Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.37

Mode is 24, so modal class is (20–30). From the formula of mode we find. 1 2
24 20 27 f1 10
54 f f
= + − ×
− − or,
1
1 2

4 270 10f

54 (f f )

= −

− +

or,^11
4 270 10f 270 10f
54 44 10
= − = −
− 14 + f^1 + 27 + f^2 + 15 = 100
or, f 1 + f 2 = 100 – 56 = 44 ...........(1)
or, 40 = 270 – 10f 1
or, 10f 1 = 230 or, f 1 = 23. From (1) , f 2 = 44 – 23 = 11 ∴ f 1 = 23, f 2 = 11

5. The following are the monthly salaries in rupees of 20 employees of a firm :
   130 125 110 100 80 76 98 103 122 66
   145 151 65 71 118 140 116 85 95 151
   The firm gives bonuses of 10, 15, 20, 25 and 30 for individuals in the respective salary group : exceeding 60
   but not excedding 80, exceeding 80 but not exceeding 100 and so on up to exceeding 140 but not
   exceeding 160. Find the average bonus paid per employee. Solution: From the monthly salaries of the employees, we find the number of employees lying in the salary groups mentioned as follows : Table : Calculation of average bonus Salary () bonus
   f x fx
   Exceeding 60 but not exceeding 80 5 10 50
   ” 80 ” 100 4 15 60
   ” 100 ” 120 4 20 80
   ” 120 ” 140 4 25 100
   ” 140 ” 160 3 30 90
   Total 20 380

( )

A.M. x fx^380 Rs. 19.

f 20

=∑ = =

∑

6. Marks obtained by 30 students in History of a Test Examination 2012 of some school are as
   follows :
   34 36 10 21 31 32 22 43 48 36
   48 22 39 26 34 39 10 17 47 38
   40 51 35 52 41 32 30 35 53 23
   construct a frequency table with class intervals 10–19. 20–29 etc. Calculate the median and mode from the
   frequency distribution.