Shift Invariance (of Measures):
Shift invariance is a property of descriptive statistics . If a statistic is shiftinvariant, it possesses the following property for any data set

or, in equivalent form

In other words, if a statistic
Measures of central location  like the mean , the median , the trimmed mean , the mode , the weighted mean  are shift invariant.
Shift invariance is an important requirement imposed on many classes of statistical measures, e.g. measures of central tendency and measures of dispersion . If the beginning of the scale used to measure the primary data
For example, consider
Suppose a researcher has chosen a measure
(i) Subtract 200 (dollars) from each

(ii) Subtract 200 (dollars) from the old value of
For a measure that is shift invariant, the result in both cases is always the same  i.e. for any data set and any value of the shift
A general practical recommendation: if the data at hand are measured on a scale with the zero point chosen quite arbitrarily (normally such data may take on both negative and positive values), and the quantity of interest is expressed in the same units as the data