{"id":5227,"date":"2010-10-12T22:07:08","date_gmt":"2010-10-12T14:07:08","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=5227"},"modified":"2015-07-06T15:02:36","modified_gmt":"2015-07-06T07:02:36","slug":"singapore-wealth-mean-and-median","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/singapore-wealth-mean-and-median-5227","title":{"rendered":"Singapore wealth - mean and median?"},"content":{"rendered":"

Singapore has rapidly developed into a wealthy country during the last 50 years.<\/p>\n

In a recent Straits Times article, \"Singaporeans ranked 4th for personal wealth\" (Sat 9th Oct 2010, article no longer available), journalist Gabriel Chen writes:<\/p>\n

\n

Singaporeans are the fourth richest people in the world in terms of personal wealth [with an average adult wealth of US$255000] and second richest in Asia-Pacific, according to a Credit Suisse report.<\/p>\n

[Singapore is] behind Switzerland (US$372,692), Norway (US$326,530) and Australia (US$320,909), but ahead of major developed economies like France, the United States and Britain in the Swiss bank's inaugural Global Wealth Report, out yesterday. [...]<\/p>\n<\/blockquote>\n

\"Wealth\" is defined as \"real\" assets (like housing) plus cash and investments minus debt.<\/p>\n

Now, the next sentence caught my eye (emphasis is mine):<\/p>\n

\n

While Singapore's mean<\/strong> wealth of US$255,488 is extremely high, its median<\/strong> wealth is approximately just one-ninth of that, at US$30,092 per adult. Median<\/strong> refers to the wealth for the \"middle\" of the adult population distribution here, while mean<\/strong> is the average.<\/p>\n<\/blockquote>\n

This raises some interesting issues, one of which is mentioned in the article:<\/p>\n

\n

While the disparity between median and average wealth here seems to imply a high level of wealth inequality, DBS economist Irvin Seah disagrees.<\/p>\n<\/blockquote>\n

It certainly does imply such inequality. In an earlier article, I pointed out that Singapore's Gini Coefficient<\/a> (a measure of wealth equality) is quite high, indicating a fairly poor distribution of wealth. Singapore's Gini Coefficient comes somewhere between China's and the USA's.<\/p>\n

Back to the article. I was not sure about this next conclusion, so I decided to investigate it:<\/p>\n

\n

The findings suggest most of the wealth is accumulated around the middle to upper-middle income group, with \"most Singaporeans doing better than their peers in other countries\", Mr Seah said.<\/p>\n<\/blockquote>\n

If the wealth were normally<\/b> distributed, then we would expect the graph of the situation to look like the following, with the mean (average), median (mid-point, where 1\/2 of the population is above and half is below that figure) and mode (the most-often occurring wealth figure) all being equal to $250,000 (in round figures).<\/p>\n

\"mean-median-mode-normal\"<\/p>\n

However, according to the article, the median is around $30,000. What will the graph look like now?<\/p>\n

It turns out it will look something like this (where each class interval is $20000 wide, and the first mid-point is $10,000):<\/p>\n

\"singapore-wealth-distribution\"<\/p>\n

I'm assuming, of course, that no one has wealth beyond $500,000 so that my graph is readable. This is not the case and there are quite a few millionaires in Singapore. I'm also assuming there are around 3 million adults in Singapore.<\/p>\n

Our graph shows the distribution is (heavily) skewed to the right.<\/p>\n

So yes, Singapore has quite a high proportion of quite wealthy people, but don't miss that very large number of people (over a million) in the $0 to $20,000 interval. There are many battlers in Singapore.<\/p>\n

See the 17 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"

\"singapore-wealth-distribution\"<\/a>When we have a distribution with a high mean but a low median, what does it look like?<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[125,134],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/5227"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=5227"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/5227\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=5227"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=5227"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=5227"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}