Today is another beginner's tip for people new to using SPSS. What is the standard deviation of a dataset and how do I use SPSS to calculate it.
Standard Deviation is a measure of how widely dispersed our dataset is. It is a fairer and more comprehensive way of describing a dataset than just using a simple mean, median or mode. It actually describes how widely a dataset is dispersed from its mean. This of course means that in order to be really useful, you also need to know the units that your standard deviation is in and the mean of the dataset that it refers to as well. On it's own a standard deviation figure is unlikely to be very useful. A low standard deviation figure implies a tight or little dispersed dataset and conversely a large standard deviation implies a widely dispersed dataset.
It is useful to know how standard deviation is calculated as well so here goes.
It is the square root of the mean of the square of the differences of each variable in the dataset from the datasets mean. So in order to calculate it the sum of all of the squares of each piece of data's difference from the mean of the data set is taken. To get the mean it is then divided by the number of pieces of data and the square root of that is taken.
It is probably most easily illustrated by example. Image a dataset of 3 items - 9, 8, 7, 6 , 5
The mean of this data is 7 and so the square of difference from the mean for the data is 4 (9-7)^1 , 1 (8-7)^1 , 0 , 1 , 4
So the sum of the square of the differences is 10. There are 5 items in the data set and so the mean of this figure is 2 (10/5), and the square root of it is 1.414.
So for our very simple distribution the mean is 7 and the square root is 1.414. Obviously it can be far more complicated to calculate for larger and more
In SPSS to calculate the standard deviation for a dataset it is a very simple process. Select your variables, click STATISTICS and select Standard Deviation as well as Mean and click CONTINUE. SPSS will now very quickly and simply calculate the mean and standard deviation of your data.
I will post more in my next post about standard deviation as it is an important concept in statistics and so for anyone using SPSS.