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# Morrison on Metrics: Trimmed Means and Weighted Averages

Trimmed means and weighted averages are less familiar ways to describe metrics than averages, medians, and quartiles. The middle figure of a sorted list of metrics (the median), the total of all the figures divided by the number of them (the average), and the midpoint between the high or low and the median (the quartiles) are standard fare. That said, the other two numbers are useful ways to describe a collection of metrics.

A trimmed mean calculation shaves off some number of extreme values. A common choice is to omit the 2 1/2 percent of the values at the low end and the 2 1/2 percent at the high end of a sorted list. Thus, if you have the ratio of inside spending to external spend for 300 law departments sorted high to low, you would drop the seven smallest ratios and the seven largest ratios. Then calculate the average (aka the mean) as normal.

The advantage of a trimmed mean is that the figure excludes unusual, outlier metrics. If you have from a whole set of law departments their lawyers per billion in of revenue, a trimmed mean drops those that might have recorded no lawyers, for example, or no revenue. I like trimmed means because averages are comfortable for people but they are often distorted by weird numbers at the extremes. The median isn't influenced by extreme figures. I suppose one could calculate a "trimmed median" by using the same technique of lopping off a small portion at either end and then determining the median.

A weighted average, by contrast, gives more influence to larger law departments. It does so because it adds up all of the figures for the metric that is in the numerator (the top number of a fraction) and divides it by the sum of all of the numbers in the denominator (the bottom number). Whereas averages add up all the ratios and divide by the number of participants, the weighted average adds up both pieces of the ratio and divides them. Very large law departments shift the weighted average more than the smaller ones.

I like the weighted average because I find that small law departments often exhibit anomalous metrics. If you have only one lawyer, you're ratio of paralegals per lawyer must necessarily be strange. If you have 60 lawyers, that same ratio has probably settled down to a fairly typical number. To give more influence to the 60-lawyer department than to the solo department make sense to me if the purpose is to give a better overall picture of a benchmark metric.

Let me close with examples from the General Counsel Benchmarks survey. Let's look at lawyers as a percentage of total legal staff (lawyers divided by lawyers plus paralegals plus all others in the department). For almost 600 legal departments around the world, the old-fashioned average for that benchmark was 58.158%. The median was 57.142%; the trimmed mean (top and bottom 2.5%, or 16 eliminated) was 58.024% and the weighted average was 57.142%. Not much difference among the four calculations - all indicating that lawyers make up a bit more than half of all the members of this huge set of legal departments - but metrically sophisticated in-house counsel should understand the terms and their calculations.

### Rees Morrison

Rees Morrison, Esq. is a partner at Altman Weil, Inc. with countless interests in legal data analytics. He is also the founder of General Counsel Metrics, LLC....

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