This statistics calculator is intended for calculation of the mean, median and mode values in a given set of data. Enter the data set of input numbers in the appropriate field of this Mean, Median, Mode Calculator and calculate the above parameters as well as the number of input data set elements (dataset size). You can paste the data copied from a spreadsheet or csv-file or enter manually using comma, space or enter as separators.
Mean Median and Mode
In statistics, a central tendency is a central or typical value for a probability distribution. The most common measures of central tendency are the arithmetic mean (or simply mean), the median and the mode. They are actually different ways to tell us what value in a data set is typical or best represents this data set.
In the case of a dataset of n values \(\{ { x }_{ 1 },{ x }_{ 2 },…,{ x }_{ n }\}\), we have the following definitions for the above “avarages”.
• Mean. This is simply the sum of all the elements divided by the number of elements in the data set:
$$\bar { x } =\frac { 1 }{ n } \sum _{ i=1 }^{ n }{ { x }_{ i } } .$$
• Median. This is the middle value that separates the higher half from the lower half of the data set. When we have a data set ordered from lowest to highest value \(\{ { x }_{ 1 }\le { x }_{ 2 }\le …\le { x }_{ n }\}\), the median \(\overset { \sim }{ x }\) is the data point separating the upper half of the data values from the lower half.
In case \(n\) is odd the median is the data set value at position \(k\):
$$\overset { \sim }{ x }={ x }_{ k }, \,\,\,\, k=\frac { n+1 }{ 2 } .$$
In case \(n\) is even the median is the average of the values at positions \(k\) and \(k+1\):
$$\overset { \sim }{ x } ={ \frac { { x }_{ k }+{ x }_{ k+1 } }{ 2 } } , \,\,\,\, k=\frac { n }{ 2 } .$$
• Mode. This is the most frequent value in the data set. There can be more then one mode value for some data sets.
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Check out our other statistics calculators such as Covariance Calculator or Standard Deviation Calculator.