Many of us are familiar with the normal distribution from standardized school test
scores, as most result in a bell-shaped curve, with students hoping to at least fall in
the middle of the curve.What is a cumulative distribution?
A cumulative distribution is a plot of the number of observations that fall in or below
an interval. For example, they are often used to determine where scores fall in a stan-
dardized test. For example, the x-axis (see bar graph illustration on next page) shows
the intervals of scores (such as the interval labeled 35 shows any score from 32.5 to
37.5, and so on) and the y-axis shows the number of students scoring in or below each
interval. This graphically illustrates for the students (and teachers) how well they did
on the test compared to other students.What are skewnessand symmetry?
Skewness is when there is asymmetry in the distribution of the sample data values. In
this case, the values on one side of the distribution seem to be further from the “mid-
dle” range than values on the other side. Symmetry essentially means balance: when
the data values are distributed in the same way above and below (or on both sides of)
262 the middle of the sample.
A “normal” curve has a bell shape to it into which the majority of a sampling of statistics falls within a certain
average range.