Question

Subtract 5 from each of the numbers in problem 5 (i.e., you now have 31.2,41.1,42.1… etc.).

a) Calculate the variance (s²)
b) Are you surprised by the results? Why or why not?
c) What happens to the mean? (You don't need to do the actual calculation unless you're not sure what's going on).
d) What happens to the median? (Again, you don't need to do the calculation unless you're not sure what's happening)

Answer 1

Subtracting a constant from each data point in a set will decrease the mean and median by that constant but will not affect the variance or standard deviation.

Step-by-step explanation:

The variance of a set of numbers measures the spread of the numbers in the data set. When you subtract a constant from each number in the data set, the spread doesn't change. Therefore, when you subtract 5 from each number in the original problem, the variance remains the same.

The mean or average will decrease by 5, because you have subtracted 5 from each data point. The median, being the middle value in an ordered set, will also decrease by 5 for the same reason. These are the expected results, and as such, should not be surprising because linear transformations of data affect measures of central tendency but not the measures of spread such as variance or standard deviation.