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 Introduction > Step-by-Step Statistics > Gentle Introduction > Variance, Standard Deviations and Standard Error |
Variance, Standard Deviations and Standard Error Variance measures the spread of your results. On its own, the variance isn't the most useful statistic, however, taking the square root of the variance gives you the standard deviation which indicates how much your data deviates from the mean. If the spread of your data is close to the mean, the standard deviation will be small and vice versa. If your data are normally distributed, around 67% of your results should fall within your mean, plus or minus your standard deviation, and 95% of your results should fall within two standard deviations, plus or minus your mean.For example, you have conducted an experiment to determine what effect rust infestation has on flower initiation of strawberry. On the 1st April, you dissected strawberry crowns and counted flower initials. The mean number of flower initials was found to be 25, with a standard deviation of 3. You can conclude that 67% of strawberry crowns contain between 22 and 28 flowers, and 95% contain between 19 and 31 flowers on 1st April. Statistical programmes should automatically calculate the standard deviation of your data, although you may have to select this option from a pull down menu. In Excel, the standard deviation can be calculated using the equation =STDEV(range of cells). The standard error takes into account the size of the sample you're working with. As with the standard deviation, the standard error will generally be automatically calculated by your statistical package. If you're using Excel, you can calculate it by dividing the standard deviation by the square root of number of samples you have =(STDEV(range of cells))/SQRT(number of samples). The standard error is often incorporated into graphs as error bars.
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