5.10 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSMeasures of Central Tendency and Measures of Dispersion
(ii) For counting mean, all the data are utilised. It can be determined even when only the number of
items and their aggregate are known.
(iii) It is capable of further mathematical treatment.
(iv) It provides a good basis to compare two or more frequency distributions.
(v) Mean does not necessitate the arrangement of data.
5.1.1.6. Disadvantages of Arithmetic Mean
(i) It may give considerable weight to extreme items. Mean of 2, 6, 301 is 103 and more of the values is
adequately represented by the mean 103.
(ii) In some cases, arithmetic mean may give misleading impressions. For example, average number of
patients admitted in a hospital is 10.7 per day, Here mean is a useful information but does not represent
the actual item.
(iii) It can hardly be located by inspection.
Example 12 : Fifty students appeared in an examination. The results of passed students are given below :
Marks No. of students
40 6
50 14
60 7
70 5
80 4
90 4
The average marks for all the students is 52. Find out the average marks of students who failed in the
examination.
Table : Calculation of Arithmetic Mean
Marks (x) f fx
40 6 240
50 14 700
60 7 420
70 5 350
80 4 320
90 4 360
Total N = 40 fx = 2390x fx^2390
= f = 40
∑
∑ = 59.75, n^1 = 40
Let average marks of failed students = x 2 , n 2 = 10