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Maths Exercices
 
Statistics

Central Tendency Measures
Measures of Dispersion
Measures of skewness and kurtosis

Mode

The mode of a set of data is the value or values which occurs most often.

Steps to determine the mode:

Step 1. Count the number of times each value in a set occurs.
Step 2.  
 
  • If one value occurs more time than any other, it is the mode.
  • If two or more values occur more time than any other, they are all modes of the set.
  • If all values occur the same number of time, there is no mode.

Find the mode of: 2, 3, 4, 4, 2, 3, 4
Number 2 occurs 2 times,
Number 3 occurs 2 times,
Number 4 occurs 3 times,
So the number with most occurrances is 4 and is the Mode of this distribution.


Another method for determining mode is to use the empirical relation between mean, median and mode which os found to hold for unimodal distributions that do not deviate much from symmetry. The realion is:

Mode for grouped data.
In the computation of the value of the mode for grouped data, it is necessary to identify the class interval that contains the mode. This interval, called the modal class, contains the hightest frequency in the distribution. The next step after getting the modal class in to determine the mode within the class. To do it, we can use the formula:


where:
  • l and u respectively denote the lower and upper class-boundaries of the class in which the mode lies.
  • f is the frequency of the modal class.
  • f1 is the frequency of previous class of the modal class.
  • f2 is the frequency of next class of the modal class.

This table shows the monthly income of different families in a special locality. Find the income earned by the most number of families.

Income
Families
1000-2000
10
2000-3000
14
3000-4000
10
4000-5000
12

The modal class is 2000-3000.
To find the mode, we use the formula:


The mode is: 2500

Advantages:

  • It is applicable to nominal data.
  • It is unaffected by extreme values.

Disadvantages:

  • It may not be unique in a set of data.
  • It can not be manipulated using the rules of algebra.

Ejercicios