MATH 1200: Finding Mean and Standard Deviation of a Probability Distribution

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 Mean

In order to find the mean, we will use the formula and the TI83/84 calculator.

First press STAT and then press ENTER to select 1:Edit. If the lists are not cleared, then clear the lists. Enter the x data in and the P(x) in . The result is shown below.

We must now multiply each x by its corresponding p(x), and then sum up 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 followed by 2nd 2 to type an . The typing is visible at the bottom of the calculator screen. Press ENTER. This process multiples each x by its corresponding p(x) and places the results in .

We now have all the products of all the x and p(x) pairs, so now we must sum those products, that is, 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 3 to type an . Now press ) followed by ENTER. The result is the require sum.

Thus = 32.16 .