Question

You compute the mean, median, range, and standard deviation of 20 numbers. If you add 10 to each number, what effect does that have on the following statistics?

i) The mean is:

a) increased by 10 b) decreased by 10 c) increased by 200 d) stays the same

ii) The median is:

a) increased by 10 b) decreased by 10 c) increased by 200 d) stays the same

iii) The range is:

a) increased by 10 b) decreased by 10 c) increased by 200 d) stays the same

iv) The standard deviation is:

a) increased by 10 b) decreased by 10 c) increased by 200 d) stays the same

Answer 1

mean(x+10)=mean(x)+10

median(x+10)=median(x)+10

Range(x+10) = Max(x+10)-min(x+10)=max(x)-min(x) = range (x)

Var(x+10) = var(x)