RAWALPINDI BOARD 2016
PAPER STATISTICS PART-1
Time: 20 Minutes
(Objective Part)
Note: Four Answers are given against each column A,B,C&D. Select the. Write answer and only separet answer sheet.

Fill the circle A,B,Cor D with pen or marker in front of that question number.

• A quantity computed from a population is called:

(a) Constant
(b) Variable
(c) Parameter
(d) Statistic

• The process of systematic arrangement of data into rows and Columns is called:

(a) Classification
(b) Tabulation
(c) Stub                         
(d) Box-head

• The graph of a cumulative frequency distribution is known as:

(a) Histogram
(b) Ogive         
(c) Pie-chart
(d) None of these

• The meditscof the data -2, 0, 2, 5, -1 is:

(a) 2   
(b) 4
(c) 0
(d) -2

• Which of the following average can have more than one value.

(a) Mean
(b) Median
(c) Mode 
(d) G.M

• The first moment about mean is:

(a) Mean
(b) Zero
(c) One 
(d) Variance

• If    = 10 and Q3 = 30 , then coefficient of quartile deviation is:

(a) 3    
(b) 1/2  
(c) 2/3   
(d) 1

• When A >3 then the distribution is called:

(a) Mesokurtic 
(b) Platy
(c) Lepto kurtic
(d) Normal

• Current year quantities are used as weights in:

(a) Laspeyre's
(b) Paasche's
(c) Fisher's
(d) Chain index numbers

• In chain base method the base period is:

(a) Fixed
(b) Not fixed
(c) Constant
(d) None of these

• If two dice are rolled, the possible outcomes are:

(a) 6
(b) 36 
(c) 1
(d) 16

• If A and B are two mutually exclusive events, Then P(Arl B) =

(a) 1/2   
(b) 1  
(c) a
(d) 0

• For a continuous variable "x" L (x)dx =?

(a) 2
(b) Zero
(c) 1  
(d) co

• If x is a random variable then E(5x+2) is:

(a) 5 E(x)  
(b) 5 E(x)+2
(c) 5+E(x)
(d) 2 E(x)+5

• Binomial distribution has parameters:

(a) 2
(b) 3
(c) P
(d) c72

• In hypergeometric distribution, the successive trails are:

(a) Independent  
(b) Dependent
(c) Some times independent  
(d) None of these

• The mean of the hypergeometric distribution is: nN  n+ k  nk Nk

(a) k
(b) N   
(c) K    
(d) N

 Time: 2:40 Hours
(Sujective Part)
Marks:
SECTION-I

2. Write short answers of any Eight Parts.16

• Define descriptive statistics.
• Define Secondary data.
• Define weighted mean. 
• Define harmonic mean.
• Define weighted index number.
• What are quantity index numbers?
• Define a value index number.
• Write the formula for Fisher's Index Number.
• Describe the empricial relation between mean, median and mode.
• The sum of deviations of 15 values from 20 is 45. Find A.Mean.
• For a certain distribution if E(x-15)=5,E(x-18)=0 an E(x - 21) = -21, what is the value of mean and Why?
• How many methods are used for selection of base period?

3. Write short answers of any Eight Parts. 16

• What will be the coefficient of variation = 75000,E tv = 2500 and Ef = 100
• For any two events 'A' and 'B' the probability of A = 0.6 as probability of B=0.8. Find P(AUB).
• What is tabulation?   
  
• What is frequency polygon?
• Define the term disperssion.
• If var(x)=--16, then find var(2x) and var(3x-20).
• Define moments.
• What do you know about skewness?
• Give the Bowley's formula of coefficient of skewness.
• Write mathematical definition of probability.
• What are equally likely events?
• From a pack of 52 cards, find the probability of a black card.

4.Write short answers of any Six Parts.12

• What is meant by mathematical expectation of a random variable?
• A random variable 'x' has a binomial distribution with n = 5 and p=0.2. Find P(x=2).
• Write down parameter, mean and variance of hypergeometric distribution.    
• Define continuous random variable.
• Write down any four laws of mathematical expection.
• Define continuous random variable.
• Given X=0, 1,2 and P(x)=5/40, 25/40, 10/40. Find E(x).
• Define Bernoulli trial.
• Given N = 10, n = 2 and k = 3. Find P(x=0).

SECTION-I

Attempt any `questions. Vac!). questions'iaitties-8. marks.

 5.(a) Find the geometric mean from the following frequency distribution.

(b)Reciprocals of 8 values of x are 0.0667,0.1111, 0.0833,
0.0556, 0.0500, 0.0357, 0.0278, 0.0222. Calculate median of x.

6.(a) Find the coefficient of S.D. from the following data.

(b) In a frequency distribution, the coefficient of skewness is 0.6.
If the sum of upper and lower quartiles is 100 and median is
38. Find the value of the upper quartiles.

7.(a) Calculate Index number of prices taking the average of the
price of 1st 5 years as base year from the following data.

(b) Two good dice are rolled. Find the probability of:

• The sum is exactly seven
• The two dice show the same number.

8.(a) Probabi ity distribution of a random variable (x) is given as:

Find the value of 'a' (ii) Findprobability distribution of Y=3

(b) Find E(x) and Var(x) for following probability distribution.

9.(a) An events has probability P=2/5. Find the complete binomial
distribution when n=4.

(b) Given that 'x' is .a hypergeometric random variable with N=8,
n=3 and k=5. Compute P(x s 3).