Podcast
Questions and Answers
What characterizes a positively skewed distribution?
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?
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?
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?
What is true regarding the skewness of a symmetric distribution?
When using Pearson’s Coefficient of Skewness, what is the condition for a negatively skewed distribution?
When using Pearson’s Coefficient of Skewness, what is the condition for a negatively skewed distribution?
How is kurtosis classified when K > 3?
How is kurtosis classified when K > 3?
Which statement is false about scores in a positively skewed distribution?
Which statement is false about scores in a positively skewed distribution?
What does a negative skew indicate about the scores relative to the mean?
What does a negative skew indicate about the scores relative to the mean?
What characterizes a symmetrical distribution?
What characterizes a symmetrical distribution?
Which of the following distributions is characterized by a single peak?
Which of the following distributions is characterized by a single peak?
What happens to the normal curve as it extends away from the mean?
What happens to the normal curve as it extends away from the mean?
In which type of distribution is it possible for the mean, median, and mode to differ significantly?
In which type of distribution is it possible for the mean, median, and mode to differ significantly?
Which statement accurately describes the total area under a normal curve?
Which statement accurately describes the total area under a normal curve?
What type of skewness indicates a longer tail on the right side of the distribution?
What type of skewness indicates a longer tail on the right side of the distribution?
Which of these is NOT a characteristic of a normal distribution?
Which of these is NOT a characteristic of a normal distribution?
Which distribution is described as having more than one peak?
Which distribution is described as having more than one peak?
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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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