# What is the correct way to represent the variation around an average percentage?

This is an example of my data: I understand that the mean should be calculated by (Total number "Yes" / Total number of websites)*100, however I want to represent the variation around this mean in the results. What is a suitable way of doing this? I'm not sure if the standard deviation will be meaning less due to the variation in sample size...

## 1 Answer

Hi Dan the best way would be to use a standard deviation.

# Std/Variance

The standard deviation uses. Check this post out on the variance and standard deviation if you would like to read up more on it. Pretty much they are just measures of dispersion. Whether you are discussing the real values or the percentages the standard deviation works.

In fact in finance where the general interest is in relative prices (a percentage) rather than actual prices, the volatility (or risk) is generally discussed as the standard deviation.

## Other measures of dispersion

There are other measures of dispersion however such as the coefficient of dispersion which is calculated as $$\begin{equation} \frac{ X_{max}-X_{min} }{X_{max}+X_{min}} \end{equation}$$ based on the range or $$\begin{equation} \frac{ Q_{3}-Q_{1} }{Q_{3}+Q_{1}} \end{equation}$$ in terms of the quantiles, where X represents your variable of interest. This is not what you should however. Rather stick to the standard deviation and variance.

If you are interested in reading more about the measures of dispersion please see this link and similarly this link, they explain it simply.

## Plotting

I would also consider plotting a histogram of your percentages and discussing the distribution. A quick search will lead you to implementing this in excel.Comment on the distribution of your data (percentages).

More often than not in statistics the simplest answer is the best answer. Good luck!