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Sample Variance Formula In Statistics


Population Variance Formula

The population Variance Formula in mathematics is sigma squared equals the sum of x minus the mean squared divided by n.

\[\ \huge \sigma^{2}=\frac{\sum\left(x-\overline{x}\right)^{2}}{n}\]

The variance of a sample is defined by slightly different formula:

\[\ \huge S^{2}=\frac{\sum\left(x-\overline{x}\right)^{2}}{n-1}\]

Where,
\[\ \sigma^{2}$= Variance\]
x = Item given in the data
\[\ \overline{x} = Mean of the data\]
n = Total number of items.
\[\ s^{2} = Sample variance\]

Let us understand the concept of population variance in detail below. Take an example, where one teacher needs to find out the average speed for the students taking in reading the comprehension pages. Each student is assigned six pages in the classrooms to read.

A teacher could find the average time here but this information is not just the right technique to analyze the clear picture of her students. Few of them read content very fast while others are just the average. It gives the average taken to read the total content not the actual details about each of the students.

So, you need to find the sample variance of the collected data here. Variance in simple words could be defined as the how far a set of numbers are spread out. This is actually very different from calculating the average or mean of data from a set of number. The variance formula is already given at the top for your reference.

You just need to plugin values in the formula and calculated the needed output. When there is equal difference between first, second, and the third term then find the average or mean here. In case, the difference between terms is larger then you should find the variance for a particular set of data.

The two most common categories of Variance include – Population Variance and the Sample Variance. Population is defined as the total number of members in a particular group while sample is just a part of the population that is used to describe the whole group.


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