A Field Guide to Lies: Critical Thinking in the Information Age Read Free

all by itself, it’s usually indicating the mean, but you can’t be certain.
    The mean is the most commonly used of the three and is calculated by adding up all the observations or reports you have and dividing by the number of observations or reports. For example, the average wealth of the people in a room is simply the total wealth divided by the number of people. If the room has ten people whose networth is $100,000 each, the room has a total net worth of $1 million, and you can figure the mean without having to pull out a calculator: It is $100,000. If a different room has ten people whose net worth varies from $50,000 to $150,000 each, but totals $1 million, the mean is still $100,000 (because we simply take the total $1 million and divide by the ten people, regardless of what any individual makes).
    The median is the middle number in a set of numbers (statisticians call this set a “distribution”): Half the observations are above it and half are below. Remember, the point of an average is to be able to represent a whole lot of data with a single number. The median does a better job of this when some of your observations are very, very different from the majority of them, what statisticians call outliers.
    If we visit a room with nine people, suppose eight of them have a net worth of near $100,000 and one person is on the verge of bankruptcy with a net worth of negative $500,000, owing to his debts. Here’s the makeup of the room:
Person 1: −$500,000
Person 2:  $96,000
Person 3:  $97,000
Person 4:  $99,000
Person 5:  $100,000
Person 6:  $101,000
Person 7:  $101,000
Person 8:  $101,000
Person 9:  $104,000
    Now we take the sum and obtain a total of $299,000. Divide by the total number of observations, nine, and the mean is $33,222 perperson. But the mean doesn’t seem to do a very good job of characterizing the room. It suggests that your fund-raiser might not want to visit these people, when it’s really only one odd person, one outlier, bringing down the average. This is the problem with the mean: It is sensitive to outliers.
    The median here would be $100,000: Four people make less than that amount, and four people make more. The mode is $101,000, the number that appears more often than the others. Both the median and the mode are more helpful in this particular example.
    There are many ways that averages can be used to manipulate what you want others to see in your data.
    Let’s suppose that you and two friends founded a small start-up company with five employees. It’s the end of the year and you want to report your finances to your employees, so that they can feel good about all the long hours and cold pizzas they’ve eaten, and so that you can attract investors. Let’s say that four employees—programmers—each earned $70,000 per year, and one employee—a receptionist/office manager—earned $50,000 per year. That’s an average (mean) employee salary of $66,000 per year (4 × $70,000) + (1 × $50,000), divided by 5. You and your two friends each took home $100,000 per year in salary. Your payroll costs were therefore (4 × $70,000) + (1 × $50,000) + (3 × $100,000) = $630,000. Now, let’s say your company brought in $210,000 in profits and you divided it equally among you and your co-founders as bonuses, giving you $100,000 + $70,000 each. How are you going to report this?
    You could say:
Average salary of employees: $66,000
Average salary + profits of owners: $170,000
    This is true but probably doesn’t look good to anyone except you and your mom. If your employees get wind of this, they may feel undercompensated. Potential investors may feel that the founders are overcompensated. So instead, you could report this:
Average salary of employees: $66,000
Average salary of owners: $100,000
Profits: $210,000
    That looks better to potential investors. And you can just leave out the fact that you divided the profits among the owners, and leave out that last line—that part about the