The sum of the ages is found to be 78 and dividing by 10 gives us the sample mean age as 7.8 years.
The standard deviation requires the same mathematical operator and so it would be helpful to recall this knowledge from your past. For this example the indexing notation would be i = 1 and because it is a sample we use a small n on the top of the Σ which would be 10. We know which ones to add by the indexing notation, the i = 1 and the n or capital N for the population. See: measure of spread, population variance, standard deviation. In this case it is X 1 through X 10 which is all of them. The Greek letter (sigma) is the most common symbol for the population standard deviation. The i in the formula tells us which of the observations to add together. To calculate the mean we are told by the formula to add up all these numbers, ages in this case, and then divide the sum by 10, the total number of animals in the sample.Īnimal number one, the cat Purr, is designated as X 1, animal number 2, Toto, is designated as X 2 and so on through Dundee who is animal number 10 and is designated as X 10. Purr is animal number one and is a 9 year old cat, Toto is animal number 2 and is a 1 year old puppy and so on. AnimalĮach observation represents a particular animal in the sample. The first number will be number 1 and the second number 2 and so on. If we list each value, or observation, in a column, you can give each one an index number. Let’s say we have a sample of animals from the local animal shelter and we are interested in their average age. The Σ symbol tells us to add a specific list of numbers. Like all mathematical symbols it tells us what to do: just as the plus sign tells us to add and the x tells us to multiply. The symbol is the capital Greek letter sigma thats why its called sigma notation stands for sum the expression to the right of the tells you. It is called Sigma notation because the symbol is the Greek capital letter sigma: Σ.
#Sigma symbol statistics how to
Both formulas have a mathematical symbol that tells us how to make the calculations.
\stackrel is the symbol for the sample mean.
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