variation and the mean

[bob4000]

mathematically why does the mean change when an x-value is changed in a list, but the variation doesn't. if someone could show me a relevant formula which can satisfy this or any other info i would be very grateful for

thnak you

[mathman]

If you change all the values on the list by the same amount, the mean changes with it, but the variance, which measures the fluctuations around the mean doesn't change. If you shift one value only, both the mean and the variance will change.