What impact should unit conversion have on the relationship between standard deviation and variance?
For example, when the units are kilograms, the sd is 3.156 kg , and the variance is 9.96 kg which is the sd^2.
However, when we convert this to grams, the sd is 3,156 g (the equivalent of 3.156 kg) but the variance is 9,963,829 g (the equivalent of 9,963.829 kg).
What is the correct way of doing this? For reference, I am working with a dataset that has been converted to kg, but the original units are grams.
set.seed(1) in_kg <- runif(10, 0, 10) sd(in_kg) var(in_kg) in_grams <- in_kg*1000 sd(in_grams) var(in_grams)
> sd(in_kg)  3.156553 > var(in_kg)  9.963829 > sd(in_grams)  3156.553 > var(in_grams)  9963829