CSS Statistics Past Paper 2025

Instructions specific to this paper

• First attempted Part-I (MCQS) on the separate OMR Answer Book which shall be taken back
• Overwriting/cutting of the options/answers will not be given credit.
• There is no negative marking. All MCQs must be attempted.
• Answers given anywhere else, other than the OMR Answer Sheet, will not be considered.
• Attempt ONLY FOUR questions from PART-II. ALL questions carry EQUAL marks.

Questions

1. Q. 210 marks

   (a) What is the purpose of frequency distribution and what are its desirable qualities? For a certain frequency distribution, the mean was 40.5 and the median 36. Find the mode approximately using the formula connecting the three. (b) Define Statistics. Discuss the importance of study of statistics by giving examples. How (10) (20) it can help the extension of scientific knowledge?

2. Q. 310 marks

   (a) Explain what is meant by the skewness of the distribution, and define a suitable measure of Skewness. For given p.d.f. f(x) = k(x-x²), 0≤x≤1 Find the Skewness and discuss. (b) Define the normal distribution and obtain its mean and variance. Show that for the (10) (20) normal distribution, the mean, mode and median are the same.

3. Q. 410 marks

   (a) If X has a binomial distribution, then show that E(X) = np, Var(X) = npq. Derive the m.g.f of the binomial distribution and explain its uses? (b) What are the main characteristics of the Poisson distribution? Explain with the help of (10) (20) examples. Also give its properties, applications and relationship with other distributions. Q. No. 5.(a) From the following set of values: (10) Y 6.5 5.3 8.6 1.2 4.2 2.9 1.1 3.0 X 3.2 2.7 4.5 1.0 2.0 1.7 0.6 1.9 1) Compute the residuals and verify that they add to zero and draw the conclusion about the results. 2) Compute the standard error of estimate, Sy.x (b) Under what conditions the correlation among the random variables exists. Also describe (10) (20) the properties of correlation coefficient. Calculate the correlation co-efficient for a sample of 20 pairs of observations, given that Mean of X = 2, Mean of Y = 8, ΣΧ² = 180, ΣΥ² = 1424 and ΣΧΥ = 404 Also interpret its results.

4. Q. 610 marks

   (a) What is finite-correction factor? When is it appropriately used in sampling applications and when can it, without the great undesirable consequences, be ignored? (10) (20) (b) Given the population 2, 4, 8, 8, 10, 10. 1) How many samples of size n = 2 can be drawn without replacement from this population? 2) Compute and tabulate the sampling distribution of the mean for samples of size n = 2.

5. Q. 710 marks

   (a) Explain what is meant by: (i) a statistical hypothesis, (ii) test-statistic, (iii) test of significance, (iv) level of significance, (v) type-I error and type-II error (b) The weights of 4 persons before they stopped smoking and 5 weeks after they stopped (10) (20) smoking are as follows: Person 1 2 3 4 Before 148 176 153 116 After 154 176 151 121 Use the t-test for paired observations to test the hypothesis at the 0.05 level of significance, that giving up smoking has no effect on a person's weight.

6. Q. 810 marks

   (a) Explain the procedure of randomization in a completely randomized design where we have 3 varieties of wheat and 18 experimental plots available. Also explain what is explained by significant F value in an experiment. (b) Four varieties of wheat were tried in a randomized complete block design in four (10) (20) replications. Yield in kilogram per plot is shown in the table given below. Test the hypothesis that there is no difference in the means of four varieties. α = 0.05. Replicates Varieties V1 V2 V3 V4 I 2 5 4 1 II 2 3 3 1 III 4 6 6 2 IV 1 4 2 3

Standard FPSC instructions

Printed on this and every CSS paper.

• Part-II is to be attempted on the separate Answer Book.
• All the parts (if any) of each question must be attempted at one place instead of at different places.
• Write Q. No. in the Answer Book in accordance with Q. No. in the question paper.
• No page/space be left blank between the answers. All the blank pages of the Answer Book must be crossed.
• Extra attempt of any question or any part of the attempted question will not be considered.