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Measures of Central Tendency

Exploring The Mean, Median, And Mode

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Measures of central tendency are numbers that describe what is average or typical of the distribution of data. There are three main measures of central tendency: mean, median, and mode.

Mean

The mean is the best-known and most widely used measure of central tendency. It is what most people call the "average." It is used to describe the distribution of interval-ratio variables such as age, income, and education.

The mean is calculated by adding up all the scores and dividing the result by the number of scores in the distribution. For example, if five families have 0, 2, 2, 3, and 5 children respectively, the mean number of children is (0 + 2 + 2 + 3 + 5)/5 = 12/5 = 2.4. This means that the five households each have an average of 2.4 children.

Median

The median represents the exact middle of a distribution so that half of the cases are above it and half are below it. It is the middle case in a distribution when the scores are arranged in order from lowest to highest.

For example, let’s suppose we have the following list of numbers: 5, 7, 10, 43, 2, 69, 31, 6, 22. First, we must arrange the numbers in order from lowest to highest. The result is this: 2, 5, 6, 7, 10, 22, 31, 43, 69. The median is 10 because it is the exact middle number. There are four numbers below 10 and four numbers above 10.

What happens if we have an even number of cases in our distribution? If we add the number 87 to the end of our list of numbers above, we have 10 total numbers in our distribution, so there is no single middle number. In this case, you average the scores for the two middle numbers. In our new list, the two middle numbers are 10 and 22. So, we take the average of those two numbers: (10 + 22) /2 = 16. Our median is now 16.

Mode

The mode is the category or score with the highest frequency in the distribution. In other words, it is the most common score, or the score that appears the highest number of times in a distribution. For example, let’s say we are looking at pets owned by 100 families, with the distribution looking like this:

Animal      Number of families who own it
Dog                   60
Cat                    35
Fish                   17
Hamster            13
Snake                 3

The mode here is "dog" since more families own a dog than any other animal. The mode is always the category or score, not the frequency of that score. For instance, in the above example, the mode is "dog," not 60, which is the number of times dog appears.

Some distributions do not have a mode at all. That is, each category has the same frequency. Other distributions might have more than one mode. For example, when a distribution has two scores or categories with the same highest frequency, it is often referred to as "bimodal."

The mode is the only measure of central tendency that can be used with nominal variables.

References

Frankfort-Nachmias, C. & Leon-Guerrero, A. (2006). Social Statistics for a Diverse Society. Thousand Oaks, CA: Pine Forge Press.

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