## Thursday, June 1, 2023

• Thursday, June 01, 2023
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Paper BBA-122

Time Allowed: Three Hours] [Maximum Marks: 80

Note: (1) Attempt any four questions from Section A.

(2) Attempt two questions each from Section B and Section C respectively.

SECTION-A

1. Discuss the important functions of Statistics.

2. Calculate the three years monthly moving averages from the following data:

January                    57

February                 65

March                     63

April                      72

May                       69

June                       78

July                        82

August                  81

September            90

October                92

November           95

December            97

3. Seven students obtained the following ranks in Maths and Statistics. Find their rank correlation.

Rank in Maths 7 1 4 6 5 3 2

Rank in Statistics:     5 1 2 3.5 3.5 7 6

4. Define geometric mean. What are its merits and demerits?

5. Compute coefficient of Quartile Deviation from the following data:

Students No. 4 7 15 8 7 2
Marks 10 20 30 40 50 80

6. Calculate Karl Pearson's coefficient of Skewness:

Measure                         Place A Place B
Mean                 256.5 240.8
Median                 201.1 201.6
Standard Deviation. 215.0         181.0

SECTION-B

7. (a) State the various uses of statistics in business.

(b) From the data given below, find the mean, median, mode.

Marks No. of Candidates
1-5         7
6—10 10
11-15 16
16-20 30
21-25 24
26-30 17
31-35 10
36-40 5
41-45 1

8. Find Karl Pearson's coefficient of correlation:

Age of Husband Age of Wife
(in years)                 (in years)
20                     18
22                     20
23                     22
25                     24
25                     21
28                     26
29                     26
30                     25
30                     27
34                     29

9. From the following information :

Mean                            20 100
Standard Deviation                             5 12
Correlation Coefficient                                 0.8

(a) Calculate two regression lines.

(b) Find the likely sales when advertisement expenditure is Rs. 25 crores.

10. (a) The arithmetic mean and standard deviation of a series of 20 items were calculated by a student as 20 cm and 5 cm respectively. But while calculating an item 13 was misread as 30. Find the correct arithmetic mean and standard deviation.

(b) Find the missing frequency from the following data when:
11. (a) Explain and illustrate the difference between fixed base and chain base index numbers.

(b) From the following data, construct a cost-of-living index number by using family budget method for 2016 with 2006 as base year:
12. (a) Highlight the importance of Time Series analysis for a business.

(b) Fit a straight-line trend by the method of least squares and also calculate the trend values from the following data:

Year Production
2010 12
2011 10
2012 14
2013 11
2014 13
2015 15
2016 16

13. (a) State and explain the uses of index numbers.

(b) Calculate Fisher's index from the following data and prove that it satisfies both the time reversal and factor reversal tests :

Commodity 2015 2016
Price             Expenditure     Price Expenditure
A 8                           80     10     120
B 10                 120     12     96
C 5                            40     5     50
D 4                           56     3     69
E 20                         100    25    150

14. Calculate Bowley's coefficient of skewness when:

Age No. of Person  (in years)
20-25 50
25-30 70
30-35 80
35-40 180
40-45 150
45-50 120
50-55 70
55-60 50