Measures of Central Tendency

Central Tendency: A Single quantity which enables us to know the average characteristics of the data under consideration. Use of central tendency is a technique to analyse the data.

Various Measures of Central Tendency

  1. Arithmetic mean or mean or average
  2. Median
  3. Mode

Mean

It is the ratio of the sum of all values of the variable and the number of observations.

Mean of Raw Data

$$ \overline{x} = \frac {1}{n} \sum_{i=1}^{n} x_{i} $$

Mean of Ungrouped Data

$$ \overline{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}} $$

Median

It is the middle most value of arrayed data. It divides the arrayed data into two equal parts.

When the number of observations (n) is odd, the median is the value of (n+1)/2 observation.

When the number of observations (n) is even, the median is the mean of the (n/2) and (n/2 + 1) observations.

Mode

The observation that occurs most frequently in the data is called mode of the data. It is an observation with the maximum frequency in the given data.