Why do we use Medians

[TMNT]

why do we use medians and not average, ive never understood that,

say we have $100k, $500k, $1000k
the median is $500k, average is $533k
which is fair

but if we have 100, 100, 100, 1000 1000
the median is $100k,
yet the average is $460k

if you get a few lower end trashed houses for example in a month or a short period of time, the median is $100k when the average prie for the area is $460k, which is far more reasonable,

in fact I think its quite silly

 

[tambourineman]

why do we use medians and not average, ive never understood that,

say we have $100k, $500k, $1000k
the median is $500k, average is $533k
which is fair

but if we have 100, 100, 100, 1000 1000
the median is $100k,
yet the average is $460k

if you get a few lower end trashed houses for example in a month or a short period of time, the median is $100k when the average prie for the area is $460k, which is far more reasonable,

in fact I think its quite silly

I would ask the same question about auction clearance rates

 

[Aaron Sice]

medians were originally used to differentiate between anomalies in the market place.

for example, if your median went up $100k this month, you knew that more expensive homes sold in the area versus less expensive ones.

the issue was about 20? 30? years ago when unit sales were skewing the figures WAY down - so a seperate class was created for them.

now we have the problem of people waiting for median monthly values like earning season in the Dow Jones Index makes for wild speculations about "growth" when the reality is what it has always been - it's a highly subjective figure that must be dissected further to understand the true market underneath.

 

[Peter_Tersteeg]

say we have $100k, $500k, $1000k
the median is $500k, average is $533k
which is fair

but if we have 100, 100, 100, 1000 1000
the median is $100k,
yet the average is $460k

What if you've got:
100, 100, 100, 100, 1,000,000
The median is 100
The average is 200,100

The first 4 might be the normal residential house in the area, the other is the palace built by the king and is not indicative of the market.

In statistics we use medians because it tends to elimiate the extreme ends of the sample from contaminating the result.

If you looked at the average income of people in North Korea, you might come to the conclusion that they're reasonably well compared to the cost of living. If you look at the median income you may realise that they're an oppressed people living in poverty and starvation with an elite rulling class.

Understanding the context of the statistical sample helps too.

 

[vaughan]

why do we use medians and not average, ive never understood that,

say we have $100k, $500k, $1000k
the median is $500k, average is $533k
which is fair

but if we have 100, 100, 100, 1000 1000
the median is $100k,
yet the average is $460k

if you get a few lower end trashed houses for example in a month or a short period of time, the median is $100k when the average prie for the area is $460k, which is far more reasonable,

in fact I think its quite silly

It doesn't make sense with the data you've used as the example, but it does make sense with real house data.

In an area there is likely to be dozens or hundreds of houses, most of them will be quite similarly priced. There will be one or two that will be really cheap, or really expensive.

A mean will change significantly when the cheap or expensive houses are included, but the median will not. However if all the houses increase or decrease in value then the median and mean will both indicate this. It s the overall increase and decrease that we should be more interested in rather than the actual median value.

Things can get weird with averages: for instance, its a fact that the majority of people have more than the average number of legs. This is because even in a very large population, if just one person has only one leg then the average will be slightly less than 2 (1.999999). Everybody except for the unfortunate one-legged person will have 2.0 legs which is more than the average.

It's good that you're questioning the statistics and how they are calculated. You'll start to realise that they are a bit dodgy at best, but they are the best we've got.

 

[Aaron_C]

I don't use medians.

 

[Shadow]

why do we use medians and not average, ive never understood that,

say we have $100k, $500k, $1000k
the median is $500k, average is $533k
which is fair

but if we have 100, 100, 100, 1000 1000
the median is $100k,
yet the average is $460k

When measuring house prices we want to know what a 'typical' house costs, or by how much a 'typical' house changed in value.

In your example, a typical house is $100K, and the median accurately reflects this. The majority of properties in a suburb are usually similarly priced, but there will be a handful of outliers.

The outliers are not representative of a 'typical' house, so a median is useful since it will be largely unaffected by these outliers.

A mean will not represent a 'typical' house when there are a few very very expensive (or cheap) houses in the data set that skew the mean.

 

[Rixter]

Yes, the median price provides a more realistic representation of sold prices in an area.

Like others above have mentioned, it doesnt let sold prices at the extremities skew results as much.

 

[Ed Barton]

A mean will not represent a 'typical' house when there are a few very very expensive (or cheap) houses in the data set that skew the mean.

I think some here don't know the difference between median and mean...

Median - line up all the sales prices from low to high in order and the median is the one in the middle.

Mean - also, mostly known as 'average'. Add up all the prices and divide by the number of sales.

eg -

seven houses sold in Edville. 20k, 55k, 60k, 75k, 90k, 110k, 2m...

The median is 75k

The mean (average) is 20+55+60+75+90+110+2000/7= 344k

Is a 'typical' house in Edville worth 75k or 344k?

Next month/year/whatever there is another seven sales. 25k, 60k, 65k, 85k, 90k, 110k, 950k.

The median is 85k

The mean (average) is 25+60+65+85+90+110+950= 198k

The median went up slightly but the mean went down dramatically. Did the typical house go up or down in value?

That's why median is important.

#very simple example.

 

[pinkboy]

Bit like judging in diving and gymnastics etc - they scratch out the highest and lowest judges score and use the middle 3 scores to give the 'fairest' score. Because the judging (much like property prices) are subjective, but that's all we have to go on.

pinkboy

 

[BayView]

why do we use medians and not average, ive never understood that,

say we have $100k, $500k, $1000k
the median is $500k, average is $533k
which is fair

but if we have 100, 100, 100, 1000 1000
the median is $100k,
yet the average is $460k

if you get a few lower end trashed houses for example in a month or a short period of time, the median is $100k when the average prie for the area is $460k, which is far more reasonable,

in fact I think its quite silly

I've been bangin' on about this one since day 1 here.

The problem is that a lot of cheaper end sales can make it appear that values have dropped, when they haven't, and vice versa.

And of course; the media practically use it as the official guide to housing prices....

 

[wategos]

As others have said the median makes much more sense and is more useful with larger sample sizes since it removes the distorting effect of extreme values.

With very small sample sizes both median and mean can be useless.

 

[HotRod]

A system that some companies use is to track the sale price of individual properties over time to derive growth, I think.

That would provide a much better feel for growth, that just following the median price which may not relate to any one property.

 

[The Fence]

Things can get weird with averages: for instance, its a fact that the majority of people have more than the average number of legs. This is because even in a very large population, if just one person has only one leg then the average will be slightly less than 2 (1.999999). Everybody except for the unfortunate one-legged person will have 2.0 legs which is more than the average.

Wonder if that average will ever get over 2.0...?
Now that'd be weird...

Cant have a median of legs can ya...?

 

[Scott No Mates]

Bit like judging in diving and gymnastics etc - they scratch out the highest and lowest judges score and use the middle 3 scores to give the 'fairest' score. Because the judging (much like property prices) are subjective, but that's all we have to go on.

pinkboy

It is not all that we have to go on but what the lazy can access.

Stats are just that, someone else's take on the matter at hand.

Have you (or anyone) really taken an interest in what is churned out by domain/re? Oh, it has jumped x%

What utter BS - these figures can be horrifically distorted by several factors eg: new development sales all settling putting 50+ sales of new units into the recorded sales.

Take the figures apart, order a full sales report for 2 years then dissect them. Categorise the sales: units 1/2/3 bed, houses 2/3/4 etc. Work out your median/mean for each type of unit or house. Hmmmm amazing how your stats differ from the published average/median prices. Which would you rely upon? Now do some sophisticated modelling ie bell curve distribution, 5% confidence levels etc then you will have something that you can chew over and take to your next OFI before putting in your offer. (sure there are a few more things to consider but we are talking statistical modelling not val theory).

[Pinkboy - those judges are onto something]

 

[Ed Barton]

I've been bangin' on about this one since day 1 here.

The problem is that a lot of cheaper end sales can make it appear that values have dropped, when they haven't, and vice versa.

And of course; the media practically use it as the official guide to housing prices....

What you are describing is compositional bias. All the housing price data providers adjust for compositional bias, by stratified medians, repeat sales, or hedonics.

 

[Deltaberry]

Medians mean the figure won't be skewed by a few outliers.

 

[Scott No Mates]

Medians mean the figure won't be skewed by a few outliers.

But the median can be skewed by the release of new developments where they statistically form more than the normalised market, whether it be another 50 units in an area where 200 units are sold annually, there can be a substantial skewing of the median. Hence the need to have several medians not just a suburb, house or unit median - there are subgroups which will reveal a more poignant result.

 

[vaughan]

Cant have a median of legs can ya...?

Actually, yes you can; only it would be a median of "people" not legs. In fact, median would be a better way to measure the quantities involved.

The data set would look like this:

1, 2,... 2,... 2, 2

The median is 2 which is a sensible result.

 

[marty998]

That would be the "mode" or most common number of legs?