How do I find a median class Median for grouped data

At grouped data is the calculation of the Medians a little more complicated. Here is the arithmetic sequence:

  • Formation of Frequency table (including cumulative frequencies)
  • Determination of the class min which the Median is: where is the value (n + 1) / 2. This is now called Median class designated (n = total number of entries)
  • Determination of the lower (= xmust) and upper Class boundary (x) from m
  • Identify the Class breadthH (results from upper class limit - lower class limit).
  • Subtract the accumulated frequency of all classes up to the class m (i.e. classes 1 to m-1) from n / 2 -> position of the median in the median class
  • Division of the position by the number of values ​​in the class = relative order of magnitude of the median (proportions of the whole of the class)
  • Multiplication of the relative class share by the class width = absolute order of magnitude of the median within the class
  • Addition of the lower class limit (in which the median lies) to the absolute size of the median (in the class) = final result = median Z


Figure: Formula for the median for grouped data


Example: Time consumed in solving a task

Figure: Example - table for the time consumed in solving a task

n = 37, the median is the 18th value, this is in class 5 (4.5-5.5 minutes duration), therefore:

Figure: Calculation of the median for the example "time consumption"

The median is therefore 5.