Definition:Data Coding

Definition

Data coding is a technique for simplifying manual arithmetic.

It is also useful for reducing rounding errors when using a computer.

When calculating an mean or standard deviation, the following two rules can be used:

$(1): \quad$ If each datum is multiplied by a constant $b$, then the mean and standard deviation are each multiplied by constant $b$

$(2): \quad$ If a constant $a$ is added to each datum, then the mean is increased by $a$ but the standard deviation is not affected.

Arbitrary Origin

Let a set of data have a data coding applied such that a constant $a$ is added to each datum.

The constant $a$ is referred to as an arbitrary origin.

Examples

Arbitrary Example

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:

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

The standard deviation is:

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

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:

$0 \cdotp 002 \, 94$

Also known as

The technique of data coding is also referred to as just coding, but this invites ambiguity.

Hence that usage is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.

Also see

• Results about data coding can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): data coding
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): data coding