http://www.ck12.org Chapter 5. The Shape, Center and Spread of a Normal Distribution - Basic
You have probably noticed that the measurements of the diameter of the golf ball were not all the same. In spite of
the different measurements, you should have seen that the majority of the measurements clustered around the value
of 1.6 inches, with a few measurements to the right of this value and a few measurements to the left of this value.
The resulting shape looks like a bell and is the shape that represents thenormal distributionof the data.
In the real world, no examples match this smooth curve perfectly, but many data plots, like the one you made,
are approximately normal. For this reason, it is often said that normal distribution is ’assumed.’ When normal
distribution is assumed, the resulting bell-shaped curve is symmetric - the right side is a mirror image of the left
side. If the blue line is the mirror (the line of symmetry) you can see that the green section is the mirror image of the
yellow section. The line of symmetry also goes through thex−axis.
If you took all of the measurements for the diameter of the golf ball, added them and divided the total by the number
of measurements, you would know the mean (average) of the measurements. It is at the mean that the line of
symmetry intersects thex−axis. For this reason, the mean is used to describe the center of a normal distribution.
You can see that the two colors spread out from the line of symmetry and seem to flatten out the further left and
right they go. This tells you that the data spreads out, in both directions, away from the mean. This spread of the
data is called the standard deviation and it describes exactly how the data moves away from the mean. In a normal
distribution, on either side of the line of symmetry, the curve appears to change its shape from being concave down
(looking like an upside-down bowl) to being concave up (looking like a right side up bowl). Where this happens
is called the inflection point of the curve. If a vertical line is drawn from the inflection point to thex−axis, the
difference between where the line of symmetry goes through thex−axis and where this line goes through thex−axis
represents the amount of the spread of the data away from the mean.
Approximately 68% of all the data is located between these inflection points.
For now, that is all you have to know about standard deviation. It is the spread of the data away from the mean. In
the next lesson, you will learn more about this topic.
Now you should be able to complete the statement that was given in the introduction.
“The typical measurement of the diameter is approximately 1. 6 inches, give or take 0. 4 inches.”