Distribution Curves

In the Unit 1 we finished by discussing the importance of frequency tables and relative frequency histogram.  Below is an example of the histogram we used.  If we were to connect each bar on the histogram with a curved line we would have what is called a distribution curve.

The shape of a distribution curve is very important. If both sides of the curve looked the same (are mirror images of each other), we would say the distribution was symmetrical. When a distribution is symmetrical, the mean, median and the mode are all the same number. The following graphic shows a symmetrical distribution curve.

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If a distribution curve is not symmetrical, then the left half of the curve is different from the right half and it is called asymmetrical. When the data values at the left have a higher frequency than the data values to the right of the distribution, the curve has a positive skew. When a data set is positively skewed, the mode is smaller than the median, which is smaller than the mean. If the data values at the right have a higher frequency than those to the left, then the data would have a negative skew. In this case, the mode is larger than the median, which is larger than the mean.

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In addition to skewness, we can also make observations about the number of modes in our distribution.  When a distribution has one mode, we say it is unimodal. When it has two modes, it is bimodal.  Note that the modes do not have to be the same value, but should be distinguishable from the surrounding data values.

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