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Mode

Mode (Z ) is that value which has the maximum concentration of observations around it. This can also be described as the most common value among the given observations.

  1. In discrete frequency distribution, the observation having the highest frequency is called Mode.

Example
What is the modal value for the numbers 5, 8, 6, 4, 10, 15, 18, 10?
Solution
The mode for the given observations is 10, as it occurs in the maximum number of times.
  1. If in an ungrouped data, any observation is not repeating, then Mode (Z) can be found using the relation
     
    Mean – Mode = 3(Mean – Median).
     
    Description: 93882.png 
  2. In continuous frequency distribution, following formula is applicable:
     
    Description: 93901.png
     
    Description: 93918.png 
     
    The class with highest frequency is chosen as the modal class. 

Example
 Find the modal mark for the given distribution.
Marks 0–20 20–40 40–60 60–80 80–100
Students 5 18 48 12
5
Solution
Marks No. of Students
0–20 5
20–40 18 (f–1)
40–60 48 (f0)
60–80 12 (f1)
80–100 5
 
From the table, LCB of the modal class is l = 40 and C = 20.
 
Description: 93946.png 

 

Note: A distribution having one mode is called unimodal.
A distribution having two modes is called bimodal.
A distribution having more than two modes is called multimodal.

Properties of Mode

Median is affected by change in origin as well as change in scale.
 
Let y = a + bx be the relation between two variables x and y for any two constants a and b; then the mode of y is given by yZ = a + bxZ (where, xZ is the mode of x).

Merits

  1. It can be easily understood.
  2. It can be located in some cases by inspection.
  3. It is capable of being ascertained graphically.
  4. It is not affected by extreme values.
  5. It represents the most frequent value and hence it is very often in practice.
  6. The arrangement of data is not necessary if the items are a few.

Demerits

  1. There are different formulae for its calculations which ordinarily give different answers.
  2. Mode is determinate. Some series have two or more than two modes.
  3. It cannot be subjected to algebraic treatments. For example, the combined mode cannot be calculated for the modes of two series.
  4. It is an unstable measure as it is affected more by sampling fluctuations.
  5. Mode for the series with unequal class-intervals cannot be calculated.

Comparison Among Mean, Median and Mode

 

Mean

Median

Mode

Average

It is a calculated average.

It is a positional average.

It is a positional average.

Calculations

It is based on all the observations.

It is the middle most value which divides the series into two equal parts.

It is the value around which the terms of the series tend to concentrate densely.

Treatment

It is capable of mathematical treatments.

It is not capable of mathematical treatments.

It is not capable of mathematical treatments.

Items

It involves all the items for calculations.

Does not consider all the items.

Does not consider all the items.

Array

Does not require arraying.

Arraying of the values of the items in the series is essential.

Arraying of the values of the items in the series is essential.

Extreme Values

It is affected by the extreme and abnormal values of the items in the series.

It is not affected by the extreme values.

It is not affected by the extreme values.

Result

There is only one mean.

There is only one median.

In a series, there may be one Mode or more than one Mode or no Mode.

Reliability

Most reliable measure

Less reliable

Less reliable

Use

It is simple and widely used in statistical treatment and interpretation.

Not popular and is used only in appropriate cases.

Not popular and is used only in appropriate cases.





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