In statistics, the mean is always reported with the standard deviation. It is important to know the standard deviation in order to analyze the data. Now, what is standard deviation? Well it is the mean of the mean. Another way of explaining is that it measures how spread out the data is. For statisticians, the standard deviation determines if the experiment or the benefits works. For example, when conducting a research about the social behaviors of a person in an awkward situation, the psychologist would write down the data they received. With that information, they calculate the average of how people react in that sample. Once they find the average, they have to calculate the standard deviation to see if their predictions were correct or false.
When calculating the standard deviation by hand, we need to find the variance based off the mean. Variance is the measure of how far the numbers are from each other. In this website, it shows and how to calculate the variance and the standard deviation (sd). What is really important to understand is, the higher the sd is, the more spread out the data is, therefore most likely not accurate or not good depending in the situation. One example could be grades from a classroom test. If the average of the test was an seventy and the sd was a 10, it means that most of the scores were in between 60 and 80. This range is not very good considering that some really understand, but some might only understand the concept.
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