The proportion of people meeting a certain criterion is the number who meet the criterion divided by the total number of people. The percentage (not "percent") of people meeting the criterion is the proportion times 100. Thus, "percent" means "per 100." 65% of people means "65 people out of every 100 people."

In statistics, we almost always use proportions in the actual calculations, but the results are often reported in percentages because most people don't understand numbers less than 1. (If you don't, you are in BIG trouble in this course!!) Sometimes, however, even percentages turn out to be very small numbers. In this case, it is common practice to report results to the public in units like "per 1000" or "per 10,000" or even "per 100,000." Crime rates, for example, are often reported as number of crimes reported per 1000 people in the population. Murder rates are often reported per 100,000 people. The same rule applies. To get the rate per 1000, for example, calculate the proportion and then multiply that by 1000. (A proportion means "per one.")

Proportions (and other rates such as percentages) are often useful in statistics for comparing samples with unequal sample sizes. For example, suppose we have two samples, one of men and one of women. The sample of men contains 1024 men, and of them, 558 claim to be Republicans. The sample of women contains 886 women, and of them 422 claim to be Republicans. It would be silly to compare the numbers 558 and 422 because they come from different size samples.

The solution is to calculate proportions (or percentages). Among the men, the proportion of Republicans is 0.545 or 54.5%. Among the women, the proportion of Republicans is 0.476 or 47.6%. Thus, relative to sample size, more men are Republicans than women.

Another expression you often hear is that something is proportional to something else. For example, y is proportional to x. This simply means that to get the value of y from x, multiply by a constant.

y = kx

y is said to be in "direct proportion to x," and k is called the constant of proportionality. On the other hand, if k is divided by x rather than multiplied, then y is said to be "inversely proportional" to x, meaning (in the realm of positive numbers anyway) as x gets larger, y gets smaller.

y = k / x

In this case, if k = 1, then y is called the reciprocal of x.