### Calculate change of variance of a set multiplication followed by addition of two different constants

Question Sample Titled 'Calculate change of variance of a set multiplication followed by addition of two different constants'

The variance of a set of numbers is ${49}$. Each number of the set is multiplied by ${100}$ and then ${25}$ is added to each resulting number to form a new set of numbers. Find variance of the new set of numbers.

A
${490000}$
B
${490}$
C
${495}$
D
${4900}$

 Recall that variance is the square of stardard deviation. ∵   Old variance $={49}$ ∴   Old standard deviation $=\sqrt{{{49}}}={7}$  By multiplying each datum in the dataset by ${k}$times, the new standard deviation would also be multipied by ${k}$ times. ∴   New standard deviation $={7}\cdot{100}={700}$  And then by adding each datum in the dataset by ${c},$ there is no change to the standard deviation. ∴   New variance $={\left({700}\right)}^{{2}}$ $={490000}$

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