Business statistics solved numericals

Business statistics solved numericals

1. Business Statistics NMBA015 Previous Years’ Questions (Numerical) Unit I

2. Measures of Central Tendency

3. Measures of Central Tendency Mean: 3 (2006, 2007, 2010) Median: 1 (2007) Missing Frequency: 1 (2009) Combined Mean: 1 (2009) Quartiles, Deciles , Percentiles: 1 (2012) Total: 7

4. Find the arithmetic mean and standard deviation from the following data. Also find coefficient of variation. (2006) Age (less than): 10 20 30 40 50 60 70 80 No. of persons : 15 30 50 75 100 110 115 125

9. Compute mean and median from the following data: (2007) Income more than (in Rs.): 1000 2000 3000 4000 5000 6000 7000 8000 No. of persons : 72 67 59 50 36 29 4

15. An incomplete frequency distribution is given as follows. Given that the median value is 46, determine the missing frequencies using the median formula. (2009) Variable 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Total Frequency 12 30 ? 65 ? 25 18 229

19. The mean annual salary of employees of a company is Rs.30000. The mean annual salaries of male and female employees are Rs.35000 and Rs.23000, respectively. Find out the percentage of male and female employees working in the company. (2009)

22. 8 coins are tossed at a time, 256 times. The actual results of getting the numbers of heads are as follows . Find out expected frequencies. Also calculate mean and standard deviation. (2010) No. of Heads: 1 2 3 4 5 6 7 8 Total Frequency: 2 6 30 52 67 56 32 10 1 256

23.   -8 -3 -18 -2 -60 -1 -52 1 56 2 64 3 30 4 4     -8 -3 -18 -2 -60 -1 -52 1 56 2 64 3 30 4 4      

24. -8 16 32 -3 -18 9 54 -2 -60 4 120 -1 -52 1 52 1 56 1 56 2 64 4 128 3 30 9 90 4 4 16 16       -8 16 32 -3 -18 9 54 -2 -60 4 120 -1 -52 1 52 1 56 1 56 2 64 4 128 3 30 9 90 4 4 16 16        

25. Find the Q3, D7 and P69 of the following: (2012) Variable 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 7 12 18 25 16 14 8

30. Measures of Dispersion

31. Measures of Dispersion Standard Deviation: 3 (2004, 2006, 2010) Coefficient of Variation: 4 (2005, 2006, 2008, 2012) Total: 7

32. Calculate standard deviation from the following data : (2004) Age in years: 4-6 6-8 8-10 10-12 12-14 14-16 16-18 No. of students: 30 90 120 150 80 60 20

35. Find the coefficient of variation, if the sum of squares of the deviations of 10 observations taken from mean 50 is 250. (2005)  

36. Find the arithmetic mean and standard deviation from the following data. Also find coefficient of variation. (2006) Age (less than): 10 20 30 40 50 60 70 80 No. of persons : 15 30 50 75 100 110 115 125

41. Share prices of two companies A Ltd. and B Ltd. were recorded as follows. Which company’s share prices are more variable ? (2008, 2012) A Ltd. 12 13 15 14 14 14 13 17 B Ltd. 113 114 113 115 117 114 112 114

48. 8 coins are tossed at a time, 256 times. The actual results of getting the numbers of heads are as follows . Find out expected frequencies. Also calculate mean and standard deviation. (2010) No. of Heads: 1 2 3 4 5 6 7 8 Total Frequency: 2 6 30 52 67 56 32 10 1 256

49.   -8 -3 -18 -2 -60 -1 -52 1 56 2 64 3 30 4 4     -8 -3 -18 -2 -60 -1 -52 1 56 2 64 3 30 4 4      

50. -8 16 32 -3 -18 9 54 -2 -60 4 120 -1 -52 1 52 1 56 1 56 2 64 4 128 3 30 9 90 4 4 16 16       -8 16 32 -3 -18 9 54 -2 -60 4 120 -1 -52 1 52 1 56 1 56 2 64 4 128 3 30 9 90 4 4 16 16        

51. Measures of Skewness and Kurtosis

52. Measures of Skewness and Kurtosis Skewness : 2 (2008, 2010) Kurtosis: 1 (2010) Total : 3

53. Compute an appropriate measure of skewness for the following data: (2008) Sales (Rs. lakhs): Below 50 50-60 60-70 70-80 80-90 90-100 10-110 110-120 Above 120 No. of Companies: 12 30 65 78 80 55 45 25 10

60. Find the measure of skewness and kurtosis on the basis of moments for the following distribution: (2010) Marks: 5-15 15-25 25-35 35-45 45-55 No. of Students: 1 3 5 7 4