Statistics exam (MS 201) from the 2024 Level-2 Term-I finals, BUTEX affiliated colleges. Questions include frequency table construction for student marks, standard deviation properties, central moment calculations, additive probability laws, and binomial distribution proofs.
Level-2 Term-I, Final Exám-2024
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) Define Statistics. Discuss application of the subject statistic in different fields.
(b) Write difference between primary data and secondary data.
(c) Discuss method of primary data and secondary data collection.
[(1+4)+3+4 = 12]
2. (a) What do you mean frequency distribution table?
(b) Construct a frequency distribution with the suitable class interval size of marks obtained by 50 students of a class, which are given below: 23, 50, 38, 42, 63, 75, 12, 33, 26, 39, 35, 47, 43, 52, 56, 59, 64, 77, 15, 21, 51, 54, 72, 68, 36, 65, 52, 60, 27, 34, 47, 48, 55, 58, 59, 62, 51, 48, 50, 41, 57, 65, 54, 43, 56, 44, 30, 46, 67, 53.
(c) Write down difference between Histogram and Bar graph.
[2+6+4 = 12]
3. (a) Define standard deviation. Prove that standard deviation is independent on change of origin but not of scale.
(b) Prove that the standard deviation of first n natural numbers is .
(c) Define moment. Find the 1st to four central moment from the following distribution.
Class interval | 0-4 | 4-8 | 8-12 | 12-16 | 16-20 |
Frequency | 2 | 3 | 4 | 2 | 1 |