WEBVTT
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Which of the following is an accurate description of the distribution below?
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Is it A) The distribution is left skewed, B) The mean is 100, C) The distribution is right skewed, D) The distribution has a gap from 50 to 70, or E) The distribution is symmetric.
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As the only gap in the distribution is between 10 and 30, then option D, the distribution has a gap from 50 to 70, is obviously wrong.
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As the highest value in the distribution is 100, we can also rule out option B.
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This stated that the mean was equal to 100.
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If the highest value’s of 100, the mean cannot be 100.
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We’re therefore left with three options.
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Option A, the distribution is left skewed.
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Option C, the distribution is right skewed.
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And option E, the distribution is symmetric.
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These three statements correspond to the three sketches at the bottom.
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If our distribution is left skewed, the mode or highest point of the distribution is to the right of the graph.
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If our distribution is right skewed, the mode will be to the left of the graph.
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And if our distribution is symmetric, the mode, mean, and median will all be equal and will be in the middle of the graph.
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It is clear on the diagram that the mode between 70 and 80 is to the right of the graph.
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Therefore, the distribution is left skewed.
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The mode of this data is greater than the median which is greater than the mean.
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A distribution that is left skewed is often called negative skew.
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Likewise, if a distribution is right skewed, it is called a positive skew.