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, Standard Deviation and Variation

First enter the x values in and the P(x) values in .

Press 2nd MODE[QUIT] to return to the home screen. Next press STAT, right arrow to CALC and press ENTER to select 1:1-Var Stats. Press 2nd 1 to type an and then press 2nd 2 to type an . Next press ENTER. The results are shown below.

Thus, on the final screen the mean is = 32.16 and the standard deviation is is about 1.037.

The variance can be obtained by squaring the standardeviation. The square of 1.036532682 is about 1.074.