# Mean, Median, Mode, Range, Standard Deviation

## Mean

Depicted as μ, it is the average value of the sample of data. It is computed by the formula μ = (x1+x2+…+xn)/n. It is called an arithmetic mean: there are other mean values too, but the arithmetic mean is the most common.

An example is an average mark on the subject of the class students: it is calculated by adding together all students’ marks and dividing them by the number of the students.

## Median

The median is the central value of the sample of data: if one places the data in a row, the median value will divide the row into two halves. For the set with n values, the median value will be xn/2. If the sample contains an odd number of values, then the median will be the mean of two central values: (x(n+1)/2 + x(n-1)/2)/2.

For example, with the students’ marks, one can calculate the median mark by placing the marks in the row from the lowest to the highest: the mark in the center of the row will be the median. If there is an odd number of students, the median should be calculated as the mean of two central values.

## Mode

The mode of the sample of data is the value occurring most frequently in the sample. If two different values occur the same number of times, one can consider both as modes. If all values have the same frequency, the sample does not have a mode.

The mode of the sample of students’ marks will be the mark occurring most frequently in the sample.

## Range

The range is the difference between the highest and lowest values in the sample, showing the interval of data. F(x) = max(x) – min(x).

For the example with the students’ marks, the range of the sample will be the difference between the highest and the lowest mark.

## Standard Deviation

The standard deviation, depicted as σ, is the value that shows the deviation of the values from their mean. It is calculated as the square root of the sum of the squares of differences between each value and the sample’s mean, divided by the number of values in the sample.

To obtain a standard deviation for the sample of students’ marks, one should calculate the mean, calculate the differences between each mark and the mean mark, square each difference, add them together, and divide by the number of the students in the class; after that, one should calculate a square root from the obtained value. The resulted value will show the standard deviation of the marks.

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