Median of Grouped Data

In Statistics Mean, Median and Mode are known as the measures of central tendencies.

Median is the middle most value of the observations when the observations are either arranged in increasing or decreasing order.

let n be the total number of observations.If n is odd then median is the value of ${\left(\frac{\text{n+1}}{\text{2}}\right)}^{\text{th}}$observation.If n is even then median is the A.M of the values of ${\left(\frac{\text{n}}{\text{2}}\right)}^{\text{th }}$and ${\left(\frac{\text{n}}{\text{2}},\text{+ 1}\right)}^{\text{th }}$observations.

Preparing a cumulative frequency distribution table is the first step in calculating the median of the grouped data. The cumulative frequency of a class is obtained by adding the frequencies of all the classes preceding the given class. To calculate the median either the more than or less than cumulative frequency is used.

If the data is converted into a frequency distribution table it is known as grouped data. The median for the grouped data is given by  $\text{l +}\frac{\frac{\text{n}}{\text{2}}\text{- }{\text{c . }}_{\text{f}}}{\text{f}}$ × h .

Where l is lower class limit of median class.
          n is total number of observations.
          c_f is the cumulative frequency of the class preceding the median class.
          f is the frequency of the median class and h is the class size.

Number of Trees Planted       (Class - Interval)	Number of Schools      (Frequency)(f)	Cummulative Frequency (cf)
More than or equal to 5	12	12 + 8 + 14 + 20 + 6 = 60
More than or equal to 25	8	8 + 14 + 20 + 6 = 48
More than or equal to 45	14	14 + 20 + 6 = 40
More than or equal to 65	20	20 + 6 = 26
More than or equal to 85	6	6

THIS TABLE REPRESENTS THE CUMULATIVE FREQUENCY DISTRIBUTION OF THE 'MORE THAN' TYPE.

Number of trees Planted   (Class - Interval)	Number of Schools    (Frequency) (f)	Cummulative frequency (cf)
5 - 25	12	12
25 - 45	8	20
45 - 65	14	34
65 - 85	20	54
85 - 105	6	60

THIS TABLE REPRESENTS THE CUMULATIVE FREQUENCY DISTRIBUTION OF THE 'LESS THAN' TYPE