This document contains a 25 question final exam for a statistics course. The questions cover a range of statistical topics including: [1] classifying variables, [2] separating variables into discrete vs continuous categories, [3] identifying quantitative vs qualitative variables, [4] determining which measure of central tendency to use, [5] the effect of adding or multiplying values on measures of central tendency, and [6] probability questions related to sampling, distributions, and experiments. Students are asked to calculate measures like mean, variance, and probability in several multi-part questions testing their understanding of fundamental statistical concepts.

1. IUBAT–INTERNATIONAL UNIVERSITY OF BUSINESS AGRICULTURE AND TECHNOLOGY
Final examination STA 240
Full marks: 100 Time: 3 hours
ID NAME MARKS
RETURN THE QUESTION PAPER ALONG WITH THE ANSWER SCRIPT AFTER THE EXAM
1. Classify the following into nominal(N), ordinal(O), interval(I) and ratio(R) :
Age of the pupils, Gender of the students, Health status, Academic degree, Hair
color, Weight, Disease status, Place of residence, Calendar time, IQ test score.
2. Separate the following variables into discrete(D) and continuous(C) :
Number of calls received in a day, Time taken to serve a customer, Weight of
a customer, Volume of a 3c.c. bottle of milk, Size of shoes produced by BATA
3. Indicate which variables are quantitative(Qn) and which are qualitative(Ql):
Number of persons in a family, Color of cars, marital status of people, Length
of frog’s jump, Number of students in the class
4. How do I know which measure of central tendency to use?
5. What will happen to the measures of central tendency if we add or multiply each
data value by the same amount?
6. The mean weight of three dogs is 38 pounds. One of the dogs, Sparky, weighs 46
pounds. The other two dogs, Eddie and Sandy, have the same weight. Find
Eddie's weight.
7. On his first 5 biology tests, Bob received the following scores: 72, 86, 92, 63, and
77. What test score must Bob earn on his sixth test so that his average for all six
tests will be 80?
8. Find CV for the series 1, 2, 3………………. 10.
9. When should we use coefficient of variation (CV)?
10. Prove that, AM ≥ GM ≥ HM.
11. Calculate AM for the following frequency distribution:
Shoe size (x) 1 2 3 4 5
No. of shoes (f) 10 5 10 5 6
12. A sample of 500 values has a mean of 4.50. Can it be reasonably regarded as a
sample from a normal population with mean 4.00 and standard deviation 2.00?

2. 13. p(x) = x 10 ; 0<x<1
A) Find E (X).
B) Also find V(X).
14. The number of persons X, in a family chosen at random has the following
probability distribution:
X 1 2 3 4
P(X) 0.2 0.5 m 0.1
A) Find the value of m.
B) Find the average family size E (X).
C) Also find V(X).
15. Explain random sampling with an example.
16. Explain cluster sampling with an example.
17. Interpret the following results :
a) r = 0 b) r = 1 c) r = - 1 d) r = - 0.50
18. Two coins are tossed; find the probability that
a) No tail is obtained.
b) Two tails are obtained.
19. Y = 10 + 5X. Interpret α and β. When X = 10, Y =?
20. Find out the AM and GM of your mobile number?
21. Vehicles pass through a junction on a busy road at an average rate of 500 per
hour.
a. What is the expected number passing in two minutes?
b. Find the probability that this expected number pass through in a given two-
minute period.
22. A jar contains 3 red marbles, 7 green marbles and 5 white marbles. If a marble is
drawn from the jar at random, what is the probability that
a) The marble is white?
b) The marble is either white or red?
23. Variance of 1st n natural numbers is 10. Find the value of n.
24. Discuss briefly about the sources of data.
25. A die is tossed 3 times. What is the probability of
a) No fives turning up? b) 2 fives?