The image above (click for larger version) shows the missing slide from the presentation on the Economic Contribution of Estates referred to in the Means and Medians blog from last week. (1) It is important because it shows the significant difference between the mean and the median. (2)
In particular it is important because the researchers who wrote the report stressed that in such a skewed sample, the mean should not be used.
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.” (4.2.2 pg. 39)
In presenting the findings, the lead researcher, Rob Hindle stated 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”
The means and medians are not published in the report for these very reasons. However, SLE issued a press release on 16 April entitled “New Research Reveals Significant Annual investment on Tenanted Land and Crofts by Estates” with an opening line that read,
“Rural estate owners are investing an average of £69,000 per year on their tenanted farms and crofts“, new research has revealed.
The release went on to state that average income amounted to £101,422.
The more accurate figures are the medians and, as the graph shows (second set of columns from the left), the difference is startling.
Median revenue is around £22,000 (22% of the mean) and expenditure about £10,000 (14% of the mean) compared with £101,422 mean revenue and £69,145 mean expenditure
The differences for other categories – notably heritage and leisure are even more pronounced.
(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.