Shapes of Distributions
There are a few shapes that a graphical display of data, such as a histogram or frequency polygon, can take that are particularly interesting to psychologists. A graph in which scores bunch up toward either end of the abscissa (as shown in the first and second panels of Figure 2 below) is said to be skewed. The skewness of a graph is determined by the direction of its "tail." If the scores bunch up toward the high end, the graph has a negative skew. If the scores bunch up toward the low end, the graph has a positive skew. A distribution is said to be normal (bell-shaped) if the scores bunch up in the middle and then taper off fairly equally on each side such that 68% of the scores occur within +/- 1 standard deviation of the mean, 95% of the scores occur within +/- 1 standard deviations of the mean and 99% occur within +/- 3 standard deviations of the mean. The normal distribution is discussed in more detail in a subsequent section. Finally, a distribution is called a rectangular distribution if the scores are fairly evenly distributed throughout the graph. In Figure 2, the normal curve is superimposed on each of the distributions shown to demonstrate the ways in which they deviate from normality.
Figure 2.
Learning Check #3:
Below are the number of children in each of 20 families. Present these data
in a frequency histogram: 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2,
3, 4, 7.
Learning Check #4:
What shape is the distribution graphed in Learning Check #3? What would have
made the distribution take on a positive skew? A negative skew? A rectangular
shape?