Transformations of Data

Let $\{x_1,~x_2,~\ldots,~x_n\}$ be a set of data. Let $\overline{x}$, $m$ and $M$ be the mean, median and mode of the data respectively. Let $R$, $Q$ and $\sigma$ be the range, inter-quartile range and standard deviation of the data respectively.

1. Adding a constant $k$ to each data
   1. The new mean $=\overline{x}+k$
   2. The new median $=m+k$
   3. The new mode $=M+k$
   4. The new range $=R$
   5. The new inter-quartile range $=Q$
   6. The new variance $=\sigma^2$
   7. The new standard deviation $=\sigma$
2. Multiplying a constant $k$ to each data
   1. The new mean $=k\overline{x}$
   2. The new median $=km$
   3. The new mode $=kM$
   4. The new range $=kR$
   5. The new inter-quartile range $=kQ$
   6. The new variance $=k^2\sigma^2$
   7. The new standard deviation $=k\sigma$

Same Topic:

Inter-quartile Range Normal Distribution Range Standard Deviation