Paper 4: Fundamentals of Business Mathematics & Statistic

5.30 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

9. Calculate median of table given :
   Marks Students Marks Students
   (i) Less than10 5 (ii) Less than 45 20
   Less than 20 9 Less than 40 17
   Less than 30 15 Less than 35 12
   Less than 40 18 Less than 30 5
   Less than 50 20 Less than 25 2
   [Ans. (i) 21.67 marks, (ii) 33.57 marks]


10. In the following frequency distribution one frequency is missing. It is given that median of the distribution
    is 53.5, find the missing frequency.
    Variate Frequency
    20–30 8
    30–40 5
    40–50 f 3
    50–60 20
    60–70 10
    70–80 4
    [Ans. 12]
    [Note. That the class interval are unequal.]


11. The expenditure of 1000 families are as follows :
    Expenditure () No. of families 40–59 50 60–79 –– 80–99 500 100–119 –– 120–139 50 In the above table median is 87.50. Find the missing frequency.

5.1.6. MODE

Definition :

Mode is the value of the variate which occurs most frequently. It represents the most frequent value of a

series. In other words Mode is the value of the variable which has the highest frequency.

When one speak of the ‘average student’, we generally mean the modal wage, the modal student. If we

say that the modal wages obtained by workers in a factory are ` 70, we mean that the largest number of

workers get the same amount. As high as ` 100 and as low as ` 50 as wages are much less frequented and

they are non-modal.