The Problem

The number of calls received per day at a crisis hot line is distributed as follow:

x 30 31 32 33 34
P(x) 0.05 0.21 0.38 0.25 0.11

Find the mean, variance, and standard deviation of the distribution.

Finding the Variance and Standard Deviation

In order to find the variance and standard deviation, we will use the formula and the TI83/84 calculator. The mean, , must first be calculated. However, we have just found the mean to be = 32.16. Click BACK below to see this work.

On the previous page, we left our list editor as follows:

column is already filled, so we will now use to compute for each x, p(x) pair, and then we will sum the products. To do this using the the calculator, press the right arrow to move the cursor into thecolumn, and then press up arrow to highlight . Now press 2nd 1 to type an , press type an a second time. That gives us x squared. Next press and press 2nd 2 to type an . The typing is visible at the bottom of the calculator screen. Press ENTER. This process multiples each x squared by its corresponding p(x) and places the results in .

We now have all the products of x squared and p(x), so all that remains is to sum those products, the numbers in . Press 2nd Mode[QUIT] to exit the lists and return to the home screen. Press 2nd STAT[LIST], then right arrow twice to MATH. Press 5 to select 5:sum(. Press 2nd 4 to type an. Next press ) followed by ENTER. The result is the require sum.

Thus = .

To find the standard deviation , and we find that .

Now press NEXT below for a shorter method of finding the mean and standard deviation of the probability distribution.

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