Class 10 Maths Statistics Median of Grouped Data

Median of Grouped Data

 Median is a measure of central tendency which gives the value of the middle-most observation in the data. In case of ungrouped data, we first arrange the data values of the observations in ascending order. Then, if n is odd, the median is the (n+1)/2 th observation. But in case of Grouped data, it is difficult to find (n+1)/2 th observation. We use formula to find Median.
We first find cumulative frequency & then locate the class whose cumulative frequency is greater than (and nearest to) n/2 , where n is total observations. This is called the median class

where l = lower limit of median class,

  • n = number of observations,
  • cf = cumulative frequency of class preceding the median class,
  • f = frequency of median class,
  • h = class size (assuming class size to be equal).

Numerical: The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median.

Solution:

Step 1: Find Cumulative Frequency

Step 2: Find Median Class

Step 3: Apply formula to find Median

 

Applying the formula, Median =  125 + (34 -22)/20 * 20   = 137

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