next up previous contents index
Next: Multiplying by a constant Up: Location and Spread Previous: Other Measures of Spread

   
Adding a Constant

The list of numbers: 1, 3, 4, 4 has average equal to 3 and SD equal to 1.414. Suppose a constant, say c=10, is added to each number on the list, thus yielding 11, 13, 14, 14. What is the average and SD of this new list?

Compare the dotplots of the old and new list:



                          O
                    O   O O
         Old:   --+---------+---------+---------+---------+--
                  0         5        10        15        20


                                              O
                                        O   O O
         New:   --+---------+---------+---------+---------+--
                  0         5        10        15        20



The dotplots or histograms look the same, except that the new histogram has been shifted 10 units to the right. Therefore, the new average  should be 10 units larger than the old average, but the new SD  should be equal to the old SD. This may be verified by actual computations for the list 11, 13, 14, 14: i.e. new average equals 13, new SD equals 1.414.

Subtracting by a constant will move the histogram to the left instead of to the right. Therefore the average will also move left, the SD will remain unchanged.

\fbox{ \parbox{5.5in}{
\vspace*{1ex}
Adding a positive constant $c$\space to a l...
...t the same constant
from the average. The SD remains unchanged.
\vspace*{1ex}
}}




2003-09-08