Quantitative Data Analysis Normal and Skewed Distributions
(1) Normal Distribution:
Classic bell shaped curve, it is the predicted distribution when using equally likely sets of results. For example, if a light bulb has a lifetime of 100 hours we would expect some bulbs to last a little longer than 100 hours and some to last a little less.
Characteristics of a Normal Distribution:
The three measures of central tendency, mean, median and mode are all in the exact mid-point (the middle part of the graph/the peak of the curve).
The distribution is symmetrical.
(2) Skewed Distribution
This occurs when the scores are not equally distributed around the mean.
Positive Skew The best way to imagine the shape of a positive skew is to think of the scores on a very difficult exam, were few people got a high mark being plotted on a graph. Most of the scores would lie to the left side of the x axis with fewer scores being plotted at the higher end of the x axis (the right).
Revision Tip When thinking of the shape of a positive skewed distribution, think of the shape of your right foot.
Characteristics of a Positive Skewed Distribution Graph:
Central tendency order is plotted mode, median followed by the mean.
Negative Skew The best way to remember the shape of a negative skewed is to imagine the scores on a very easy exam, were few people got a low mark, were plotted on a graph. In this situation, people would obtain a higher score and therefore, most scores would sit to the right side of the x axis with fewer scores sitting to the left side of the x axis.
Revision Tip: When thinking of the shape a of negative skewed distribution, think of the shape of your left foot.
Characteristics of a Negative Skewed Distribution Graph:
Central tendency order is plotted mean, median followed by the mode.