http://www.ck12.org Chapter 6. Normal Distribution Curves
In the real world, no examples match this smooth curve perfectly. However, many data plots, like the one you made,
will approximate this smooth curve. For this reason, you will notice that the termassumeis often used when referring
to data that deals with normal distributions. When a normal distribution is assumed, the resulting bell-shaped curve
is symmetric. That is, the right side is a mirror image of the left side. In the figure below, if the blue line is the mirror
(the line of symmetry), you can see that the pink section to the left of the line of symmetry is the mirror image of the
yellow section to the right of the line of symmetry. The line of symmetry also goes through thex-axis.
If you knew all of the measurements that were plotted for the diameter of the basketball, you could calculate the
mean (average) diameter by adding the measurements and dividing the sum by the total number of values. It is at
this value that the line of symmetry intersects thex-axis. In other words, the mean of a normal distribution is the
center, or balance point, of the distribution.
You can see that the 2 colors form a peak at the top of the line of symmetry and then spread out to the left and to
the right from the line of symmetry. The shape of the bell flattens out the further it moves away from the line of
symmetry. In other words, the data spreads out in both directions away from the mean. This spread of the data
is measured by thestandard deviation, and it describes exactly how the data moves away from the mean. You
will learn more about standard deviation in the next concept. For now, that is all you have to know about standard
deviation−it is a measure of the spread of the data away from the mean.
Now you should be able to complete the following statement regarding the measurements of the diameter of the
basketball:
“The typical measurement of the diameter is approximately9.4 inches, give or take0.4 inches.”
This statement assumes that the mean of the measurements was 9.4 inches and the standard deviation of the
measurements was 0.4 inches. It also assumes that the standard deviation is the difference between the mean and the
first tick mark to the left of the mean.
In each of the following examples, complete the statement. Fill in the first blank in each statement with the mean and
the second blank in each statement with the standard deviation. Assume that the standard deviation is the difference
between the mean and the first tick mark to the left of the mean.
Example A
“The typical measurement is approximately __ in the bank, give or take __.”
“The typical measurement is approximately$500 in the bank, give or take$50.”