# eli5 Why do we use median salary instead of mean salary?

848 views

Wouldnt mean salary be a better representation of the public then median?

In: Other

Mean is very susceptible to outliers – if 99 people make \$10/hour and 1 person makes \$1 million/hour, would you say that ~\$10,000/hour or \$10/hour is a better reflection of a typical person’s income?

> Say you paid your rent on Monday with a personal check of \$408, and the other 14 purchases were your twice-a-day Starbucks latte habit. There were 14 checks for \$3 and one check for \$408, so the median check was \$3.

The mean is more significantly affected by outliers (large numbers well outside the norm – the mega rich) than the median.

It depends on the situation, I don’t know in what context you are asking. But a mean averages all points of data even if they are extreme. So for example if you have 5 people making 10 000\$ and 1 making 100 000\$, their average is 25 000\$, which could be misleading, but their median is 10 000 \$ which is more representative of the majority.

Because means are not robust and are too easily swayed by outliers.

Take a place where 99 people make US\$ 1 and 1 person makes US\$ 10000. The mean will be US\$ 100.99, the median will be US\$ 1. Now, which number reflects reality best?

Different statistics say different things.

You use Midian numbers when you have large outliers and your goal is to represent the “typical” number. This applies to income* quite well.

With income, you have a relatively small percentage of income earners who earn a HUGE amount of the total income. That means an average is somewhere between the “normal” people and these huge income earners. That means the average, or mean, is going to skew higher than the normal person earns.

Let’s switch to a new example. How many fingers does the typical person have?

Answer: the typical person has 10 fingers. But the average person has fewer than 10 fingers due to the number of people with missing fingers due to accidents (and people born with extra fingers are less common than those with fewer fingers).

The average provides a true number, but not a useful one. The median provides the best answer.

*I changed from the word “salary” to the word “Income” because I know the distribution of incomes, I am less certain on the definition and distribution of the word “salary.”

Both are used. Which is better depends on what you’re interested in knowing. Median is better to know what a “typical” person makes, which is why it’s more often cited.

A sales team may make on (mean) average \$200k, but there could be a few superstars making \$500k+. If you’re wondering if you should take the sales roll, you’ll want a better idea what you should expect to make and median makes more sense in that context.

It’s been said before but: medians are more resistant to outliers. If you are looking for what the *average* American person makes, you want the *median* of what *all* Americans make, because the *mean* of every American citizen pooled together will be dramatically higher than this middle value, due to the wealthy minority’s income being so high.

For example, 10% of households hold something like 65% of all wealth in the US. The lower 50% of the population make about 50,000 / year. So your median value would give you a similar value to that, while the mean would be significantly higher.