Math 101 for Ministers


MEDIAN is NOT the same as MEAN also known as average.

Mean is the average of a set of numbers.

Let’s do some Math 101 here:

Here’s a list of 10 numbers arranged in descending order (ie, from largest to smallest):

900 859 801 735 699 550 450 380 200 199

The MEAN (Average) is: (900+859+801+735+699+550+450+380+200+199)/10 = 5773/10 = 577.3

The MEDIAN is defined as the number IN THE MIDDLE of the sequence of numbers above.

Since the sequence is even (10 numbers), the MEDIAN then is the number between the 5th and 6th which we will find by: (699+550)/2 = 1309/2 = 624.5

Because we were given an EVEN set of numbers the MEDIAN is the average of the two numbers in the middle. If, however, we were given say ODD set of numbers, the MEDIAN would be the number in the middle of the sequence.

You will notice that the value of MEAN (Average) is not necessarily the same as the value of MEDIAN but it is possible that the MEDIAN could be higher or lower than the MEAN.

The salary report suggests that the ministerial salaries be pegged at the “median of the top 1000 Singaporean wage earners”.

So, while the number 1000 seems like a lot, the reality is that the salary is being proposed to be pegged to the AVERAGE of the 500th and 501th top Singaporean wage earner. The number 1000 is a red herring, serving to confuse people who would have understood MEAN not MEDIAN.

The report is trying to ensure that not too many Singaporeans earn more than the ministers.or to put it another way, there would only be about 500 Singaporeans or so who could be earning more than the ministers. This is very self-serving.

Which then begs the question. Why 500? Why not 5000? Or even 50,000? Are the ministers only working for the top 500? Not the 5,000,000+ we have in Singapore?

Watch this video of  DPM Teo speaking in the parliament on January 16th 2012. Quite sad really.

16 thoughts on “Math 101 for Ministers

  1. Do you realise that if it were “mean” instead of “median”, the pay of ministers would in fact be HIGHER?
    This is due to the fact that a median mitigates the effects of outliers (specifically, those earning astronomical salaries), while mean does not.

    Thus, using the median instead of mean is in fact much fairer. So, of course if you are unhappy about the fact that the median was used, you can simply write in to say that the mean should be used instead! I’m sure they’d be more than happy to change that. But unfortunately I think most of us prefer the median to be used.

  2. The use of “median” in this context is superfluous. We can simply benchmark the 500th top wage earner. Those ranked 501 to 1000 are inconsequential. Median plays a useful role when we wish to characterize a population, by the ‘middle’ guy, not an artificially fixed number where the median is not influenced at all by the bottom half. Either the ones in charge are incompetent or they are out to hoodwink the people.

      1. 1000 definitely sounds much better than 500, and completely right. Otherwise imagine the potential shock and awe among the peasants, green-eyed with envy lesser mortals. Oh horror!

  3. Dude, did u even read the report? They’re suppose to apply a 40% discount on this median of top 1000 Singapore Citizens. So your shocking statement of “… to put it another way, there would only be about 500 Singaporeans or so who could be earning more than the ministers… ” is totally wrong.

  4. Good point! Median Mean. But in this case Median with a 40% discount would mean a salary that is less than 500th top wage earner… How I wish they listed a table showing where earning SG$1.1million would rank the person.

    1. exactly. the reason i put up the 10 numbers in the series above it to hint that if we rank the 1000 top earners (which I think for the purposes of this exercise it should be made public with all individually identifiable info removed, just the raw numbers) then we will know how they stack up.

      then we can pick up either the 500th or the average of the 500th+501st and then apply the 40% discount (oh, how stupid it sounds).

  5. I tend to laugh when people talk about how good Singapore’s maths education is (especially Americans, who are frighteningly starting to lean towards East Asian models of exam-based education). No point in pushing kids to score highly on exams when adults need to have this kind of simple stuff explained to them. Formal education in Malaysia sucks, but when it comes to this kind of thing, we’re a bunch of natural skeptics!

    1. good for you, my northern neighbour. i don’t think this is a Singapore math education problem. if you ask any person to explain the difference between median and mean, they will be challenged. very rarely do we use median in our day to day conversations. we tend to use averages (or mean): “Oh, the day-time mean temperature for Singapore this time of the year is blah degrees centigrade.” etc.

  6. There are three methods of central tendencies, mean, mode median. In the event there is high natural skew, due to outliers, using Mean as a central gauge with be inflated by the astronomically high amounts (in this case, the super rich billionaires). As such, using Median as central tendency will be more favourable as the figures will not be subjected to the influence of high extreme values as @Frank rightfully pointed out.

    Average is simply a measure of central tendency or rather the “middle values” of any data set. It does not always refer to the Mean, though this is the most commonly associated inference in daily live when we describe an average. It is however, not a mutually exclusive relationship. Mean, Median and Average can have a threesome for all we care… Throw in Mode and it erupts into utter chaos.

    On the topic of ministerial salary however, an average person like myself, who likes things simple, would prefer no added 0 0 0 to the back of things. Simply put, your IQ might be higher than mine, your opportunities and prospects more favorable than mine but that does not mean you deserves 1000s of times more compensation for “sacrificing” your time just for being “praised” for being “special” or “unique” or “rare” a talent. A Panda, is rare, a Shark, is unique and special, a lamb during Hajj, makes a “sacrifice”. You, on the other hand, sitting in your comfy chair in office stroking yourself is a mere mortal. Mehzzz

  7. Hi, I came across your site and wasn’t able to get an email address to contact you. Would you please consider adding a link to my website on your page. Please email me back.

    Thanks!

    Harry

    1. PAP Dogs are out to hunt. Don’t give anyone your email or link. I don’t believe all those excuses that they are giving for the pay justification. It begin to make me wonder if beside overpaid them, we have indeed hired some idiots to be our ministers?

      Air force ONE, White house a PERK? My god. Is this idiot prince think the world is stupid? I think the LEE family should be ripped apart when their family is no longer in politic!

      1. RED-man –

        Why use terms like “PAP Dogs”? That is not a level of debate that I want to get into. Let’s keep to civilities and do the right thing.

        Thanks.

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