The standard deviation (s) is a very useful tool; the smaller this value is, on average the closer our individual data points sit towards the mean. With a normal distribution of data we would expect the following to hold true: 68% of the data lie within one standard deviation either side of the mean 95% of the data lie within 2 standard deviations either side of the mean. n-1 Why do we divide by n-1 rather than n? If we really want to know the mean square difference from the (which is a pretty ‘root mean’ good description of what the standard deviation is) why we divide by n just like don’t calculating other means? In fact if we were calculating the standard deviation of a whole population (e.g. if we were only interested in the people on the bus as a (tiny) whole population and did not want to use them as a sample to make estimates about a larger population) we would divide by n. But in most biological data handling situations we actually have a sample (because we don’t have time to measure every single individual in the whole population) and we use our calculation of the sample standard deviation to make inferences about the population. Using n-1 in our calculation is essentially a correction factor that makes the number we come up with from our sample a better estimate of the standard deviation of the population. So for AS and A Level Biology we stick to using the n-1 formula. If you are using a calculator or a spreadsheet to calculate standard deviation make sure you press the right button, or use the right embedded formula.
The standard deviation (s) is a very useful tool; the smaller this value is, on average the closer our individual data points sit towards the mean. With a normal distribution of data we would expect the following to hold true: 68% of the data lie within one standard deviation either side of the mean 95% of the data lie within 2 standard deviations either side of the mean. n-1 Why do we divide by n-1 rather than n? If we really want to know the ‘root mean square difference from the mean’ (which is a pretty good description of what the standard deviation is) why don’t we divide by n just like calculating other means? In fact if we were calculating the standard deviation of a whole population (e.g. if we were only interested in the people on the bus as a (tiny) whole population and did not want to use them as a sample to make estimates about a larger population) we would divide by n. But in most biological data handling situations we actually have a sample (because we don’t have time to measure every single individual in the whole population) and we use our calculation of the sample standard deviation to make inferences about the population. Using n-1 in our calculation is essentially a correction factor that makes the number we come up with from our sample a better estimate of the standard deviation of the population. So for AS and A Level Biology we stick to using the n-1 formula. If you are using a calculator or a spreadsheet to calculate standard deviation make sure you press the right button, or use the right embedded formula.