University of Delhi 2006-3rd Year B.Com Statistics Year : Part II - Question Paper

Statistics Year 2006 : IIIrd Year Part II



Q. 1. (a) explain 2 situations when geometric mean would be the improper avg. to use.
(b) In a moderately skewed distribution, the value of mode is 120 and that of median is 140. obtain the value of arithmetic mean.

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

(d) discuss the concept of simple random sampling.


Q. 2. (a) Distinguish ranging from 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 provided below:
Year - Sales
1999 - 82
2000 - 86
2001 - 81
2002 - 86
2003 - 92
2004 - 90
2005 , 99

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

(ii) What is the avg. annual change in the sales

(iii) find the pattern values for the years 1999-2005 and show that the sum of difference ranging from the true and the pattern values is equal to zero.

(iv) elaborate the expected sales for the year 2010?


Q. 3. (a) What is a variable? Distinguish ranging from a continuous and a discrete variable with the help of 2 examples of every.

(b) compute Karl Pearson’s coefficient of correlation be¬tween the variables X and Y using the subsequent 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 found samples of lamps from 2 suppliers. He had the samples tested in his own laboratory for the length of life with the subsequent 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 avg. life?

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


Q. 4. (a) Distinguish ranging from positive and negative skewness. Draw rough sketches to show the position of mean, median and mode in every case. Also, discuss the concept of Bowley’s coefficient of skewness.

(b) Represent the subsequent 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 subsequent 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 residing in 2005 as compared to 2004?



Q. 5. (a) explain briefly the issues involved in the con¬struction of index numbers.

(b) The subsequent table provide 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) compute 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 avg. speed of 60 kmph on the 1st side, at 80 kmph on the 2nd side and at 120 kmph on the 3rd side, what must have been the avg. speed on the 4th side ? ans using an improper measure of central tendency.

Earning:   Approval pending.