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Monday, 27 March 2023


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Mean vs median is pretty simple. Here's an example using a sample of five values: 2, 5, 7, 11, and 12.
Mean = 2+5+7+11+12/5 = 7.4
Median = mid-point value in the series, in this case 7

I have the sense that means and medians are often used a bit opportunistically by journalists. Or, if we're being charitable let's say that they're ignorant of the definitions and too often use the value in best agreement with the argument they're making.

When talking about something like net-worth, income, or home values, the mean can be relatively uninformative if you have a non-normal distribution of sample values. If you calculate the mean of Elon Musk's net worth plus many thousands of me, you will still have a very high net worth. If you calculate the median net worth of Elon Musk + many thousands of me... let's just say you won't be buying a new Tesla EV any time soon.

Hi Mike,

"mean" and "median" are both averages. If we take the list, 1, 2, 3, 4, 10, the median is the one half way along the list, in this case, 3. The mean is what is commonly described as the average and is the sum of all the numbers divided by the number of numbers. In this case, 20/5=4. The median is less affected (as we can see here) by 1 number being at an extreme for the list, and so is a widely accepted way of measuring incomes, which depending on country, may have incomes at extremes.

Difference between mean and median is crucial to understand. Mean wage (same as average), for instance, is total wages of everybody divided by number of people. Median wage is the wage such that half of people earn less than it and half more.

Consider a world (not unlike the one we live in) where there are 100 people. 99 of these people earn 30 zorkmids a week, one plutocrat earns 100,000 zorkmids a week. Average wage is about 1030 zorkmids a week. Median wage is 30 zorkmids a week. You can see that the median is a far more useful value if you want to know what average person can afford.

From Wikipedia we can look at median disposable income which means 'after usual deductions' and is more interesting than gross income. Measured in USD at purchasing-power-parity (all these things have technical definitions):

  • US, 2021: 46,625
  • UK, 2020: 25,407 (quite likely this will be significantly lower today however, perhaps 5-10%?)

So UK people get a little over half as much as in US. Of 44 countries in that list the UK is 20th, the US is first.

How do people buy houses in the UK? I think that they generally do not buy very many at present, as is the way with relatively poor countries with housing bubbles.

However these sums are more complicated: I do not know for instance if US numbers will include expected healthcare costs, while UK ones will (or would have until current UK government of rich morons set about systematically destroying healthcare system).

Money is a tangible thing, but it does not fit into a formula that works for everyone equally. There is of course geography and social differences... a poor person in New York City would be in the upper tier anywhere in the state of Mississippi.

More important for many of us that stopped chasing numbers is the intangible value of not striving to earn enough to put on the "show" to impress unknown other people with flashy toys and status possessions. I refuse to have any debt.

My parents both dropped out of school in the 8th grade because of the great depression, worked hard all their lives and never earned any more than the low five figures combined. They somehow kept their 4 kids in a house, assured we all completed our education and instilled the sense that there are more important things than the number on your W2.

I start my social security next month and with my pension from my work, I'm going to make three times the annual amount (adjusted) than my parents ever made in their best year. But more valuable is my attitude about money. I don't know how I'll even spend my retirement income, while others couldn't survive on it.

FWIW, the "mean" is the average as we usually compute it.You add up all the numbers and divide by how many numbers you have.

The" median" is computed as being the value that is less than exactly half of all of the values in the data set, and also greater than exactly half. So for salaries, which have a large range of values, it's a better measure of "average" in some sense because the larger values don't skew the answer as much.


Median means the middle value when numbers are listed in order from smallest to biggest. Mean, or average, is the sum of all the numbers divided by how many there are. It tends to exaggerate when there are a few very big numbers and a lot of small ones. As there often is in salaries. That is why median is usually used when talking about incomes or wealth.

The median income is probably a better benchmark for you than the mean (average) in an extremely unequal society like the U.S. The reason being that a few extremely high earners will skew the mean upwards. The median is simply the middle value if you put all incomes in an ascending list, so the 0.1 percenters won't affect it so much.

Mike, the effective difference between mean and median is this:

To calculate the median, you line up all of the numbers in ascending order, then pick the number which is exactly in the middle of the line. If you have 99 numbers, it’s the 50th from either end. If you have an even number, it’s the average of the 50th from each end.

The mean, on the other hand, is simply the average of all the numbers.

Both are important measures of sets of numbers. Both are subject to subject to severe distortion with some sets. For instance, if a population of 100 people has 99 people earning $10,000 and one person earning $1,000,000, then the mean is $19,900 (99 times $10k + 1 times $1,000k). The median is $10,000. Both are “correct”, but the recipient of the measure better understand what exactly was calculated and how.

The are other measures of a set of numbers, like standard deviation, that help to better understand the shape of the set.

In case no one has told you yet, the median is the number that is exactly half way between the high number and the low one, The mean is what is often called the average : add up all the numbers and divide the total by the quantity of numbers that were added together.

50% of households make more than this and 50% make less than this.

What most people think of as average, i.e., add all the incomes and divide by the number of incomes.

As you can imagine, even with a relatively small number of households with very high incomes, this has the effect of making the mean considerably larger than the median.

Hi Mike

The mean is all the incomes summed them divided by the number of incomes. The median is the middle value ie if you listed 51 incomes in rising numerical order the, median would be the 26th value in that list. I think the mean salary would be a bit higher because the mean is swayed by extreme values (like billionaires) in the sample. When comparing, it's recommended to use the same type of average :-)

I'm always saying quote your sources rather than pick some random figure off the internet, so I did some digging. I found these extremely up to date figures "Earnings and employment from Pay As You Earn Real Time Information, UK: March 2023" produced by the Office for National Statistic on this site:


You can download a .csv file of the data set from this link on the page:


What it says (if I have got my links in the right place) is that the median (ie the 50th percentile) monthly income in the UK this month is:

£2195 = £26340 p.a. or $32,358 USD according to XE.com.

UK income is taxed at 0% for the first c. £12k p.a., 20% from £12k to c. £50k, 40% from £50k to £150K, 45% on anything over £150k. There's an additional income tax called National Insurance of 12% paid by most employees.

Based on that, I used the this calculator https://www.moneysavingexpert.com/tax-calculator/
to work out the take home pay after all income tax of someone earning the median salary:

£21,934 per annum, £1828 per month, £422 per week.

Any goods or services purchased with this residual income would be taxed at a VAT rate of 20%.

According to this site https://www.gov.uk/government/news/uk-house-price-index-for-december-2022

the average house price nationally is currently: £294,329 ($361,224).

Average house price in London where I live is £543,099.

According to an online estate agent valuation service, small 980 sq foot 3 bed terrace houses like where I live are worth £633k! This quite ridiculous and would be completely unaffordable for me, if I didn't already own it, being 17x my final annual salary at retirement. The answer to your question "how can Brits buy houses" is most starting from scratch no longer can unless they already have equity or inherit money. I feel for the next generation trying to buy a house, it's not for something they are dubbed "generation rent". Something needs to be done about housing costs.

(Note: Not sure how sensitive these numbers might be, feel free to redact if anything seems inappropriate)

Mean and median—think of it as average and middle of the road and the bigger the difference, the more skewed the distribution is.

The mean of 2,4, 6, 8, and 10 is 6. You add all of the numbers together and divide it by the number of numbers you added together. The median is also 6 because the median is the value of the number in the middle of the series,. Half of the numbers are less than the median and half are more.

If the 5 number series was 2,3, 4, 5 and 10 it would have the same range as the series above, from 2 to 10, but the average would be 4.8 and the median would be 4.

If the median is below the mean, more values in the series are in the lowest half of the range covered by the series, if the median is higher than the mean than more values are in the upper half of the range. If the mean and the median are identical then the values are distributed evenly throughout the range.

Mike, usually wealth flows from generation to generation. You've described here a number of times the wealth of your parents and especially your grandparents. What happened to sever the usual handing down of money from generation to generation? How did you miss out on the usual intra-familial/generational financial lectures about the way to make money?

When I read things like what you've written here I always think about the novel, "God Bless You Mr. Rosewater" in which the author talks about how wealthy people know where the river of money lies and how they take buckets there to dip out what they want or need. How is it that things went so awry? How did you miss getting your "bucket"?

What is the lesson for us resolutely middle class slobs? That might also make a good story, along with your narrative of having bootstrapped yourself along the way.

Without splitting hairs: mean: average, median: midpoint.

I don't have much to add about money and all, except that I feel quite blessed, even as an agnostic, to be able to live well in a country that allowed my immigrant parents and immigrant me to join in.

One of the fruits of that is to be able to have a small place for summer stays outside Portland, Maine, which brings me circuitously to your post. Bath and its Iron Works is about 30 minutes north of our place. It is now a museum and a shipyard run by General Dynamics. Truly interesting place to visit. Sounds like your Dad made a difference, from what I know it was a sad place back in the '70s.

Bath is a charming little town by the way, with something like 4 second-hand bookshops on its Main street.

Mike, you may have already received this information from another viewer.
The "mean" income is the same as the "average" income. For a group of 11 people, you would add up their weekly/monthly/yearly income and divide by 11. To get the "median" income, you make a list of the 11 incomes, let's say listed from highest to lowest.The income number for person number 6--right in the middle of the income list--is the "median" income. The mean income is higher than the median income in the U.S. because of the relatively small number of people who have very high incomes.

Mean is the average of all the numbers in a set.
The median is the single number in the middle of the set.

The reason for talking about the median instead of the mean in statistics like this is that medians are less susceptible to distortion from big numbers at the extremes.

In the set 3,5,100, the median is 5. The average (mean) is 36.

I'm in Australia and also remember being shocked at how cheap housing is (was?) in the 'States.

Prices here are particularly inflated because home ownership is as much about wealth generation as it is about housing, maybe more-so, which drives money into homes, which in turn drives the price (and around it goes).

Obviously, there's a lot more to the economy and to general wellbeing than property prices, though. In relative terms we pay little for health care and education, fresh food is cheap, cities are accessible, the average worker gets 4-5 weeks of paid leave a year and permanent employees have a degree of job security (no-fault dismissal of permanent employees is illegal up to around the $160k wage mark).

The "mean" income is the average of all incomes in the set of data. The "median" income is middle value in a set of data, so if you had a list of 100 peoples income and you plotted them from highest to lowest the median income would be around the 50th income on the list. The problem with looking at the mean, or average, income is that the number can be greatly skewed if you have a lot of people with extremely high or very low incomes on the list, whereas the median income tells you who is sitting in the middle of the pack. Half the people earn more and half the people earn less than the person at the median income.

In the medical field, these sorts of numbers have caused a lot of pain. People who have a cancer, or other serious diagnosis are frequently quoted a "Median five year survival" and that's the number they hear and hold on to in terms of how long they will live. However, what it really means is that of 100 people with that diagnosis at that stage 50 people won't live that long, but 50 people will live longer--sometimes way longer. It's usually a bell shaped curve and there are people who define the far edges of that curve on both sides. When patients used to tell me that they had read online that they only had 2 years to live, I would review all this with them and tell them there was no reason to assume that they wouldn't be in the group that defined the better end of the curve and that we would hope for that. I had patients that I thought wouldn't live 3 months still coming to see me 20 years later, and other patients I thought were doing well drop dead the following week. After that I gave up on the illusion that I could accurately prognosticate. Every person is, after all, an "n of 1".

Mike, Mike, Mike...,
As an old man living in he South for the past 30 years and elsewhere around the USA, I would like to set the record straight as to the "prosperity" you refer to in today's commentary. I was born and raised, until 18 years old, in Oak Park. I am a proud HUSKY,
a graduate of OPRFHS in 1964. Forest Park was not unlike Oak Park with a combination of $$$,$$,$ people. Now, as you recall, River Forest was the higher end of the two adjacent villages of OP/RF. And don't think the kids from RF did not know that! By the way, I did not get to travel to many places as a ch9ld outside of Illinois and Wisconsin. Later, Uncle Sam took care of that loss of adventure for me:-)
You and I were still better off than living inside the Windy City boundaries back in the day.
Your reminiscing of cost, wages, lifestyle and comparison to today certainly brings back many examples in my mind as well. Price of cars, gas, even a Big Mac.
Thank you so very much for your quality writing on not only photography, but all the other "off-topic" topics. Keep it up as long as your able. It is greatly appreciated.
Regards, Michael (or Mickey)...Never Mike as that was my father. The differentiation was used my my mother when either of us was in the proverbial doghouse.

Dear Mike,
a thought just occured to me: maybe you would be interested to know that your $98k benchmark exceeds the annual salary of the prime minister in as many as 14 (out of 27) European Union countries (according to Wikipedia).
Therefore, you are close to the median value in that sense as well.

Interesting personal and family history. For some reason while reading it I had an image pop into my head of your life as a Wes Anderson movie. He would have turned your trip on an ocean liner into some quirky weird looking segment.

So if British people are earning so little, how are they buying houses to live in?

Same as in Australia, parents who have the means help their children to get into the property market. The so-called "Bank of Mum and Dad". And of course those who already hold property have something to sell at market prices when they want to move and buy elsewhere.

Not everybody likes French. I do. Not everybody likes singer Michel Sardou. I have my problems with him, too.
Here is his song "Le France", complaining how France, the country, gave up and betrayed France, the vessel.


Quite impressive.

As to the British housing market: It is a Ponzi scheme. Thatcherism at its worst. We will live long enough to see it break down.

Median: If you stack a bunch of photos in Photoshop (or Affinity Photo or whatever) for the purpose of removing objects from the final composite any moving objects who were in the frame in any one of the photos, it probably makes sense to you to use the median and not the mean. You want the pixel with the objects in it to disappear completely, not be partly there.

Much has been said here already about means and medians but one point I didn't see I'll provide.

If the distribution is a well behaved "normal" (aka Gaussian) distribution - the classic bell shape with the peak in the middle - then median = mean. And of course, many other metrics about variance and standard deviations can be readily calculated.

However, many populations of things are not Gaussian in their distribution (income is a great example, various queue lengths often are, too) and demonstrate various kinds of skews or long tails.

While intro classes usually tell the student "assume a normal distribution" for their homework problems, real life is often not that convenient. All kinds of cool statistical tools silently misbehave when the data is coming from a distribution that was assumed Gaussian, but isn't.

He who assumes his sample is from a normal distribution without testing to see if this is so is *begging* the data to lie to him - and it will usually comply.

Brighton is an outlier (like Austin, Texas); everything south of a line drawn halfway up UK will be in the upper half of the bell curve unless it has atypical issues (think falling off a cliff - east coast Norfolk) or being unlucky enough to be in the path or adjacent to a big infrastructure project (HS2). The north has more affordable housing but the environment often has issues (think rust belt USA but not as extreme). If you're in an average job things have been tough for years, but by and large people get by (same as USA), gig economy sucks but with some luck and perseverance people survive and some actually prosper. Spare cash for Leicas doesn't exist except for the rich, the average guy gets by with a used Nikon, Canon or Sony if they want to improve on their camera phone (no - they can't afford a recent iPhone, they'll be using an old android with a cracked screen).

As a graduate in stat and econ, I think using one number or a few to represent the distribution is only good if is a “normal” distribution. And even that you cannot use mean/median/mode but must include the standard deviation as well.

Similar to the example used but witv distubtuon choice then if given normal (like bell curve of iq stereotype) then you still have to say whether it is 100 with standard deviation of say 50 vs 5. The later mean 100 is a good but with a 50 it is so wide spread even bell curve or normal distribution does not help you.

Average lie, in brief.

Now real world most distribution are not “normal” and in fact some calculation use poisson which is very bias toward one end. And you may have to hear a term call long tail which indicate some use even if most people use and give up and that is a very “biased” distribution. For most people using camera film one is long gone. But for people in the long tail it is really a golden age as many throw away …


You next issue is house price and income. That depends a lot. Cf across country is not really made sense. How much a flat cost in japan, Hong Kong and Singapore or even London new York etc (easily us$1m) and will you even consider to live in a flat already in USA ring a bell.

Now even worst is quality of life. …

Excellent explanation from Lee there in the featured comments.

To put it in photographic terms:
If the mean and median are significantly different then it's a clue that your histogram is either "exposed to the right" or "exposed to the left". In countries like the US with huge income inequality, you're probably looking at blown-out highlights (ie a few ultra rich) and the rest of the histogram barely showing anything :)

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