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

Name a few descriptive measures of data

• Mean• Median• Mode• Quartiles• Deciles• Percentiles

What are the elements and variables in a data set?

• Elements:– 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

Distinguish between qualitative and quantitative variables in statistics.

• Quantitative Variables:– 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

What are the sources of collecting data?

• Primary source• Secondary source

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)

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, . . .nwhere n – no. of trials

x – no. of successes p – probability of success q – probability of failures

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!

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

Write any two properties of Normal distribution

• Mean = Median = Mode• Coefficient of skewness = 0• Normal curve is symmetric one• It is a unimodal distribution

State Baye’s Theorem

Define conditional Probability

What are mutually exclusive/disjoint events?

What are independent and dependent events?

What are equally likely events?

The following information regarding the top ten Fortune 500 companies was presented in an issue of

Fortune MagazineCompany Sales $Millions Sales Ranks Profits $

MillionsProfits Rank

General Motors 161,135 1 2,956 30

Ford Motor 144,416 2 22,071 2

Wal-Mart Stores

139,208 3 4,430 14

Exxon 100,697 4 6,370 5

General Electric 100,469 5 9,269 3

Int’l Business machines

81,667 6 6,328 6

Citigroup 76,431 7 5,807 8

Philip Moris 57,813 8 5,372 9

Boeing 56,154 9 1,120 82

AT and T 53,588 10 6,398 4

• 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?

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

40 - 44 10

• (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

• (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?