Means and Medians

Two weeks ago, on 23 April 2014, Scottish Land and Estates (the body that represents some of Scotland’s landowners) held its Spring conference at which it published a report on the economic contribution of estates in Scotland. (1) A week before that, on 16 April, it issued a Press Release headlined “New Research Reveals Significant Annual Investment on Tenanted Farms and Crofts by Estates”

It included the results from 143 estates surveyed that were involved in renting land for farming and stated that these had, on average, 11 tenants per estate covering, on average, 221 hectares. Total annual expenditure on agricultural and crofting tenancies amounted to £10.8 million, primarily on repairs and capital costs, equating to £26.58 per hectare and an average total annual expenditure per estate of £69,145. Average income amounted to £101,422.

Douglas McAdam, the Chief Executive of SLE said that,

The figures clearly demonstrate that there is significant investment by estates and our members are willing to invest further if we can create a stable climate that encourages investment. These are averages and investment does of course vary …. However, we are being told by members who do invest substantially that their continuing commitment is being jeopardised by the re-emergence of a potential absolute right to buy for tenants.”

It was clear that SLE wished to emphasise a) how much estates were investing and b) that possible land reform would jeopardise this in the future.

Fair comment.

So it was with some interest that when I came to read the relevant section of the Economic  Assessment report (4.2.2 pg. 39) and saw these figures, I also read a note of caution. The authors of the report write that, “It should, however, be stressed that the overall average values are very heavily influenced by the large and very large estates and the median figures for average income and investment are significantly lower.” (2)

Today, SLE published a series of videos of the various presentations given at its conference. Among them was one given by Rob Hindle (on YouTube here) who was the lead researcher for the economic study. (3) In a couple of slides (around 40min in) he describes the caveats on using economic figures including that the sample is “weighted towards larger estates”, that users should “be confident in the report but use with care” and that the “median is more representative of the sample”.

In particular, he warns that, “the mean average [is] significantly skewed by the bigger numbers at one end of the spectrum – so don’t do it – it’s not helpful. You need to start looking for the middle point but be aware even so that the middle point ..there are very big differences between the numbers at one end and the numbers at the other end so the middle point is again to be treated with caution

So what are the median values?

They are not published in the report. But I spoke to someone who was at the conference who remembered seeing a slide that had shown the difference – the “significantly lower” figures – contrasted in blue and red as an example of why the “median is more representative of the sample”. So I looked for this slide in SLE’s video.

It’s not there.

Did my friend mis-remember? I phoned him up and asked. “No, definitely – it was there. The difference was very stark – not just for tenancy figures but other expenditures as well.”

How stark?”, I asked.

I don’t remember exactly – much lower though – less than a quarter – even less I think in some cases.”

In the video there is one slide (at around 40min) that shows the differences for some of the data. The median number of tenants is 3 compared with a mean of 11, for example. But there’s no information on expenditure and revenue figures.

So was this information in the presentation given at the conference? If it was, why does it not appear in the video presentation?

Maybe it doesn’t really matter. What is important is that SLE misrepresented the levels of investment in its press release by picking the “mean” figure when it knew that the median was more appropriate.

I  have contacted the researchers and asked if they could send me a copy of the presentation. They may, of course need to ask the permission of their client, SLE, who commissioned the report. I will keep folk posted on what transpires.


(1) I should emphasise that the report is an excellent report and I plan to blog at greater length on its findings.

(2)  the mean of a sample is the total of all the values divided by the number of values. The median is the middle value in a distribution of values. So, for example in a town with 100 houses where 99 were worth £100 each and one was worth £1 million, the mean would be £10,099 (1,009,900 divided by 100). But describing the average house price in town as being £10,999 is obviously misleading. In a skewed distribution, the median is more useful and in this case is £100 (the middle value when all values are lined up from smallest to largest) – in this case a far better representation of the average or typical price of a house.

(3) I have downloaded a copy of the video for reference.