Calculate online the mean, median, and mode of a statistical sample with ungrouped data or data grouped by range and frequency. Use a period as the decimal separator.
Mean
Median
Mode
The statistical mean is the average of a set of numbers. It is a measure used to represent a typical or central value within a group of data.
The statistical mean x is calculated by summing all values in the sample and dividing by the total number of data points.
Where:
The statistical median is a measure of central tendency that represents the value dividing a set of ordered data into two equal parts. To calculate the median, it is essential to use a reliable median calculator, especially when working with large data sets or grouped data.
To calculate the median, first order the data from smallest to largest. If the number of data points is odd, the median is the central value. If it is even, take the average of the two central values.
For grouped data, a specific formula is used, which our median calculator applies automatically.
For ungrouped data:
For grouped data:
Where:
The statistical mode is the value that appears most frequently in a data set. To efficiently calculate the mode, especially in large data sets or grouped data, it is recommended to use a specialized mode calculator.
To calculate the mode, identify the value or values that appear most frequently in the data set. For grouped data, a specific formula is used, which our mode calculator implements to provide accurate results.
For ungrouped data:
For grouped data:
Where:
The main difference between median and mode is that the median represents the central value of an ordered data set, while the mode is the most frequent value. Calculating the median requires ordering the data, while calculating the mode involves counting frequencies. Our median and mode calculators can efficiently perform both calculations, whether for simple or grouped data, providing accurate results in seconds.
Grouped and ungrouped data are two different ways of organizing statistical information. Ungrouped data are individual values, while grouped data are organized into intervals or categories. The choice between using grouped or ungrouped data affects how the median and mode are calculated, so it is crucial to understand this difference when using a median calculator or a mode calculator.
Grouped data are presented in intervals or classes. For example, student ages at a university could be grouped as follows:
In this case, calculating the median or mode requires using the specific formulas for grouped data mentioned above.
Ungrouped data are individual values without grouping. Continuing with the age example, it could be:
For these data, calculating the median involves ordering them and finding the central value, while the mode would be simply the most repeated value (in this case, 21 and 23 each appear twice, so there would be two modes).
Using a median and mode calculator is especially useful when working with large data sets, whether grouped or ungrouped, as it automates these calculations and reduces the margin of error.