#### Let's Take A Closer Look

Explaining complicated subject matter simply since 1986

#### Measures of central tendency are the basic mathematics of a thing

Non-statisticians call those measures averages. The one most of us have in mind when we say average is the arithmetic mean. Arithmetic means (referred to as means) are the most-used types of average. Means are calculated by arranging all of the values in a data set from lowest to highest and dividing by the number of cases in that data set. Remember your computers are only processing what you feed them. Who’s in charge of computer diets where you work?

#### Means are best when you have lists that need only to be added together and divided

Because it’s a calculated number, the mean is skewed downwards by low values, upwards by high ones, and is totally distorted by wildly varying data sets. If the boss’ \$10 million is included, the increase in your company’s average salary will look as if you pay your people more than you actually do. Arithmetic means are often not whole numbers, as in the average American household has 1.6 children and 2.3 vehicles.

#### The median is the midpoint when the values are lined up in order

Count in from both ends to find the midpoint. If your dataset has an odd number of values, the median is the number in the middle. If your dataset has an even number of values, average the two values in the middle. Statisticians find it ironic that one way of measuring central tendency is calculated by using another way.

#### Medians are a better measurement than means because they are not affected by extreme values

The downside is that the median only measures a position in a column of numbers arranged in order from lowest to highest, and does not take into account the actual values of the data. I’d like to see more medians and fewer means in reports and news items.

#### The mode is the value that occurs more than all the others.

Modes are not good descriptors of data sets. Modes indicate only what values occur more often than the others. They may or may not be somewhere around the middle of your data set. Modes are the easiest to define, but analysts rarely pay attention to them.

#### Take a look at the 11 data points in the data set below

• What’s the mean? I’ve got a calculator, so it’s 3,477 units of whatever those numbers stand for divided by 11 data points, which is 316.0909, or what sensible people call 316.
• What’s the median? Count in from the ends to find the middle value, and you’ll see it’s 276.
• What’s the mode? I don’t see one. Sure, 304 and 307 are close, as are 273 and 276, but I see no value occurring more than once.
• Which measure of central tendency do you think does the best job of describing the data set above? If you said the median (276), we agree. Those with sharp eyes know the mean (316) has been inflated by that last value (393).

#### Why do the sports channels insist on telling us a basketball player averages 14.7 points, 9.2 rebounds, and 6.3 assists?

We all know that player never once tallied 14.7 points, 9.2 rebounds, or 6.3 assists, never could, and never will. Not any more than you have 2.3 kids or your garage holds 1.8 cars. It is better to use whole numbers and report that the player averages nearly 15 (round up) points, 9 rebounds, and 6 assists. The same thing works in reports. Use whole numbers and people will better remember your illustration.

When you are dealing with things that show a decimal, the numbers to the right of it imply a precision when there is none

When you see tenths, hundredths, and thousandths reported, as I did with 316.0909, they’re almost always as useless as trying to measure which of the Seven Dwarfs is the tallest.

#### Let’s give up saying average when what we really mean is typical

Typical describes the overall sense of something that may also be called normal or standard or common, but it is not an average.

• American Heritage Dictionary says typical describes someone or something that exhibits the traits, characteristics, and qualities that have all the characteristics that you would expect.
• Online Etymology Dictionary says typical is from a Latin word meaning symbolic.
• Cambridge Dictionary says synonyms for typical include usual, normal, and ordinary.
• Something is typical when it captures the overall essence.
• Typical is also used ironically, as in “That’s so typical of government — all veterans’ offices are closed on Veterans Day.”

#### Is typical anything like stereotype?

It can be. People from around the world say typical American tourists are ignorant, loud, thoughtless, and arrogant. Or maybe that’s average (sic) American tourists. When generalized like this (with all of those negative descriptions), typical is moving into stereotype territory. All these things about stereotypes are true:

• Stereotypes are one-size-fits-all expectations and beliefs about a category of people.
• Stereotypes are oversimplified assumptions that originate from broad generalizations and are often biased.
• Stereotypes are most often based on hot-button issues such as race, color, religion, nationality, gender, and culture differences.
• Most stereotypes are critical, prejudicial, and negative.
• Stereotypes promote an us-vs-them mentality.
• Stereotypes conform to a simplified and standardized set of expectations, and have been called images perpetuated without change.
• When it’s sold as a costume on Amazon, it’s a stereotype.

#### Extra credit

What does the N on the side of the University of Nebraska football helmet stand for?*

#### Bonus

It’s even more fun when stereotypes are idioms, too. Couch potatoes are slackers who spend most of their time lying on the couch with a remote control in one hand and a beer in the other. Couch potatoes are such stereotypes that artists make and sell costumes, books, plush toys, throw pillows, T-shirts, hoodies, Christmas ornaments, and \$200 couch potato sculptures.

A couch potato is a stereotype; your worthless brother-in-law being a couch potato on your couch is typical

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*As they like to say in Colorado, “Knowledge.” This, too, is a stereotype.