This Frequency Distribution Calculator is intended for calculation of the number of times a data value occurs in a given data set. The frequency can be presented in the form of absolute, relative or cumulative frequency. Using ▼ or ▲ buttons one can sort the output data by the element or frequency value. Enter the data set values in the appropriate field of this calculator and get the frequency distribution as well as the number of input elements (dataset size), mean and median values of the data set. You can paste the data copied from a spreadsheet or csv-file or enter manually using comma, space or enter as separators.
Frequency Distribution
In statistics, a frequency distribution is a list, table or graph that displays the frequency of various outcomes (values) in a data set. There are different types of frequencies.
• A frequency (or absolute frequency) is the count of a value occurrences within a data set.
• A relative frequency is a frequency divided by the count of all values. Relative frequencies can be written as fractions, percents, or decimals.
• A cumulative frequency associated with a value of an ordered data set is the count of the value occurrences plus sum of all the previous values counts. The cumulative frequency of the last value is always equal to the total for all the values occurrences which is the data set size.
Along with the frequencies our Frequency Distribution Calculator computes the mean and median values of the given 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 \(k+1\):
$$\overset { \sim }{ x } ={ \frac { { x }_{ k }+{ x }_{ k+1 } }{ 2 } } , \,\,\,\, k=\frac { n }{ 2 } .$$
Related calculators
Check out our other statistics calculators such as Outlier Calculator or Quartile Calculator.