1. What is a Binomial Distribution? What are its Mean and Variance? Highlight its relation with Normal Distribution.

What are the characteristics of a good Central Tendency?

Calculate Arithmetic Mean and Median from the following frequency distribution. Also obtain the value of Mode from the value of arithmetic mean and median without calculating it separately.

Height No. of persons
60 -63 8
63 -66 28
66 -69 118
69 -72 66
72 -75 16
75 -78 4

Describe the method of fitting polynomials.

Fit a straight line trend by the method of least squares.

Year 2003 2004 2005 2006 2007 2008 2009
Output 81 92 100 105 112 120 126

4. What are the advantages and disadvantages of sampling? Explain the procedure of drawing a simple random sample without replacement.

5. Distinguish between the concepts of regression and correlation. Estimate the linear regression y a +bx from the following data

x 2 3 4 5
Y 5 3 8 7

6. Compute standard deviation using the following data:

Class Interval 4-5 6-7 8-9 10 -11 12 -13 14 -15
Frequency 4 10 20 15 8 3

7. What is t -test? How is it used to examine the significance of the difference between two samples?

8. Discuss the desirable properties of an estimator.

9. A machine produces ball bearings with diameter 0.5 inches. The standard deviation of ball bearings is known to be 0.005 inches. A sample of 100 ball bearings is selected and their average diameter is found to be 0.498 inches. Determine the 99 per cent confidence interval.

10. From the data calculate Fisher's ideal index and show that it satisfies time reversal test.

2010 2011
Good Price Qnty. Price Qnty.
A 12 20 14 30
B 14 13 20 15
C 10 12 15 20
D 6 8 4 10
E 8 5 6 5

11. There are 3 boxes. Box A contains 10 bulbs of which 4 are defective. Box B has 6 bulbs of which 1 is defective and in Box C out of 8 bulbs 3 are defective. We select a box at random and a bulb is drawn from it. What is the probability that it is defective?

12. Write a short note on rank correlation coefficient.

13. Distinguish between Type and Type -II errors.

14. Prove that the sum of squares of the deviations of a given set of observations taken from their arithmetic mean is minimum.