Ques 1.

Calculate the mean and standard deviation for the following data:

Ques 2.

Given the following sample of 20 numbers: 
15 45 52 43 50 59 41 47 56 79 72 18 45 54 78 12 41 48 58 14
(i) Compute mean, variance and standard deviation.
(ii) If the largest value in the above set of numbers is changed to 500, to what extent are the mean
and variance affected by the change? Justify your answer.

Ques 3.

(a) Write two merits and two demerits of Median.
(b) An incomplete frequency distribution is given as follows
12 30 ? 65 25 18

Given that median value of 200 observations is 46, determine the missing frequencies using the median formula.

Ques 4.

Box X contains 5 red and 4 blue balls, Box Y contains 2 red and 5 blue balls. A ball is drawn at random from each box. Find the probability of drawing one red and one blue ball.

Ques 5.

A Manager of a car company wants to estimate the relationship between age of cars and annual maintenance cost. The following data from six cars of same model are obtained as:

(a) Construct a scatter diagram for the data given above. 
(b) Fit a best linear regression line, by considering annual maintenance cost as the dependent
variable and the age of the car as the independent variable. 
(c) Use this regression line to predict the annual maintenance cost for the car of age 8 years

Ques 6.

Suppose A and B are two independent events, associated with a random experiment. If the probability of occurrence of either A or B equals 0.6; while probability that only A occurs equals 0.4, then determine the probability of occurrence of event B.

Ques 7.

A chemical firm wants to determine how four catalysts differ in yield. The firm runs the experiment in three of its plants, types A, B, C. In each plant, the yield is measured with each catalyst. The yield (in quintals) are as follows:

(a) Perform an ANOVA and comment whether the yield due to a particular catalyst is
significant or not at 5% level of significance. Given F3,6= 4.76. (5)
(b) Construct ANOVA table for one-way classification.

Ques 8.

Explain the following with the help of an example each: 
a) Binomial distribution
b) t-test for mean
c) Properties of good estimator
d) F-test for Equality of two variances