What is a Skewed Distribution?A skewed distribution represents a set of scores or numbers that is not equal on both sides. This results from a few scores in a data set falling farther to one end or the other. This arrangement is quite common in real world settings, especially when smaller numbers of scores are involved.On the normal distribution curve, the Measures of Central Tendency (mean, median, and mode) are in the same spot at the middle of the curve. The curve is symmetrical. Let's say 9 basketball players see how many of 20 free throws each can make. Their scores are: 8, 9, 9, 10, 10, 10, 11, 11, 12 In this case, the results follow a normal distribution curve. The "averages" are all 10.
When a set of scores is skewed, the "averages" are not at the exact center and the curve is asymmetrical. The mode remains at the highest part of the curve, the median is still the middle score, and the mean is pulled in the direction of the outliers. When low scores pull the mean toward the left tail, the skew is negative. For example, if the scores were: 2, 5, 6, 7, 8, 10, 10, 11, 12, the mode would still be 10, but the median would drop to 8, and the mean would be pulled down to 7.9. This also means that some players need lots of work on their free throws.
The curve tends to become normal with higher numbers of scores. Many statistical tools are correctly applied under the assumption that the curve is normal. Less powerful statistics (called nonparametric) can be applied for small samples or when the distribution is skewed. These tools are based on the median rather than the mean.
|
