Top 3 and top 10 – trimmed means

We use Yuen’s method (1974) with 20 percent trimmed means. In contrast to the mean, the 20 percent of the largest and smallest observations, is able to downplay the effect of extreme values and better capture the central tendency.

The frequently applied measure of location – median – is a 50 percent trimmed mean.

In some situations the 20 percent trimmed mean could be better than the median. Reason for this is that the trimmed mean has superior mathematical properties that include but are not limited to a smaller standardard error under normality.

Top 3. In practice this means we use positions 2-4 to calculate the top 3. In the case of the FT ComMetrics Blog Index this allows us to exclude Google from the top 3 numbers – an extreme outlier that results in a skewness whereby the sample mean of the top three would not be the best measure of central tendency.

Top 10. We use 2-11 again excluding the extreme outlier Google in the FT ComMetrics Blog Index.

Generally, we calculate 3 – 8 for the top 10, thereby cutting off the bottom 20% and the top 20%.  In the case of the FT ComMetrics Blog Index the numbers were close together so we did not see the need for doing this except for excluding nr. 1 to avoid skewing the trend.

Bottom Line
Our objective is to indicate where the center of the majority values is regarding the blogs we benchmark. Using the trimmed mean makes our measures more sensitive to the bulk of data collected and less sensitive to extreme values such as the Google blog’s numbers – the overflyer of the FT ComMetrics Blog Index.
When the distribution is skewed as is the case in our sample(s) of blogs, the mean does not represent the center of the majority of blog’s regarding a particular measure. In turn, the trimmed mean can give one a better sense of where the center of majority lies as far as a sample of blogs is concerned.

Yuen, K. K. (1974). The two-sample trimmed t for unequal population variances. Biometrika, 61, 165-170.
Ng, M. (2008). Beyond the t-test and F-test. Observer, 21(II), pp. 31, 33.