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. Arrow down to FreqList: then press 2nd 2. Arrow down to Calculate. 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.

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