168 14.15 Applied Statistics
Most communicators need to master nothing more complicated than a few principles of applied statistics in order to overcome their innumeracy.
Applied statistics are not to be feared. They are based on basic, simple, fourth-grade arithmetic – addition, subtraction, multiplication and division. Mathematicians will tell you that algebra and calculus provide the support for the assumptions and techniques of statistics, but applied statistics do not require computation beyond basic arithmetic.
It is important for communicators to brush up on their basic mathematical terminology in order to be able to interpret the data they find in many reports, studies, documents, and other types of information resources. The following are a few commonly confused terms:
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percent |
a standard way of expressing a fraction, where the denominator (the bottom number) equals 100; so 1/4 equals 25 percent (4 X 25 = 100), 1/3 equals 33 percent (3 X 33 = 99 rounded to 100), 1/5 equals 20 percent (5 X 20 = 100), and so forth |
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percent change |
a way to express a relationship between an “old” number and a “change” or a “new” number and a “change;” for example, last year’s budget is $500,000 and the current budget is $600,000. The “change” is $100,000. To express this as a percent change from last year to this, you have to divide the “change” by the “old” number, or $100,000 / $500,000 = 0.2 = 20 percent. The new budget is therefore 20 percent higher than the previous year’s budget. To figure what percent of spending in the current budget is “new” you have to divide the “change” by the higher “new” figure, or $100,000 / $600,000 = 0.1666… = 16.7 percent |
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percentage point |
a way to compare two numbers that are already expressed as percents; for example, the March unemployment figure is 5 percent, the April unemployment figure is 6 percent, and the change is 1 percentage point. The percent change is 1 (the change) divided by 5 (the old number) or 20 percent |
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mean |
the arithmetic average of a set of values |
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median |
the middle value in a group, where values have been ranked from top to bottom |
Let’s look at the important differences between a mean and a median. The mean is the arithmetic average of a set of values. To compute a mean, you simply add up the values and divide by the number of values.
For example, let’s say that among 100 workers at a company, 95 make $30,000 and 5 make $300,000 a year. The mean salary is therefore (95 times 30,000) plus (5 times 300,000) divided by 100 OR 4,350,000 divided by 100 OR $43,500. This simple arithmetic average provides information about the average salary for workers at the company. But does it accurately describe salaries at this company?
If you answered no or not always, then you understand how important it is to evaluate how a figure is arrived at. A better way to portray salaries for this company is to use the median figure rather than the mean.
The median is the middle value in a group, where values have been ranked from top to bottom. A median figure is more likely to smooth out very wide differences between the highest and lowest values in the group.
For example, the middle value in our group of 100 salaries in our imaginary company ranked from top to bottom is the average of the salary of the 50th and 51st highest paid people. In this case, the median is therefore $30,000. The median figure clearly tells you more accurately about the salaries for the majority of people in the company.
In most cases, it is necessary to understand how both figures were arrived at and what some of the reasons might be for significant differences between the mean and the median.