Mode

Mode

 Mode is the value or measure that occurs most frequently in a distribution. It is the score with maximum frequency in a frequency distribution. In a set of data, there will be more than one item with maximum frequency, then all these values are modes of the distribution. If there are two values with highest frequency, then the distribution is bi modal and if there are more than two values, then it is multimodal. If all the values in a distribution is repeated equal number of times, or not at all repeated, then all the scores can be taken as mode or it can be considered as the distribution has no mode.

 Characteristics of Mode

 It is the most frequently occurring value in a distribution.

It is ill defined and is a rough measure of central tendency.

It does not depend on other values

It can not be used for further calculations

 It is possible to calculate mode of an open ended distribution.

Mode can be easily computed and simple to understand

 It is not affected by extreme values.

  It is not a stable measure of central tendency

 Computation of Mode from Ungrouped Data

In the case of ungrouped data, mode is the score that occur maximum number of times. That is, it is the most frequent item in a set of data  and is the value that has the maximum frequency.

Example

 Compute mode from the following distribution: 38, 29, 45, 34, 45, 54, 56, 34, 45, 45. Here, 45 occurs the most number of times ie., four times. Hence, the value of mode is 45. ( Whatever be the other values, mode is 45, unless the other values repeat 4 or more times)

Computation of Mode from Grouped Data

 In data which is given in the form of a frequency distribution (grouped data or continuous series), Mode is computed using the formula, Mode (Mo) = 3Md – 2M Where, Md is the median and M is the Mean of the given distribution. The Mean and Median are first computed and subsequently Mode is computed. Mode can also be computed directly from the frequency distribution table without calculating mean and median.

Where, l (l1)lower limit of the modal class l2= upper limit of the modal class , f1=frequency of the modal class, f0= frequency of the class preceding (before) the modal class f2= frequency of the class succeeding (after) the modal class

Example: The following data is on  the different income groups of 45 farmers in a village.