MODERN ALCHEMIST

Average and Probability

The first statistics tool we will work with is the average.

What is the average of 80, 90, and 100?

You may have been taught previously to calculate an average by adding up all the numbers present, and then dividing by the quantity of numbers. Using the above example, this would be

80 + 90 + 100   270
------------- = --- = 90
      3          3

Assume that a student has the following grades:

79, 90, 90, 90, 90, 91, 91, 91, 98 The math for the calculation becomes:

79 + 90 + 90 + 90 + 90 + 90 + 91 + 91 + 91 + 98   900
----------------------------------------------- = --- = 90
                      10                           10

To make things more simple, you could reduce the above to:

79 + 5(90) + 3(91) + 98   900
----------------------- = --- = 90
            10            10

One more way of doing the calculation:

1/10 = 0.1
5/10 = 0.5
3/10 = 0.3

(0.1)79 + 0.5(90) + 0.3(91) + (0.1)98 = 90 We will use this last form for a probability experiment later on.

What is the probability that a coin toss will result in tails?

Possible answers include:

"fifty-fifty"
"one to one"
50%
0.5

The first two answers are common expressions. The third and fourth answers are more technical, and more appropriate for our purposes.

What is the probability that a one die (die is the singular of the plural dice) will roll to a 6?

1/6
.1666 (to 4 sig figs)
16.67%

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