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What Is 'Typicality'?

It's often useful to calculate or estimate a "Typical" value for a certain measurement:

• A Mean (or "average") is calculated by adding the quantities of all data points, then dividing by the total number of data points available. They are simple to calculate, but are prone to having outliers that that skew the average too high or low to be representative.
• A Median is calculated by sorting the values from high to low, then finding the quantity of the data point in the middle of the range. By definition, 50% of the values will be below the Median. Comparing the Median to the Mean can tell you if the average is influenced by outliers.
• A Mode is the value that occurs most frequently in the set. They are useful for finding clusters of data.
• A Midrange is the value halfway between the highest and lowest data points.

These are all tools that can help your system analysis if you use them right, but they can be misleading if you use the wrong tool for the situation.

Josh Kaufman Explains 'Typicality'

The average household net worth of a person who reads the Wall Street Journal is $1.7 million.

Seems that WSJ readers are extremely well off, right? Yes, but less than you might think.

Bill Gates and Warren Buffett read the Wall Street Journal, and their wealth is measured in the billions-significantly more than even the top 0.01% of business professionals. Simply by existing, high net-worth executives like Gates and Buffet skew the average much higher than it would be otherwise.

If you're relying on the average to tell you how much the typical Wall Street Journal reader is worth, you're making a mistake.

Many forms of analysis rely on defining Typicality: identifying a normal or typical value for some important measurement. There are four common methods of calculating a typical value: mean, median, mode, and midrange.

A Mean (or average) is calculated by adding the quantities of all data points, then dividing by the total number of data points available. Averages are simple to calculate, but are prone to Gates & Buffet Syndrome: the presence of outliers that skew the average too high or low to be representative. (Exclude the outliers, however, and the average becomes more accurate.)

A Median is calculated by sorting the values in order of high to low, then finding the quantity of the data point in the middle of the range. Medians are actually a specific form of analysis called a percentile: the median is the value that expresses the 50th percentile. By definition, 50% of the values in the set will be below the median. Often, calculating the median and comparing it to the mean can tell you if the average is being influenced by a few heavy hitters.

A Mode is the value that occurs most frequently in a set of data. Modes are useful for finding clusters of data-a set can have multiple modes, which can alert you to potentially interesting Interdependencies in the system that produced that data.

A Midrange is the value halfway between the highest and lowest data point in a set of values. To calculate the midrange, add the highest and lowest values, then divide by two. Midranges are best used for quick estimates-it's fast, and you only need to know two data points, but they can be easily skewed by outliers that are abnormally high or low, like Bill Gates's bank balance.

Means, medians, modes, and midranges are useful analytical tools that can indicate typical results-provided you're careful enough to use the right tool for the job.

Questions About 'Typicality'

• Would using a mean be appropriate for the analysis you're conducting, or would using a median or mode be a more accurate assessment?
• How can you remember to use a median instead of misusing a mean?

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"It ain’t what you don’t know that hurts you. It’s what you know that ain’t so."

Will Rogers, American cowboy and comedian

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