The GEOMETRIC MEAN is LESS THROWN by OUTLIERS
So, if you have a basket of 9 products all increased by 1% but just one item increased by 500%... how should THAT fact be reflected in the figures.
Without the math:
The Arithmetic mean gives 50.9%
the Geometric mean gives 1.9%
So in home economic terms, if turkey, chips, electricity, bread, milk, shampoo, toothpaste, washing machines and underwear have all increased by 1%, but domestic gas has increased by 500% which value; 50.9% or 1.9% better reflects a meaningful value. Look there is no right or wrong answer! It depends on context and what you will do with it.
Since in this example it is domestic gas that has gone up, it may not really be all that sensible to say RPI is up by 51% on average, because with a whopping rise in gas price like this, we'd all switch to electric convection heaters!
...BUT, if it were bread that went up.... then we'd probably have to take it on the chin (or eat brioche?).
It is very much true that if this is the pattern of activity which is being described by the inflation figures, the geometric mean sounds favourable to government, but the whole thing could work in reverse. If everything was going up a lot other than, say electronic goods, the geometric mean would look higher.
So the stats enquiry says geometric means are better estimators of the impact of inflation on us the general public, but government won't switch to that for the RPI. Why is that?
...because it will look like they are cheating, even if actually, they are not....