# A comment on median vs. mean, and job-stratified wage growth

#### A comment on median vs. mean, and job-stratified wage growth

–* by New Deal democrat*

Before today’s avalanche of data, I wanted to comment briefly on the Employment Cost Index for Q4 that was reported yesterday.

This index has the advantage of weighting for type of employment. If low wage workers gain a disproportionate number of jobs, that will tend to hold down *average* wages. But the ECI hold the weighting of low, medium, and high wage jobs constant, so that it tells us how much pay for the *same job* varies from quarter to quarter. And because it is a median vs. average measure, it isn’t skewed by disproportionate gains at the very high end.

The quarter over quarter change in the ECI is shown in red in the graph below, since the peak in wage growth in 2021, compared with average nonsupervisory wage growth (light blue) and average total private wage growth (dark blue):

All three show deceleration, and all three are currently between 4.0% and 4.5% growth YoY, as shown in the graph below:

Note that average hourly wages spiked during the pandemic lockdown period, when low wage service workers were very disproportionately laid off. When they were rehired in 2021, and seemingly every retail business had a “help wanted” sign on their front window or roadside sign, average hourly wages for lower income, nonsupervisory workers spiked far more than other wages. By contrast, the wage paid for *the same work* was not affected by the pandemic layoffs, but did increase sharply as the unemployment rate fell to historical lows.

This “*game of reverse musical chairs*,” as I have called it over the past couple of years, has pretty much come to an end, and more typical wage growth for an expansion has ensued.

Tomorrow both average wage measures will be updated for January as part of the jobs report. I anticipate further deceleration.

The Big Story: a 100+ year near-record decline in commodity prices is enabling continued record wage growth and employment, Angry Bear, by New Deal democrat

It is puzzling to many/most that ‘median’ and ‘mean’ have different meanings.

Those who are really into statistics insist there’s a big difference between the two.

There is, kinda.

A

medianis the middle value of the list of values in a data set. Themeanis the arithmetic average of those values. (If there is no middle, as in a data set with an even number of values, the median is the arithmetic average of the two values on either side of the middle.)Median – Wikipedia

“The basic feature of the median in describing data compared to the mean (often simply described as the “average”) is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center.”

(I remember being taught that the ‘big difference’ between the two is that a

medianactually has to be member of the data set, while anaverageneed not be. Not quite true as it turns out, which probably adds to the confusion.)If the median and the mean are the same, then the population is distributed normally and statistics that assume a normal (gaussian) distribution can be used. If the mean and median diverge significantly, then the population isn’t distributed normally and you need to use nonparametric statistics to avoid a type 2 error.

The mean is the average. The median is the point where half the values are above and half below.

Here’s an illustration. Bill Gates walks into a bar. Now the average person in the bar is a billionaire.

Hope that helps.

Hmmm:

Lets assume. Joel comes to AZ or Bill ends up in NYC for business. Bill wanders up to Providence RI. The two of them grab a beer or two at The Eddy. Both of us make decent money. So the average would be from the two of us and a median decided from the higher and the lower salary. In walks Bill Gates and the numbers go out the window as there are now three of us. What do you see? I am not saying I am right either.

I took a lot of statistics courses back in the day. Modern physics at its heart is very much statistical in nature. Probability & quantum physics go hand in hand.

If the mean is the average, then (probably) the average is the mean. Hope this helps.

@Fred,

No, it doesn’t.

“Mean” has a specific mathematical definition. “Median” has a different specific mathematical definition. “Average” is a colloquial term, lacks a formal mathematical definition, and has been applied to both mean and median. Of course, when a population is distributed normally (Gaussian), the mean and median coincide. In other cases (e.g., a Poisson distribution), the mean and median can diverge substantially. When your mean and median diverge significantly, it suggests that in the underlying population you’re sampling from, the property you’re measuring isn’t distributed normally.

I took a statistics course in high school and a semester of basic statistics in grad school. I did regressions for my dissertation data, and I’ve coauthored many scientific articles over the past several decades that use basic statistics. Mean and median, variance and standard deviation are all high school level statistics.

In other words, the term

averagedoes have a precise definition, when used with data.But the word

averagedoes have a lot of different meanings.As does

mean, oddly enough.@Fred,

“In this example, the median would be 3, it would seem.”

Wrong. The median for that series is 4.

The mean is 5. The average is either the mean or the median, depending on what you want it to be. Mean and median have rigorous mathematical definitions.

@Fred,

“As does

mean, oddly enough.”Well, yes. For example, some people would regard teasing as being “mean.” It can also be used to refer to someone of low social class. It can also be a synonym for “intend.” So yes, “mean” can mean a lot of different things, depending on context.

However, in the mathematical sense, it has this meaning: the value obtained by dividing the sum of several quantities by their number.