Coding data is a technique used to simplify calculations when analyzing a data set, particularly when finding the mean and standard deviation. This method involves transforming the original data values to a new set of coded values.

Purpose of Coding

Coding helps to make data analysis easier, especially when dealing with large data sets. By converting the original values to coded values, calculations can become simpler and more efficient. This is especially useful when the original data values are large or have a wide range.

Coded Values

To code the data, a new variable is created, typically using a linear transformation. The general formula for coding data is:
\[
y = \frac{x - a}{b}
\]
Where:

\(y\) is the coded value.

\(x\) is the original value.

\(a\) is a constant.

\(b\) is a constant.

By using this transformation, the mean of the coded values will be:
\[
\bar{y} = \frac{\bar{x} - a}{b}
\]

Mean and Standard Deviation of Coded Data

When calculating the mean of coded data, if the constant \(a\) is subtracted from each original value, the mean will also adjust by \(a\). The standard deviation remains unchanged since it measures dispersion:
\[
s_y = s_x
\]
Where:

\(s_y\) is the standard deviation of the coded data.

\(s_x\) is the standard deviation of the original data.

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