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High School Mathematics - 2
11.9 Normal and Skewed Distributions

Normal and skewed distributions:
  • The probability distributions we studied so far are discrete probability distributions because they have only a finite number of possible values.
  • A discrete probability distribution can be represented by a histogram.
  • For a continuous probability distribution, the outcome can be any value in an interval of real numbers.
  • Continuous probability distributions are represented by curves instead of histograms.
  • Such curves are often called a bell curve.
  • Many distributions with symmetric curves or histograms are normal distributions.
  • In normal distributions scores are more concentrated in the middle than in the tails.
  • A curve or histogram that is not symmetric represents a skewed distribution.
    • Positive skew: The right tail is longer and the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed.
    • Negative skew: The left tail is longer and the mass of the distribution is concentrated on the right of the figure. The distribution is said to be left-skewed.

Q 1: Determine whether the data 14, 15, 11, 13, 13, 14, 15, 14, 12, 13, 14, 15 appear to be positively skewed, negatively skewed, or normal distributed.

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