Mass Media, Mathematics and the

Mathematics as a tool of the media can influence the values, beliefs, and ideas of its readers and listeners. As a result, students and consumers of information must learn how to recognize sound and usable data in a wilderness of numbers.

Thinking Critically about Numbers

The use of critical thinking skills can enable information consumers to analyze and critique the mathematics, data, and statistics that are reported in the media. Statistical methods and statistical terms are frequently used in articles dealing with social and economic trends, business conditions, opinion polls, and the census. But writers often do not use these terms accurately, and results are usually presented within a limited context. Consequently, the jargon can seem like semantic nonsense for readers, listeners, and viewers. In addition, results may be misleading, depending on the argument of the writers.

Critical thinking ability is radically different from using numbers just to add, subtract, multiply, and divide accurately. Our technological society requires everyone to know how and why crucial issues are put in mathematical form by the media. For instance, college admission requirements that use a combination of test scores and high school rank can be used by the media to report either a positive or a negative message.

Radio, television, newspapers, and the Internet are changing the way mathematics is viewed and, in turn, increasing the importance of mathematical modeling in the media. Students and consumers must be prepared to ask and answer different questions, such as:

• Is this the best mathematical model for the information being presented? What methods of mathematical analysis will best support the position?
• What variables should be included in the analysis to strengthen the position?
• Can mathematical models minimize the appearance of important data?
• Will percentages or fractions make a more striking impression?

Thinking Critically about Statistics

Students and consumers must understand when information is distorted or misrepresented because of a misuse of statistics. For example, the word "average" is frequently used in the media to convey information consisely. Yet mathematically, the average value can have different interpretations, and therefore may yield a biased picture of reality.

When the word "average" is encountered, several things must be considered. For instance, what form of average is being used? Statisticians use three types of averages, or measures of central tendency: mean, median, and mode. Data can be made to appear more favorable depending on which measure is chosen.

To calculate the mean, all of the values in a data set are summed up then divided by the total number of values. Hence, very high or low values can influence the average. For example, using the mean to determine the average salary of workers in a company will give the appearance of higher pay if the owner's much higher pay is included. Depending on the research question, the average calculated in this manner yields a misleadingly high figure.

With a median, which is the value that falls in the middle of the ranked distribution of data points, the data show that half the employees make more than that value, and half make less. The mode, the most frequently occurring value in a data set, reveals the most common pay. In this example, both the median and mode will be considerably less than the mean because they are less influenced by the owner's higher pay.

Another question to ask is "Who is included in the average?" If only tall people were included in a calculation of "average" height, the resulting mean would not represent the population as a whole.

Yet another question is "How large is the sample?" A sample is a portion of the population that is evaluated to gain information with the intention of generalizing to the whole. An inadequate statistical sample size will not produce conclusive results. For example, results cited from a small "independent" laboratory may be relying on an experimental study of six cases, hardly enough to determine any degree of significance in the results. (One could also ask: Which laboratory? How small?)

Consider what happens to percentages when a coin is tossed 10 times versus 1000 times. Ten tosses may give the result of 8 heads and 2 tails for an 80 percent result of heads. Yet 80 percent would be misleading, because one thousand tosses will bring the result closer to the actual probability of 50 percent.

Finally, the degree of significance also reveals the accuracy of the data. For most purposes, 5 percent is thought to be significant. This level of significance indicates that the probability that the results were generated randomly is less than 5 percent.

Thinking Critically about Graphs

Technological advancements have made graphics a vital mathematical feature in the media. Although pictorial graphs are commonly used because they are appealing to the eye, they have a high potential for misuse—and they can further compound misused statistics.

Consider a survey in which American citizens were asked whether they agreed with a decision made by the president of the United States. The percentage of "yes" and "no" responses would predictably follow a pattern based on partisanship, as shown in the figure. But if responses from both parties are combined, the percentages of "yes" and "no" responses are fairly even.

One media report could show only the top graph, giving the indication that Americans strongly favored the president's decision. Another report could show only the middle graph, indicating strong opposition. Both graphs are accurate, but each one by itself shows only part of the picture. Hence, a conscientious media reporter must clearly indicate who was polled.

Another misuse of graphs involves proportions. For example, by simply changing the proportion on the ordinate and abscissa , or by completely eliminating the scale, a person preparing a graph can make it appear to rise or fall more quickly and thus give the impression of a drastic increase or decrease. (Darrell Huff, the author of How to Lie with Statistics, calls these "gee-whiz" graphs.) Furthermore, the use of proportions for objects can be misleading when a one-dimensional picture is represented in two dimenions.

The height of a moneybag may represent the comparison of two salaries where one salary is double the other. If the pricier money bag is made twice as tall as the other, yet the same proportion is maintained, the numbers still say two-to-one, but the visual impression—which is the dominating one most of the time—says the ratio is four-to-one.

see also Central Tendency, Measures of; Data Collection and Interpretation; Graphs; Polls and Polling; Probability, Experimental; Statistical Analysis.

Randy Lattimore

Bibliography

Huff, Darrell. How to Lie with Statistics. New York: W. W. Norton, 1954.

Tate, W. F. "Mathematizing and the Democracy: The Need for an Education That Is Multicultural and Social Reconstructionist." In Campus and Classroom: Making Schooling Multicultural. C. A. Grant and M. L. Gomez, eds. Englewood Cliffs, NJ: Merrill, 1996.

SHARK ATTACKS: ON THE RISE?

Headlines may state that certain harmful events are increasing in frequency, duration, or severity. But just because a calculated number may be slightly higher than before does not necessarily mean that an event is worsening. In fact, a small increase could, in reality, be a decrease depending on the margin of error, which is partly determined by how the data were collected and analyzed.

Moreover, repeated news coverage can give the impression that numbers of events are increasing. For example, heavy coverage of shark attacks in 2001 gave the impression that attacks were increasing, even though 2001 statistically was considered a typical year.