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I'm just reading some statistics.

Last year there were 3000 observations, this year there are only 1000. This is described as showing a "fall by a factor of 3".

This phrase doesn't ring true. If a factor of 3 is a 1/3, then a fall by a third would be down to 2000. So the phrase is meant to represent a fall to a third.

Am I right in thinking the phrase 'by a factor of' can only refer to an increase?

cheers, Ian

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It makes perfect sense to me. But this is a question about language, not mathematics. –  TonyK Sep 14 '11 at 11:11
I second @TonyK's comment that this is a question about language. In fact, I think this could be a good fit for English.SE (as well). –  Srivatsan Sep 14 '11 at 11:20
@TonyK : You said the phrase made perfect sense. Did you interpret it as a fall to a 1/3 of the previous value, or a fall by a 1/3? Personally I see this a question regarding mathematical language - though such a tag didn't exist. –  ianmayo Sep 14 '11 at 12:27
I just saw on the news earlier tonight that over the past ten years, robberies on Sydney trains had fallen by 114%. I'm not sure how to interpret the negative number of robberies. Perhaps criminals are now threatening to hurt people who don't take money from them. –  Gerry Myerson Sep 14 '11 at 13:31
reduced by a factor of 3 seems OK to me. But I do object to 3 times less as ambiguous. –  GEdgar Sep 14 '11 at 13:37

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