FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.31Calculation.
Mode cannot be determined in a series of individual observations unless it is converted to a discrete series
(or continuous series). In a discrete series the value of the variate having the maximum frequency is the
modal class. However, the exact location of mode is done by interpolation formula like median.
Location of modal value in case of discrete series is possible if there is concentration of items at on point.
If again there are two or more values having same maximum frequencies, (i.e. more concentration), it
becomes difficult to determine mode. Such items are known as bimodal, tri-modal or multi-modal
accordingly as the items concentrate at 2, 3 or more values.
(A) For. Individual Observations
The individual observations are to be first converted to discrete series (if possible).
Then the variate having the maximum will be the mode.
Example 34 : Calculate mode from the data (given) :
(Marks) : 10, 14, 24, 27, 24, 12, 11, 17.
Marks Frequency
10 1
11 1
12 1
14 1
17 1
24 2
27 1(Individual observation are converted into a discrete series)
Here marks 24 occurs maximum number of times, i.e. 2. Hence the modal marks is 24, or mode = 24 marks.
Alternatively :
Arranging the numbers : 10, 11, 12, 14, 17, (24, 24) 27.
Now 24 occurs maximum number of times, i.e. 2. ∴ Mode = 24 marks.
[Note. When there are two or more values having the same maximum frequency, then mode is ill-defined.
Such a sense is known as bimodal or multi-modal as the case may be.]
Example 35 : Compute mode from the following data.
Marks obtained : 24, 14, 20, 17, 20, 14.
Marks Frequency
14 2
17 1
20 2
24 1[Here 14 occurs 2 times (max.) and 20 occurs 2 times (max.)
∴ mode is ill-defined.]