Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.41

6. Find A.M and mode of : 7, 4, 10, 15, 7, 3, 5, 2, 9, 12 [Ans. 7.4 ; 7]


7. Find G.M. of 3, 12, 48 [Ans. 12]


8. For a symmetry distribution mode and A.M. are respectively 12.30 and 18-48 ; find median of the
   distribution. [Ans. 16.42]


9. The mean marks of 100 students was found to be 40. Later on it was discovered that marks 53 was
   misread as 83. Find the corrected mean marks [Ans. 39.70]


10. A.M. of 7, x – 2, 10, x + 3 is 9 find x [Ans. 9]


11. Find G.M. of 8 observations : 2 occuring 4 times, 4 occuring twice 8 and 32 occuring once each.
    [Ans. 4]


12. Find H.M. of the observations
    1 1 1 1, , ,
    2 4 5 6 and

1

8 [Ans. 5

1

]

13. If the means of two groups of m and n observations are 40 and 50 respectively and the combined
    group mean is 42, find the ratio m : n. [Ans. 4 :1]


14. Find mean and mode of the 9 observations 9, 2, 5, 3, 5, 7, 5, 1, 8 [Ans. 5, 5]


15. If two groups have number of observations 10 and 5 and means 50 and 20 respectively, find the
    grouped mean. [Ans. 40]


16. Two variables x and y are related by y=x 5 10 − and each of them has 5 observation. If mean of x is 45,
    find the mean of y. [Ans. 4]


17. Find H.M. of 1 2 32 3 4, , , .....,n 1n+ , occuring with frequencies 1, 2, 3, ...., n respectively [Ans. 1]

[Hints : H.M.

1 2 3 .... n

1.2 2.^3 3.^4 ..... n.n 1

(^23) n
= + + + +

• 
  
  
  
  • 
    
    
    
    • 
      
      
      
      • +^ n(n 1 / 2)
        2 3 4 .... n 1
      
      
      
      
    
    
    
    
  
  
  
  

= +

+ + + + +

( )

( )

n n 1 / 2 1

n n 1 / 2

= + =

+

18. If the relation between two variables x and y be 2x + 5y = 24 and mode of y is 4, find mode of x.
    [Ans. 2]


19. Find median of the 10 observations 9, 4, 6, 2, 3, 4, 4, 6, 8, 7 [Ans. 5]


20. The mean of 10 observations was found to be 20. Later on one observation 24 was wrongly noted
    as 34. Find the corrected mean. [Ans. 19]


21. Prove that for two numbers 2 and 4, AM × HM = (G.M.)^2.


22. If the relation between two variables x and y is 2x + 3y = 7, and median of y is 2, find the median of x.

[Ans.^12 ]

23. If two groups of 50 and 100 observations have means 4 and 2 respectively, find the mean of the
    combined group. [Ans.^323 ]


24. If a variable x takes 10 values 1, 2, 3, ...., 10 with frequency as its values in each case, then find the
    arithmetic mean of x. [Ans. 7]

[Hints : A.M.
1 2^2232 ...... 10^2
= 1 2 3 ..... 10++ + ++ + ++ & etc.]