QUANTITATIVE METHODS

General:

Overall performance of the candidates was quite satisfactory. Most of the questions were successfully attempted by a large number of the candidates. Major reason for failure is the lack of understanding of the concepts. More emphasis should be laid on this aspect of the subject in teaching.

Question-wise comments are as under:

Q.1

In part (a) the first step was to form a relationship between the interest earned on stocks yielding 4%, 5% and 8%. This could have been done either by using a single variable or by using three variables. Majority of the students failed to apply simple logic to determine the above. However, many students did manage to secure full marks.

In part (b) of the question, quite a large number of the candidates were unable to take the first step of taking 1/3^x as equal to (3)^-x before taking the log on both sides. Some of them did not know that log of 1 is zero; others unnecessarily made things complicated by breaking down 12 into 2 x 2 x 3. However, quite a large number of the candidates successfully solved this part.

Q.2

Part (a) was quite simple i.e. finding the thirteenth term of the Arithmetic Progression (AP). Most of the candidates got full marks for this part. However, some of the candidates calculated total number of seats, instead of finding the number of seats in the 13^th row. It showed that the candidates wrote the formulas and applied them without knowing whether or not these are appropriate. Part (b) of the question was not properly tackled by a considerable number of the candidates. Some of them did not know the meaning of simple discount, others were unable to convert nine months into year(s).

Q.3

In part (a) of the question, the candidates were first required to determine the amount left after two years’ loss. Majority of them failed to calculate this amount. Perhaps they are familiar with the determination of the future amount with profit but not with loss. However, a large number of the candidates adopted the correct procedure for the second part, they were awarded marks for this part if it was correctly done.

Part (b) of the question was a straightforward question of determining the present value of equal quarterly payments. Majority of the candidates did obtain full marks for this part of the question. However, some of them used the formula for finding the future value of an annuity and got it all wrong.

Q.4

(a)

Most of the candidates were able to demonstrate their understanding on Differentiation of functions. Majority of the students attempted it correctly whether they used the chain rule method or not.

(b)

Again almost all the students attempted this question but a few got confused with the differentiation of quotient.

Q.5

The marginal cost estimation through differentiation of cost function was done by almost all the students and many of them did it correctly. But it was felt that the concept was not very much clear to all the candidates which was evident from the fact that only a few were able to calculate the actual marginal cost and worked out the difference with the estimated one. The concept of average cost function was however, clear to most of the students.

Q.6

Part (a) of the question was very simple, if the candidates knew that for two equal matrices, corresponding elements of both are equal. Majority of the students gave correct answers.

In part (b), majority of the candidates correctly computed the values of PQ, QC and PQC but only a small number of them gave correct interpretations for these values.

Q.7

In this question, the candidates were required to calculate a weighted price index using Laspeyre’s formula and index of value. They were also required to interpret their results. Majority of the candidates computed the price index but only few could correctly calculate the value index. Only a small number of the candidates gave the interpretation of their results. This clearly shows that the candidates are not aware of the meaning of these indices and therefore it would be difficult for them to apply these indices in the real world situations/settings.

Q.8

Majority of the candidates were successful in arriving at the correct value of ‘r’, the linear correlation co-efficient. Some students assigned a positive sign to ‘r’ which was incorrect. A positive value of r meant that with the increasing age of the cars, their prices, on the average, would also increase which is against common sense.

One of the basic principle about r is that its value ranges between –1 and 1, yet a number of candidates obtained answers much beyond these limits.

(b)

The major mistake which most of the candidates made was that they added the ⁸C2 , ⁶C2  and ¹⁰C2  values instead of multiplying them.

Q.9

(a)

Almost half of the students were able to attempt this question of probability correctly. Some got confused with the application of correct formula while others were not quite clear of the concept. Some students were not clear about the terms “Exactly one” and “At least one”

(b)

Majority of the candidates calculated mean and standard deviation correctly, however only about half of them were able to do the questions on probability correctly. A common mistake which many students made was that they calculated the probability of x £ 4 instead of x < 4.

(c)

Quite a good number of students did apply the hypergeometric distribution for calculating the probability and got the correct answer.

Q.10

In part (a) of this question, the candidates were required to state the formula of standard error for infinite population and then substituting values of 60 and 240, (240 being 4 times of 60) to conclude that the standard error will be halved. This simple point that if sample size is increased four fold, standard error will only be reduced to one half was missed by a very large number of the candidates. Majority of the candidates only mentioned that standard error would be reduced but only a few of them indicated to what extent.

In part (b) of the question, candidates were required to answer four queries, all relating to hypothesis testing. The first three were answered correctly by a significant number of the candidates but part (iv) was rarely attempted.

Namely P-value for right tailed test = Pr(z>2) = 0.5 minus area for z=2. In the first three parts, the candidates generally committed the following mistakes.

(1)

Alternative hypothesis was not correctly stated : it was one tailed test but was treated as two-tailed test.

(2)

Correct Z value could not be ascertained.

(3)

Reason for using Z distribution i.e. n >30, was not given by most of the students. . Some of the candidates stated the reason that since s is given they would use Z distribution but this was not correct as sample standard deviation (s) was given and not the population standard deviation (s).

Q.11

Only a small number of the candidates attempted this question, and only a few of those who attempted gave the correct solution. Some of the candidates did not know that the question relates to proportions/percentages. They treated it as the question of difference of means.