Mean, Median and Mode


Mean is the ratio of sum of all observations divided by number of observations.
Mean = (Sum of observations)/(number of observations)

Mean of tabulated data

Let the frequencies of n observations x1, x2, x3, x4,..., xn be f1, f2, f3, f4,...,fn respectively. Then, we define mean to be,
Mean = (f1x1 + f2x2 + f3x3 + f4x4 + ... + fnxn)/(f1 + f2 + f3 + f4 + ... + fn = ∑(f·x)/∑f

where ∑ is Greek letter showing summation.

Mean of grouped data

In a class interval, we take x as the value of the class mark and use the formula
Mean = ∑(f·x)/∑f


Median is the value of the middle term of the data arranged in ascending or descending order of magnitudes.

  1. When the number of observations is odd, the there will be only one mid term and this term is the median.
  2. When the number of observations is even, the there will be two middle terms. The average of these two terms is the median.


The observation which occurs maximum number of times is called the mode of the data. In a tabulated data the observation with maximum frequency is the mode.