We calculate all our own means and medians based on our data-set, and depending on the Edition. For the UK Edition, a market wide median will include all listed stocks on the UK, including all AIM stocks and ISDX stocks.
We generally believe that using medians is the most appropriate average to use in the stock market. Many stock market investors are interested in smaller companies, thus using market cap weighted averages (means) can significantly skew the data towards large caps which can then be unrepresentative of the whole distribution.
We also publish means using equal weightings rather than market cap weightings for the same reason, but using a special process designed to minimise the impact of outliers. Means can become massively skewed by outlier data (for example a company on a P/E ratio of 10,000 can skew the UK mean P/E ratio upwards by 5 points), so we use a process known as 'winsorization' which replaces the 3% outliers with the border values, effectively normalising the edge cases.