the following distributions is characterized by a single peak?

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

    What happens to the normal curve as it extends away from the mean?

    <p>It approaches, but never touches, the x-axis.</p> Signup and view all the answers

    In which type of distribution is it possible for the mean, median, and mode to differ significantly?

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

    Which statement accurately describes the total area under a normal curve?

    <p>It is equal to 1.</p> Signup and view all the answers

    What type of skewness indicates a longer tail on the right side of the distribution?

    <p>Positively skewed</p> Signup and view all the answers

    Which of these is NOT a characteristic of a normal distribution?

    <p>The total area under the curve is less than 1.</p> Signup and view all the answers

    Which distribution is described as having more than one peak?

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

    Study Notes

    Distribution Shapes

    • The shape of a distribution reveals information about the central tendency and variability of the data.
    • Three common types of distributions are: normal, skewed, and multimodal.

    Symmetrical Distributions

    • Symmetrical distributions have identical frequencies on the left and right tails.
    • The mean, median, and mode are equal or approximately equal in symmetrical distributions.
    • There are two main types of symmetrical distributions: uniform distributions and bell-shaped distributions.
    • Uniform distributions show equal frequencies for all values or groups of values.

    Normal or Bell-Shaped Distribution

    • The mean, median, and mode are equal in a normal distribution.
    • The normal curve is bell-shaped and symmetrical around the mean.
    • The area under the curve totals 1.
    • The curve approaches, but never touches, the x-axis as it extends away from the mean.

    Skewed Distributions

    • Skewed distributions are asymmetrical, with one tail extending further than the other.
    • The direction of the longer tail indicates whether the distribution is skewed to the right or left.

    Skewed to the Right or Positively Skewed Distribution

    • Scores are concentrated at the lower end of the distribution.
    • The mean is greater than the median, which is greater than the mode: mean > median > mode
    • The majority of scores fall below the mean.
    • There are more low scores than high scores.

    Skewed to the Left or Negatively Skewed Distribution

    • Scores are concentrated at the higher end of the distribution.
    • The mean is less than the median, which is less than the mode: mean < median < mode
    • The majority of scores fall above the mean.
    • There are more high scores than low scores.

    Measuring Skewness

    • Skewness measures the asymmetry of a distribution.
    • Symmetrical distributions have a skewness of 0.
    • Distributions skewed to the right have a positive skewness.
    • Distributions skewed to the left have a negative skewness.

    Peakedness of Distribution (Kurtosis)

    • Leptokurtic: High and thin distribution with greater peakedness than a normal distribution.
    • Mesokurtic: Normal in shape, with a similar peakedness to a normal distribution.
    • Platykurtic: Flat and spread out, with less peakedness than a normal distribution.

    Measuring Kurtosis

    • K > 3: Leptokurtic
    • K = 3: Mesokurtic
    • K < 3: Platykurtic

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    Related Documents

    Distribution Shapes PDF

    Description

    This quiz explores the various shapes of distributions, including normal, skewed, and multimodal types. Learn how symmetrical distributions function, and understand the significance of the mean, median, and mode in different distribution shapes. Test your knowledge on the characteristics and implications of these distributions.

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