Of the three measures of central tendency, the mode is the simplest to calculate but is used less often than either the mean or the median. The concept of central tendency is widely used in everyday life as well as in academic research. For any kind of information, it is important to know what describes the typical case as well as the range of variation. The mode is the only measure of central tendency appropriate for nominal or discrete variables such as gender, ethnicity, or language. The mode can be defined as the category with the largest number, frequency, or percentage. The mode is not the frequency but the category. So, for example, the U.S. Census Bureau data for the year 2000 indicate that approximately twenty-eight million people in the United States speak Spanish, followed by approximately two million Chinese speakers and fewer numbers who speak other languages. Thus in this example, the mode of distribution of foreign-language speakers in the United States is “Spanish.” To compute the mode, list all the values (or categories) in the distribution and tally the frequencies for each value or category. The category with the most is the mode.
If a distribution has two categories with equal numbers or proportions in it, then the distribution is said to be bimodal. Suppose that, in a survey of a group of 100 college students about their political views and party affiliations, it turns out that 20 of them are Independents, 10 are Green Party affiliates, 10 are Libertarians, 30 are Democrats, and 30 are Republicans. This distribution is bimodal, with Democrats and Republicans both being modes (figure 1).
The mode can also be used for other types of variables: ordinal, interval, and ratio. However, it has a limitation that other measures of central tendency do not. It takes into account only one or two categories, the biggest ones. The median, or fiftieth percentile, cuts in half a distribution that is ordered from low to high or high to low, but extreme values at either end of the distribution do not affect the median. The mean takes each and every value into consideration. Extreme values will affect the mean, making it higher than the median if the extreme values are at the high end of the distribution (such as Bill Gates’s income in a distribution of average Americans) or lower than the median if the values are on the low end (perhaps a homeless person) of the distribution. The mode may be located anywhere in the distribution.
Occasionally researchers report a mode for grouped frequency distributions or for variables that may be collected at the ratio level, such as years of education, and collapsed into categories such as less than high school, high school, some college, and so on. If a researcher were to ask eleven people how many years of schooling they completed and got the following results, here is how the researcher could proceed.
First, the data indicate that there are three people with 16 years of education. There are more respondents in that educational category, so 16 years is the mode. Next, if the years are arranged in order, the result is: 9, 10, 11, 12, 12, 13, 14, 16, 16, 16, 20. The sixth number (13, corresponding to Gabby) is the median, because there are five cases on either side. To obtain the mean, all the years are added up (149) and divided by 11. That gives a mean of 13.5. If the years of education were collapsed into a table that showed categories, some information would be lost, but it would present the data in a way most people think about education.
|< High School||3|
|College or Higher||4|
Judgments would have to be made, though, and in some cases that might be tricky. One would have to assume that people who reported fewer than 12 years of education did not skip any grades and that all people who reported 12 years actually received a high school diploma. Unless the question were asked, one would not know if someone obtained a GED. Similarly, one would have to assume that those people who listed 16 years of education received a college degree. The mode in this case would be college or higher.
SEE ALSO Central Tendencies, Measures of; Mean, The; Standard Deviation; Statistics
U.S. Census Bureau. 2003. Language Use and English-Speaking Ability: 2000. Census 2000 Brief. Washington, DC.
M. Cristina Morales