# Statistics Regular Previous Year Question Paper Year 2006 : IIIrd Year Part II

**Q. 1**. (a) Discuss two situations when geometric mean would be the appropriate average to use.

(b) In a moderately skewed distribution, the value of mode is 120 and that of median is 140. Find the value of arithmetic mean.

(c) State the additive and multiplicative models of time series.

(d) Explain the concept of simple random sampling.

**Answer : **

**Q. 2.** (a) Distinguish between primary and secondary data. What precautions should be taken whiie collecting the secondary data ?

(b) The sales of a commodity (in ‘000 of Rs.) are given below:

**Year – Sales**

1999 – 82

2000 – 86

2001 – 81

2002 – 86

2003 – 92

2004 – 90

2005 , 99

(i) Using the method of least squares, fit a straight line trend; equation to the data.

(ii) What is the average annual change in the sales

(iii) Obtain the trend values for the years 1999-2005 and show that the sum of difference between the actual and the trend values is equal to zero.

(iv) What are the expected sales for the year 2010?

**Answer : **

**Q. 3.** (a) What is a variable? Distinguish between a continuous and a discrete variable with the help of two examples of each.

(b) Calculate Karl Pearson’s coefficient of correlation be¬tween the variables X and Y using the following data :

**X – Y **

25 – 10

40 – 25

30 – 40

25 – 15

10 – 20

05 – 40

10 – 28

15 – 22

30 – 15

20 – 05

(c) A purchasing agent obtained samples of lamps from two suppliers. He had the samples tested in his own laboratory for the length of life with the following results:

**Length of Life (in hours) – Samples from**

**Company A – Company B**

700—900 – 10 – 3

900—1100 – 16 – 42

1100—1300 – 26 – 12

1300—1500 __-______ ___8__-_____ 3_________

(i) Which company’s lamps have greater average life?

(ii) Which company’s lamps are more uniform?

**Answer : **

**Q. 4.** (a) Distinguish between positive and negative skewness. Draw rough sketches to show the position of mean, median and mode in each case. Also, explain the concept of Bowley’s coefficient of skewness.

(b) Represent the following data with the help of a suitable dia¬gram :

**Subject- ___________No. of Students________**

_______**_Stream_-_______________College A – College B-**

Arts – 1200 – 750

Science – 900 – 500

Commerce – 600 – 300

Vocational ___-_______300 __-______450

(c) An enquiry into the budgets of middle class families in a city gave the following information:

** Item – % Expenditure – Prices – Prices**

_______________________________(2004) – (2005)

Food – 35 – 140 – 170

Rent – 15 – 80′ – 90

Clothing – 20 – 110 – 130

Fuel – 10 – 60 – 80

Misc.___-________20_-____________90__-_________110

What change do you notice in the cost of living in 2005 as compared to 2004?

**Answer : **

**Q. 5.** (a) Discuss briefly the problems involved in the con¬struction of index numbers.

(b) The following table gives the distribution of weekly in¬come of 160 families in a town:

**Weekly Income (Rs.)___-__________No. of Families**

2000—4000 – 20

4000—6000 – 40

6000—8000 – 50

8000—12000 – 32

12000—16000 – 16

16000—20000__-______________ 2__________

(i) Calculate the lower and upper quartile income levels.

(ii) It is decided that 80% of the families should pay income tax. What is the minimum taxable income? 6

(c) A taxi travelled around a square at an overall speed of 80 kmph. If it travelled at an average speed of 60 kmph on the first side, at 80 kmph on the second side and at 120 kmph on the third side, what must have been the average speed on the fourth side ? Answer using an appropriate measure of central tendency.

**Answer : **