Data Coding/Examples/Arbitrary Example 1

Examples of Data Coding

Let us wish to calculate the mean and standard deviation of the numbers:

$179 \cdotp 385$

$179 \cdotp 387$

$179 \cdotp 392$

We may multiply by $1000$ and then subtract $179 \, 387$ (which is the same as adding $-179 \, 387$) to give:

$-2$

$0$

$5$

The mean is:

$\dfrac {-2 + 0 + 5} 3 = 1$

$\sqrt {\dfrac {\paren {-2 - 1}^2 + \paren {0 - 1}^2 + {5 - 1}^2} 3} = \sqrt {\dfrac {26} 3} = 2 \cdotp 94$

Adding $179 \, 387$ to $1$ and multiplying by $\dfrac 1 {1000}$ gives the mean as:

$179 \cdotp 388$

Multiplying $2 \cdotp 94$ by $\dfrac 1 {1000}$ gives the standard deviation as:

$0 \cdotp 002 \, 94$