http://www.ck12.org Chapter 6. Normal Distribution Curves
Example C
Use technology to verify that the answer in Example B is correct.
Although it was not explicitly stated, you may have noticed from the previous 2 concepts that the standard deviation
of a data set is just the square root of the variance of the data set. Another way of saying this is that variance of a
data set is the square of the standard deviation of the data set. Therefore, in order to find the variance of the bowling
averages in Example B, you could have just squared the standard deviation of the bowling averages that you found
in Example A.
You can see above that the exact value returned for the standard deviation of the bowling averages was 14.08703107.
Let’s square this value and see what we get:
The calculator returned 198.4444444, which is extremely close to the answer of 198.4455556 that we got in Example
B. In fact, the only reason why these 2 answers are different at all is simply because of rounding.
Guided Practice
Justin scored 84 out of 100 on a test, and he wants to know how his score compares to those of the other students in
his class. His teacher has decided to let him figure this out for himself. Justin’s teacher told him that the test scores
were normally distributed and provided him with a list of the other test scores, which represented a small population.
These test scores were in no particular order. In other words, they were random.
Use technology to find the mean, standard deviation, and variance of these test scores, which were as follows: