# The Misuse of Averages to Confuse

“Averages” are used nearly everywhere, especially in advertisements or studies, but they can be incredibly misleading. To begin with, simply citing anything as the “average” is deceitful, whether this is intentional or not. There are three kinds of average–means, modes, and mediums–and they have significant consequences on the data they portray.

The three different kinds of averages are means, modes, and mediums, and they can portray different pictures depending on how they’re used. A mean is what you get when you take all the values in a particular set (say, hourly wages in the set of company incomes) and divide them by the number of items in that set (say, the number of hourly wages we’re looking at). This can be useful if the wages are clustered together but misleading if there are great disparities in the wages. Let’s say that five individuals work for a company and their hourly pays are \$10, \$11, \$13, \$13, and \$16. If you take the mean (adding all the values together (63) then dividing by the number of values (5)), you end up with a mean of \$12.60. In this case, it’s reasonable to conclude that most employees earn around \$12.60 an hour and knowing this “average” is useful. However, take an instance where five individuals work for a company and their hourly pays are \$7, \$7, \$7, \$8, and \$45. When you take the mean (adding all of the values together (74) then dividing by the number of values (5)), you end up with a mean of \$14.50. This value, however, isn’t accurate or useful. Prospective employees will think the pay is higher if using this “average” when they will, in reality, likely be paid significantly less. Means are useful only when the values are closely distributed around a certain point. If some values are significantly lower or higher than most of them, the so-called “average” will be skewed.

The mode is the most frequently-occurring value in a set of values, and it can often be more useful than the mean in instances where the mean is skewed by extremely high or low values. Taking the earlier example of the skewed mean, to take the mode would be to count up what value occurs the most times. In that case, a \$7 pay occurs three times, so this is the mode. By taking this, one discovers what most employees are paid and prospective employees have a better idea of what their wages will be.

The medium is the middle-value in a set of values and, though less useful than the former averages, it can be used to determine if a mean is skewed. In a set of values of 5, 6, 7, 8, and 9, the medium is 7, for it occurs at the middle of all of the values. If a medium is taken and it falls significantly higher or lower than a mean, it indicates that the data is being skewed. Take again our instance of the \$14.50 mean wage: taking the medium would indicate a pay of \$7. This falls significantly below the mean and so it indicates that the data is skewed. Mediums will fall closer to clusters of similar data: in a set of 6, 7, 8, 9, and 25, the medium is 8; In a set of 1, 6, 7, 10, and 12, the medium is 7. The medium is less useful when values are spaced far apart, but they will naturally be closer to what the mode is. Overall, mediums are less useful on their own and more useful in indicating skewed data.

Be mindful of what is really being communicated when an individual or company speaks about the “average” of a particular thing. Are they referring to the mean, the mode, or the medium? If they’re referring to the mean, which they most often are, is the data being skewed by a minority of values which are unusually high or low? These are important things to bear in mind when an average of a particular thing is cited, and if the type of average it is isn’t cited, be wary.

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