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I have a group of data series which contain hundreds of values.

I've calculated the C.V.s of these data series, but I don't know how I can recognise if they are high or low according to the C.V. values.

Is there a rule of thumb for C.V.? For example, if the C.V. value is higher than 0.4 or 40%, then is it appropriate to say it is high?

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There's no context-free meaning of "high" or "low", & no need for a rule of thumb. The quotation below illustrates usage:

Body weight has a very high coefficient of variation in fish & shellfish (17–29%) compared to the coefficient of variation for body weight in farm animals like cattle, pigs, & poultry (7–10%).

(Gjedrem & Olesen (2003), Selection and Breeding Programs in Aquaculture, p47)

See How to interpret the coefficient of variation?.

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