*TL;DR – Know your median income from your mean.*

So we published an article on the family with 5-figure monthly income and is still feeling squeezed. Economist Donald Low picked it up and had, so far, published two Facebook posts on the matter.

There’s a mighty interesting exchange of comments on both posts, and I hope everyone will go read. Not just for the substance of the online conversation, but even more so for the spirit the discussion took place.

Like what the following Facebook user ** Tan Yi Heng Jason**, who also happens to be an economist like Donald Low, had said, it’s civilised and robust.

How nice to actually see that netizens can actually have a relatively intellectual and civilised exchange even if everyone comes bearing different information and opinions. So rare that we do not see people attacking others and start calling each other names just because they hold different views.

One other comment also stood out for me. This, from Facebook user ** Kien Lee**, who also happens to run the award-winning luxury and lifestyle magazine Senatus.net,

So come, let me walk you through what ** mean income** and

**are, just in case you’ve been wondering and are too shy to ask.**

*median income*## Mean vs Median

**What is the mean?**

The mean is an average, and is the grand total (of all the numbers in the data set) divided by the number of data points.

**What is the median?**

The median is the middle value in a sample sorted into ascending order. If the sample contains an even number of values, the median is defined as the mean of the middle two.

Let’s say we have a set of five numbers:

*11, 23, 30, 47, 56*

The mean of this set is 33. The mean is the sum of all the numbers in the set (167) divided by the amount of numbers in the set (5).

The median of this set is 30, since that is the number right smack in the middle when we list the five numbers in ascending order.

## Mean Income vs Median Income

So in a perfect world, people would work the same and earn the same. Something like this, as illustrated in this Datawrapper blog.

And the mean and median income would look like this,

Unfortunately we do not live in a perfect world where everything’s equal and everyone’s treated equally, so this might be a more realistic example,

Many economists prefer to use median income or at least they prefer it when looking at highly skewed populations, in which a large part of the group is fairly close or similar to each other, but there are some distant outliers. **Mean takes outliers into consideration whereas median does not.**

One way to understand this better is to consider a group of 10 people, out of which nine are average Joes and Janes like you and me who earn a salary of $3,000 each and then we have one person who earns $30,000 in a month. How would the mean and median look like?

The mean salary works out to $5,700 and median salary is $3,000. In this case, there is an outlier of one person whose salary is 10 times that of the other nine of us, then it makes more sense to use the median number.

## Key household income trends 2017

Now that you’re, hopefully, clearer about what mean and median income are, let us look at some recent household income indicators for Singapore.

As you can see from the infographic below, total median household income has been on the rise year on year and stands at $9,023 for 2017. The median household income per household member is $2,699.

Let’s take a closer look at total household income from work and household income per capita. **Do you understand the difference between nominal and real income? **

Basically, **nominal income** is income expressed directly in money terms and is measured in current dollars. In simple terms, it simply refers to the amount on your paycheque.

**Real income** is inflation-adjusted income, that is, nominal income adjusted for inflation. Real income is sort of like the buying power of your nominal income, and is measured in constant dollars.

In modern world where costs of living are constantly going up, inflation is more the norm than deflation. As such, it is expected that real income will grow at a slower rate than nominal income to factor for inflation.

One interesting piece of information I’ve picked up as I went through the official statistics is that for the period 2012 to 2017, real growth in average household income from work per household member was faster for the lowest 50% households (4.2 to 4.6% per annum) than for the top 50% households (2.2 to 4.2 % per annum). This is something that I think we should all do better in, to help fellow Singaporeans who are at the lower rungs of the income ladder move up.

Like what Labour MP Zainal Sapari had said,

“This gross injustice and slavery of the poor must stop.”

This following chart shows the resident households by number of working persons. This will become an increasingly important one to watch as our population ages.

I thought it might be useful to include the Government transfers, which are schemes that help Singaporeans with rising costs. These include items like GST vouchers, U-Save rebates, Pioneer Generation package and Silver Support and also Workfore Income Supplement (WIS).

You can check out more of the latest household income trends here.

So now, I think we’re more or less ready to read Donald Low’s two Facebook posts and the interesting exchange for both posts.

## Donald Low’s first Facebook post

People seem to focus on the five-figure monthly salary and jump to the conclusion that the family is better off than most households. It is not; some basic facts will tell us this is very much an average or even below average Singaporean household (if we use the income per capita measure).

The average household income in Singapore among working households in 2017 was $12,000; the median was $9,000. The average household income per member was about $3,800; the median $2,700. Assuming (as the unscrambled.sg article below does) that the family makes $11,000, this family earns an income that would be considered quite average (above the median, and below the average household income). In per capita terms, its income per member of $2,200 is below both the average and median. The people who think that this family is well-to-do are quite mistaken. (The unscrambled.sg article below says that the family earns more than 64 percent of households in Singapore. But that 64 percent includes nearly 12 percent of non-working households, most of whom are retiree households that, presumably, don’t have young dependents).

All this is based on stats; I haven’t said anything about the recent studies on the psychology of inequality, which tell us that in highly unequal contexts even affluent people may feel poor. (For more on that, read this.)

It’s also quite interesting that people here are sympathetic to the idea of the “squeezed middle” in the abstract but when they are confronted with a family which is exactly that, they react negatively and pass judgement on its failure to prioritise or to distinguish between needs and wants. We’re fast becoming a low trust society that views everything in zero-sum terms: more for the middle income necessarily means less for the poor, or higher taxes on the rich.

The fact is that this trade-off is neither necessary nor inevitable. There are collective ways of financing and providing social goods (such as childcare or kindergarten education, or even tuition and CCA classes) that cost us less than the current method of relying mostly on private financing. Yes, public financing of these things increases the state’s outlay, and this may require higher taxes. But this increase is likely to be much smaller than the reduction in household expenditures on these things because of the economies of scale and scope of public financing and provision. Financing these things collectively, and making their provision universal, is likely to be cheaper for society as a whole. People are likely to quibble about the higher taxes they have to pay, but that’s because they ignore the fact that their private spending on these things will go down by more.

However, I’m pessimistic about the prospect of Singapore heading in this Pareto-improving direction. Why? Because I’m also reminded of the fact that in highly unequal societies, social trust tends to be low. This, in turn, reduces one’s willingness to accept higher taxes to finance the provision of social goods collectively. When we don’t trust fellow citizens, we are more likely to see them as undeserving scroungers exploiting society’s largesse. And when most citizens don’t support higher taxes, the state is unable to enact the programmes and provide the services that are necessary to reduce inequality.

## Donald Low’s second Facebook post

One of the questions that was raised in response to my earlier post on the TNP family that many people whacked was whether I should have used median instead of average household income. I had actually referred to the 2016 median household income per member figure (of $2,600) in my original post, and noted that if this family of five makes $11,000-$12,000, it is below the median household income per member. Anyway, I have updated my post to use the 2017 average and median income measures (for both household and per capita income) so that there’s no confusion. The conclusion is the same.

But for those who are still wondering whether to look at the median or the average, the following perspective may be useful.

Using the median removes the skew in the income distribution caused by the very high earners in society. Average incomes reflect and reproduce that skew. So usually economists prefer to use the median income measure.

But we can also easily imagine situations in which a person who’s in the middle would find the average measure more meaningful. Consider an imaginary society A of ten people, in which the first guy earns $1,000, the second $2,000, the third $3,000 and so on till the tenth guy who earns $10,000. In this society (where’s there’s no skew in the income distribution), the median and the mean are the same ($5,500) and it doesn’t matter which measure we use.

Now, consider society B where the first six people earn between $1,000 and $6,000 (as in society A), but the seventh guy earns $12,000, the eighth $13,000, the ninth $14,000 and the tenth $15,000. In this society, the median is still $5,500 but the mean (or the average) is considerably higher ($7,500). Now, put yourself in the shoes of the sixth guy earning $6,000. It would be cold comfort to know that you make more than the median. For you, the average measure better reflects your sense of relative deprivation , and (arguably) the kind of society you live in.

In an unequal and highly competitive society, I suspect many middle income households feel this way. They are not deprived in an absolute sense, but they feel quite stressed and stretched nonetheless. (And bear in mind that for this particular family, its income per member is not just lower than the average, it is also lower than the median.)

The next question that arises is whether we should care about people’s sense of deprivation (isn’t it just envy) in deciding which income measure to use. Of course we shouldn’t, which is why we generally use the median. But to the extent that we want to take people’s subjective well-being seriously and include it in our assessments of whether they are “happier” or “better off”, then we should indeed look also at the average income measure and how people “measure up” against it.

Finally, as our income distribution becomes more skewed (due perhaps to rapid technical change that favours a small segment of society that possess the capital or the cognitive ability to take advantage of those advances), I suspect that the average income measure—and the increasing gap between the average and the median—will become more important and salient. A rising average income reflects the productivity gains due to the technical advances (in a way that a stagnant median does not), while the growing gap between the average and the median reflects growing inequality. Indeed that has been the story of the US economy in the last 20 years: rising average incomes, stagnant median incomes.

What do you think?