Video: Classifying the Shape of a Distribution as Symmetric or Skewed

Which of the following is an accurate description of the distribution below? [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. [E] The distribution is symmetric.

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Video Transcript

Which of the following is an accurate description of the distribution below?

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.

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. As the highest value in the distribution is 100, we can also rule out option B. This stated that the mean was equal to 100. If the highest value’s of 100, the mean cannot be 100.

We’re therefore left with three options. Option A, the distribution is left skewed. Option C, the distribution is right skewed. And option E, the distribution is symmetric. These three statements correspond to the three sketches at the bottom. If our distribution is left skewed, the mode or highest point of the distribution is to the right of the graph. If our distribution is right skewed, the mode will be to the left of the graph. And if our distribution is symmetric, the mode, mean, and median will all be equal and will be in the middle of the graph.

It is clear on the diagram that the mode between 70 and 80 is to the right of the graph. Therefore, the distribution is left skewed. The mode of this data is greater than the median which is greater than the mean. A distribution that is left skewed is often called negative skew. Likewise, if a distribution is right skewed, it is called a positive skew.

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