Page 157 - DMGT404 RESEARCH_METHODOLOGY

Unit 8: Descriptive Statistics

Remarks: Notes
1. We may note here that P = Q , P = D = Q = M , P = Q , P = D , P = D , etc.
25 1 50 5 2 d 75 3 10 1 20 2
2. In continuation of the above, the partition values are known as Quintiles (Octiles) if a
distribution is divided in to 5 (8) equal parts.
3. The formulae for various partition values of a grouped frequency distribution, given so
far, are based on ‘less than’ type cumulative frequencies. The corresponding formulae
based on ‘greater than’ type cumulative frequencies can be written in a similar manner, as
given below:

 3N   N 
C
C
     
Q  U   4   h Q  U   4  h
1 Q 3 Q
1 f 3 f
Q Q
1 3
 iN    kN  
  N   C    N   C 
D  U    10   h P  U    100   h
i i D k K P
f f
i D k P
Here U , U , U , U are the upper limits of the corresponding classes and C denotes the
Q
1 Q 3 i D K P
greater than type cumulative frequencies.
8.2.5 Mode
Mode is that value of the variate which occurs maximum number of times in a distribution and
around which other items are densely distributed. In the words of Croxton and Cowden, “The
mode of a distribution is the value at the point around which the items tend to be most heavily
concentrated. It may be regarded the most typical of a series of values.” Further, according to
A.M. Tuttle, “Mode is the value which has the greatest frequency density in its immediate
neighbourhood.”
If the frequency distribution is regular, then mode is determined by the value corresponding to
maximum frequency. There may be a situation where concentration of observations around a
value having maximum frequency is less than the concentration of observations around some
other value. In such a situation, mode cannot be determined by the use of maximum frequency
criterion. Further, there may be concentration of observations around more than one value of
the variable and, accordingly, the distribution is said to be bimodal or multi-modal depending
upon whether it is around two or more than two values.
The concept of mode, as a measure of central tendency, is preferable to mean and median when
it is desired to know the most typical value, e.g., the most common size of shoes, the most
common size of a ready-made garment, the most common size of income, the most common
size of pocket expenditure of a college student, the most common size of a family in a locality,
the most common duration of cure of viral-fever, the most popular candidate in an election, etc.
Mode can be determined under following situations like:

When Data are either in the form of Individual Observations or in the form of Ungrouped
Frequency Distribution
Given individual observations, these are first transformed into an ungrouped frequency
distribution. The mode of an ungrouped frequency distribution can be determined in two ways,
as given below:
1. By inspection or
2. By method of grouping.

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