BUSINESS STATISTICS

(2005 onwards)

Time : Three hours Maximum : 100 marks

SECTION A — (5 ? 8 = 40 marks)

Answer any FIVE of the following.

All questions carry equal marks.

1. Mention the uses of statistics in various fields.

2. Narrate the characteristics of a good average.

3. Calculate the median from the following data :

Marks : 0–20 20–40 40–60 60–80 80–100

No. of students : 5 15 30 8 2

4. Find the mean deviation from median and its coefficient from the following data :

X : 10 11 12 13 14

Y : 3 12 18 12 3

5. Define skewness. Explain various measures.

6. What is rank correlation? State its merits.

7. What are the characteristics of index number?

8. What do you mean by interpolation?

SECTION B — (4 × 15 = 60 marks)

Answer any FOUR of the following.

All questions carry equal marks.

9. (a) The mean height of 25 male workers in a factory is 61 inches and the mean height of 35 female workers in the same factory is 58 inches. Find the combined mean height of

60 workers in the factory.

(b) The mean marks of 100 students were found to be 40. Later on, it was discovered that a score of 53 was misread as 83. Find the correct mean corresponding to the correct score.

10. Find the standard deviation for the following distribution :

Variable (V) : 0–5 5–10 10–15 15–20 20–25 25–30 30–35 35–40

Frequency (f) : 2 5 7 13 21 16 8 3

11. Calculate the coefficient of skewness.

X : 0 1 2 3 4 5 6 7

Y : 12 27 29 19 8 4 1 0

12. Define correlation. Explain its types.

13. In a competition the ranks of three judges are as follows. Decide which pair have nearest approach (use rank correlation).

Judge A : 1 5 4 8 9 6 10 7 3 2

Judge B : 4 8 7 6 5 9 10 3 2 1

Judge C : 6 7 8 1 5 10 9 2 3 4

14. Compute Fisher's ideal index from the following data :

Item 2005 2006

Price Quantity Price Quantity

A 6 50 10 56

B 2 100 2 120

C 4 60 6 60

D 10 30 12 24

E 8 40 12 36

15. Fit a straight line trend by the method of least squares for the following data and estimate the earnings for the year 2008.

Year : 1999 2000 2001 2002 2003 2004 2005 2006

Earnings (in crores) : 38 40 65 72 69 60 87 95