# BUSINESS MATHEMATICS,LOGICAL REASONING AND STATISTICS CA FOUND

#### PRACTICE PROBLEMS

1. Given the following data:
 Cities A B C D E F Density 200 500 400 700 600 300 Death rate 10 16 14 20 17 13

Find the coefficient of correlation between density and death rate.

1.   For a Private data:  {(x,y): (15,3),(11,3),(12,2),(14,0),(8,6)}.  Find the coefficient of correlation between x and y.
2.   What is the value of correlation coefficient due to person on the basis of the following data:
 X -5 -4 -3 -2 -1 0 1 2 3 4 5 Y 27 18 11 6 3 2 3 6 11 18 27

1. Calculate Karl Pearson’s coefficient of correlation from the following data:
 Values of X 100 110 115 116 120 125 130 135 Values of Y 18 18 17 16 16 15 13 10

1.  From the following data compute the coefficient of correlation between X and Y:
 X – Series Y – Series Arithmetic Mean 15 28 Sum of Squares of deviations from mean 144 225

6) For the distribution of the number of marks obtained by 49 students in a class. Calculate the mean, median and mode.

 Class 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 Frequency 5 6 15 10 6 3 3 1

7) Calculate Q3, D4, P30 from the following data:

 Marks 20 25 30 35 40 No.of students 5 14 20 11 10

8) Find the A.M.G and H.M and prove that A.M ≥ G,M ≥ H.M

 X 2 4 8 16 F 2 3 3 2

9) (i) If the absolute deviations of 5 observations from mean be 26, 15,39,24,41 Find the mean deviation about mean.

(ii) The first three quartiles of a distribution are Rs. 12, Rs.22, Rs.45; Find the Quartiles Deviation.

10)  (i) If the standard deviation of x is, what is the variance of (5 – 2x)?

(ii) There are 5 bags of wheat weighting on an average 102kgs and another 8 bags weighting 98kgs on an Average. What is combined mean of 13 bags?

11) (i) What is the coefficient of range for the following wages of 8 workers? Rs.80, Rs.65, Rs.90, Rs.60, Rs. 75, Rs. 70, Rs. 72, Rs.85.

(ii) Calculate S.D for first 10 natural numbers.

12) (i) Calculate M.D and Q.D if S.D = 60

(ii) Calculate S.D and Q.D if M.D = 60.                                                                                                                                  (ii) Calculate S.D and M.D if Q.D = 60; if the series are moderately asymmetrical.