Statistics paper (MS 201) from the 2023 Level-2 Term-II finals at BUTEX affiliated colleges. Questions include mean, median and mode for grouped defect data, geometric mean uses, standard deviation for television life expectancy, skewness, kurtosis, and probability axioms.
Level-2 Term-II, Final Exám-2023
Subject: Statistics (Code: MS 201)
Time: 3.0 Hrs. Full Marks: 72
(Use separate answer script for Part: A and Part: B)
(All parts of a question must be answered consecutively)
Part: A
(Answer any three questions)
1. (a) What is meant by statistics? Distinguish between population and sample.
(b) For two non-zero observations show that A.M ≥ G.M ≥ H.M.
(c) The production of defective bulbs in different days in an industry are shown below:
Class interval of defective bulbs | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 | Total |
No. of days | 12 | 8 | 16 | 20 | 4 | 60 |
(i) Calculate average number of defective bulbs produced per day.
(ii) Find median number of defective bulbs.
(iii) Find mode distribution of defective bulbs.
[3+3+6=12]
2. (a) Define Geometric mean. Discuss merits, demerits and uses of geometric mean.
(b) The table below shows the distribution of life expectancy of televisions manufactured by a specific company which were bought in a certain area:
Length of lives (in years) | 1-3 | 3-6 | 6-9 | 9-12 | 12-15 | 15-18 | 18-20 |
No. of televisions | 10 | 15 | 29 | 45 | 53 | 21 | 7 |
Calculate the mean deviation and standard deviation for the distribution of live expectancy.
(c) Write short notes on (i) skewness and (ii) kurtosis
[4+4+4=12]
3. (a) Define standard deviation. For any two observations, prove that standard deviation is the half of the range.
(b) Prove that standard deviation is independent on change of origin but not of scale.
(c) Find median and mode from the frequency distribution given below.
Class interval |