Data Analysis with Microsoft Excel: Updated for Office 2007

190 Fundamentals of Statistics

and a continuous random variable comes from a continuous probability

distribution. Random variables are usually written with a capital letter,

whereas lowercase letters are used to denote a particular value that the ran-

dom variable may attain. For example, if the random variable Y follows a

Poisson distribution, the probability that Y is equal to y is written as

P 1 Y 5 y 25

ly

y!

e2l

When a random variable is assigned a value (such as when we fl ip a coin

or record the number of traffi c accidents in a year), that value is called an

observation. A collection of several such observations is called a sample. If

the observations are generated or selected in a random fashion with no bias,

then the sample is known as a random sample.

In most cases, we want our samples to be random samples to give a true

picture of the underlying probability distribution. For example, say we cre-

ate a study of the weight of United States adult males. We want to know

what type of values we would be likely to get if we picked a man at ran-

dom and weighed him (here weight is our random variable). However, if our

sample is biased by selecting only men in their twenties, it would not be a

true random sample of all United States adult males. Part of the challenge of

statistics is to remove all bias from sampling.

This is difficult to do, and subtle biases can creep into even the most

carefully designed studies. By observing the distribution of values in a ran-

dom sample, we can draw some conclusions about the underlying probabil-

ity distribution. As the sample size increases, the distribution of the values

should more closely approximate the probability distribution. To return to

our example of the shooter, by observing the spread of shots around the bull’s

eye, we can estimate the probability distribution related to the shooter’s

ability to hit the target.

CONCEPT TUTORIALS

Random Samples

You can use the instructional workbook Random Samples to explore the

relationship between a probability distribution and a random sample.

To use the Random Samples workbook:

1 Open the fi le Random Samples from the Explore folder. Enable any

macros in the workbook.

2 Move through the sheets in this workbook, viewing the material on

random variables and random samples.

3 Click Explore a Random Sample from the Table of Contents column.