1. TWO MARKS What are the common types of variables used in statistics?
1. Discrete random variables
Eg: X = 0,1,2,3
2. Continuous random variables
Eg: 3 ≤ X ≤ 6

2. Name a few descriptive measures of data
Mean
Median
Mode
Quartiles
Deciles
Percentiles

3. What are the elements and variables in a data set?
Qualitative Data, Quantitative Data, Chronological and Geographical Data
Variables :
1. Discrete random variables
Eg: X = 0,1,2,3
2. Continuous random variables
Eg: 3 ≤ X ≤ 6

4. Distinguish between qualitative and quantitative variables in statistics.
These are the variables which are measurable in nature such as age, income, height etc.
Qualitative Variables:
These are the variables which are non-measurable quality characteristics such as sex, honesty, literacy, blindness etc. It is sometimes called Attributes

5. What are the sources of collecting data?
Primary source
Secondary source

6. Give the mathematical definition of probability.
Probability is the chance of getting an event in an experiment.
Mathematically, probability is defined as
Total no. of Favourable Cases n(E)
P(E) = =
Total no. of Possible Cases n(S)

7. Define Binomial Distribution.
A discrete random variable X is said to follow Binomial distribution if its probability mass function is defined as
P(X=x) = nCx px qn-x ; x = 0, 1, 2, 3, . . .n
where n – no. of trials
x – no. of successes
p – probability of success
q – probability of failures

8. Define Poisson Distribution
A discrete random variable is said to follow Poisson distribution if its probability mass function is given by
e-λ λx
P(X=x) = ; x = o,1,2,3,….∞ x!

9. Give two examples of Poisson distribution
No. of air accidents in a particular aircraft
No. of deaths due to specific disease
No. of defective pieces in a batch of lots

10. Write any two properties of Normal distribution
Mean = Median = Mode
Coefficient of skewness = 0
Normal curve is symmetric one
It is a unimodal distribution

11. State Baye’s Theorem

12. Define conditional Probability

13. What are mutually exclusive/disjoint events?

14. What are independent and dependent events?

15. What are equally likely events?

16. The following information regarding the top ten Fortune 500 companies was presented in an issue of Fortune Magazine
Company
Sales $Millions
Sales Ranks
Profits $ Millions
Profits Rank
General Motors
161,135 1
2,956 30
Ford Motor
144,416 2
22,071
Wal-Mart Stores
139,208 3
4,430 14
Exxon
100,697 4
6,370 5
General Electric
100,469
9,269
Int’l Business machines
81,667 6
6,328
Citigroup
76,431 7
5,807 8
Philip Moris
57,813
5,372 9
Boeing
56,154
1,120 82
AT and T
53,588 10
6,398

17. How many elements are in the above data set?
How many variables are in this data set?
How many observations are in this data set?
Which variables are qualitative and which are quantitative?
What measurements scale is used for each variable?

18. The following data shows the yearly income distribution of a sample of 200 employees at MNM. Inc.
Yearly Income (in $1000s)
Number of employees
20 -24 2
25 -29 48
30 – 34 60
35 – 39 80 10

19. (i) What percentage of employees has yearly income of $35,000 or more?
(ii) Is the figure(percentage) that you computed in (i) an example of statistical inference? If no, what kind of statistics does it represent?
(iii) Based on this sample the president of the company’s aid that 45% of all our employees yearly income are $35,000 or more. The president’s statement represents what kind of statistics?
(iv) With the statement made in (iii) can we assure that more than 45% of all employees yearly income are atleast $35,000? Explain

20. (v) What percentage of employees of the sample has yearly income of $29,000 or less?
(vi) How many variables are presented in the above data set?
(vii) The above data set represents the results of how many observations?