Inter (Part-I) Dera Ghazi Khan Board 2015
Statistics
Part I (Objective Type)
Time Allowed: 20 Minutes 
Max. Marks: 17

Note: You have four choices for each objective type question as A, B, C and D. The choice which you think is correct; fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question.

Question #1
Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• Statistical laws are true

(A)  On the average
(B) Always   
(C) In the long run
(D) A and C

• A graph of a cumulative frequency .distribution is called

(A) Histogram   
(B) Frequency polygon.     
(C) Ogive
(D) None of these

• The process of ranging data into rows and column is called

(A) Frequency distribution
(B) classification
(C) Tabulation
(D) Array

• The sum of derivations from arithmetic mean is

(A) 0    
(B) 1         
(C) 2              
(D) 3   

• The most frequent value of the data if it exists is

(A) A.M
(B) G.M   
(C) Made      
(D) Median

• The mean deviation or dispersion can be negative

(A) Never
(B) Always
(C) Sometimes
(D) Often

• The variance of 5, 5, 5, 5, 5 is

(A) 25
(B) 125
(C) 5
(D) 0  

• For leptokurtic distribution

(A) b₂ > 3
(B) b₂ < 2
(C) b₂ = 3
(D) b₁ > 3

• Link relatives can be obtained dividing  by

(A)
(B)       
(C)           
(D)

• In chain base method, the base period is

(A) Fixed
(B) Changed
(C) Constant
(D) None Of These

• When a die and a coin are rolled together, all possible outcomes are

(A) 6        
(B) 2             
(C) 36           
(D) 12

• If A and Bare mutually exclusive events then P (AB) is

(A) Zero   
(B) 1             
(C) 0.5            
(D) 0.8    

• The distribution function F(x) is equal to

(A) P(x = x)
(B) P(x  x)
(C) P(x  x)
(D) None of these

• An expected value of a random variable is equal to its

(A) Mean    
(B) Variance
(C) S.D        
(D) Co-variance

• The parameters of the binominal distribution are

(A) x and n
(B) x and p
(C) n and p
(D) x, n and p

• In binominal distribution the range of x is

(A) Zero to ∞ 
(B) zero to n
(C) -1 to ∞
(D) Undefined

• The hyper geometric distribution has…………..  Parameters

(A) 2            
(B) 3             
(C) 1           
(D) 4

Inter (Part-I) Dera Ghazi Khan Board 2015
Statistics
Part I (Subjective)
Time Allowed: 2.10 Hours 
Max. Marks: 83 

Section I

2. Write short answers any Eight (8) questions of the following  

• Define Primary and Secondary data
• Define meaning of statistics in singular sense
• If the sum of deviations from x=10 for ten values is 25 then find. Arithmetic mean
• Calculate the value of median using the following information’s  = 60, h=10, f=20, N=80 and c=30
• Define the term "Geometric Mean"
• What is meant by measure of central tendency?
• Write down the mathematical grope lies of Arithmetic Mean
• Given find base year weighted Index number
• Distinguish between weighted and in weighted Index numbers
• lf the link relations are : 100, 130, 115,110 then find chain Indexes
• Write down main steps involved in construction of price index numbers
• Explain the fixed base method GO

3. Write short answers any Eight (8) questions of the following

• Differentiate between classification and Tabulation
• Differentiate between grouped and ungrouped
• What is meant by dispersion
• If variance is 5 and third moment out mean is12.8 find
• Define Range
• If Q1=88.03, Q3 = 94.90, Q2=91.47, then Compute Bowley's Coefficient of   Skewness ?
• Define Inter quartile range
• Define Mean Deviation
• Distinguish between permutation and combination
• If P(A) = 0.60. Compute P )
• Find the probability of drawing a picture card from a pack of 52 playing cards
• Define Equally Likely Events

 QUESTION NO.4 Write short answers any Six (6) questions of the following
(1) What is mathematical expectation?
(2) Given E(x) = 2.5 and Var(x) - 1.2: find E ()
(3) If E(x) = 10, then find E(5x -25)
(4) What is random Experiment?  
(5) Write down the properties of discrete probability distribution
(6) Write down two properties of Binomial experiment
(7) If n= 5 and P=0.3, then find standard deviation of a Binomial distribution
(8) Given for hyper geometric. Distribution N =10; n = 2 and K = 2, Find P(x = 0)
(9) Write mean and variance of Hyper geometric distribution

SECTION - II

Note: Attempt any three questions from this section
Question #5
(a) Find the H,M for the data given below

(b) Compute Mode from the following data

Question #6
(a) Find mean deviation from the following  data

(b) The first four moments about x = I.5 c f a variable are 1, 17, 10 and 40 find variance  

Question #7
(a) Find Laspeyr’s index number taking 1980 as base

(b) If P(A)=  ,P (AB)=B) P(=  then find (i) P(A  B) (ii) P(B) (iii) P() (iv) P()

Question #8
(a) Let x be a random variable with Prab distribution

(b) A continuous random variable x has probability function f(x) = Cx for 0 < x <2 Determine   (i) c value P(I < x < 1.5) (ii) P(Ix < 1.5)    (iii) P(x < 1.5)  

Question #9
(a) Out of 10-applicants for a job, 6 are from Lahore. If 3 applicants are selected at random, find the probability that (a) 3 are from Lahore (b) At least 2 are from Lahore
(b) Find the Mean and SD of the binominal (q + P)3

SECTION – (III)

Question #10
Attempt any three parts from A B, C and D                                5x3 15

(A) The following is the frequency distribution of number of leaves on branches of a tree, Find Mean, median and modal number of leaves per branch

(B) Calculate mean deviation from median for the following frequency distribution

(C) Compute index number by simple aggregative method taking 2000 as base for the following data

(D) For the following probability distribution

Calculate (i) E(x) and E() (ii) Show that E(2x + 5) =2E(x) + 5

(E) A committee of size 6 is to be selected at random from 8 women and 7 men. Find the probability distribution of number of women in the committee