# Statistics External & Correspondence Previous Year Question Paper Year 2005 : IIIrd Year Part II

**Q. 1. **(a) The arithmetic mean of the marks obtained by 50 students was calculated as 44. It was later discovered that a score of 36 was misread as 56. Find the correct value of the arithmetic mean of the marks obtained by the students.

(b) The arithmetic mean and standard deviation of two brands of light bulbs are given below:

** Brand I ** – **Brand II**

Arithmetic mean – 800 hours – 770 hours

Standard deviation – 100 hours – 60 hours

Calculate coefficient of variation for the two brands.

(c) In a moderately asymmetrical distribution, the mode and mean are 32.1 and 35.4 respectively. Find the value of median.

(d) “An index number is a specialised type of average.” Explain.

(e) Distinguish between positive and negative correlation,

**Answer : **

**Q. 2**. (a) What is statistics ? Discuss its importance in business.

(b) From the following data, calculate Karl Pearson’s coefficient

of correlation.

**Height of Fathers (inches**) – **Height of Sons (inches)**

66 – 65

68 – 64

69 – 67

72 – 69

65 – 64

59 – 60

62 – 59

67 – 68

61 – 60

71 – 64

(c) From the following data, calculate Bowley’s coefficient of

skewness.

**No. of Children per Family – No. of Families **

0 – 7

1 – 10

2- 16

3 – 25

4 – 18

5 – 11

6 – 8

**Answer : **

**Q. 3. **(a) Explain the various methods of collecting primary data ind point out their relative merits and demerits. 6

(b) From the following data, calculate standard deviation: 8

**x – f**

10 – 2

11 – 7

12 – 10

13 – 12

14 – 15

15 – 11

16 – 10

17 – 6

18 – 3

(c) Represent the following data by a sub-divided bar diagram.

**Years ** – 1998 – 1999 – 2000- 2001- 2002

,

**No. of
government
companies- ** 322- 674 – 867 – 1034 – 1170

**No. of nongovernment
companie -** 31- 45 – 66 – 133 – 223

**Total -** 353 – 719 – 933 – 1167 – 1393

**Answer : **

**Q. 4**. (a) What is a sample survey ? Discuss its merits and demerits.

(b) Fit a straight line trend to the following data and estimate the likely profit for the year 2003. Also calculate the trend values. 10

**Year – Profit
(in lakhs of Rs.)**

1994 – 60

1995 – 72

1996 – 75

1997 – 65

1998 – 80

1999 – 85

2000 – 95

(c) The population of a country increased by 20% in the first decade, 30% in the second decade and 45% in the third decade. Find the average rate of increase in population per decade.

**Answer : **

**Q. 5**. (a) Explain the meaning and objectives of time series analysis.

(b) From the following data, prove that Fisher’s ideal index satisfies the time reversal test and the factor reversal test:

**Base Year_____________Current Year**

**Commodity – Price – Quantity – Price – Quantity **

A- 6 – 50 – 10 – 60

B – 2 – 100 – 2 – 120

C_-_________ 4__-___0 – _ __6__-_____60

(c) From the following data, calculate Spearman’s coefficient of correlation:

**Sales Advertisement
(in lakhs of Rs.) Expenditure
(in lakhs of Rs.)-**

56 – 40

56 – 36

39 – 30

54 – 44

45 – 36

40 – 32

56 – 45

60 – 42

30 – 20

36 – 36

**Answer :**