Statistics
(Objective) 
Time Allowed:- 20 minutes
Maximum Marks: 17

Question#1

• The amount of milk produced by a cow is a
  
  (A) Constant
  (B) Discrete variable
  (C) Continuous variable
  (D) Attribute
  
  
• Mid point of the limit 5-9 is
  
  (A) 5
  (B) 7
  (C)  9.5
  (D) 5.5
  
  
• The grouped data is
  
  (A) Raw data                
  (B) Primary
  (C) Secondary
  (D) None of these
  
  
• Median divides the data into
  
  (A) 2 parts 
  (B) 4 parts
  (C) 10 parts
  (D) 3 Parts
  
  
• If x=0,4,8 G.M is
  
  (A) 2           
  (B) 10        
  (C) √8
  (D) Not possible
  
  
• Mean deviation will be minimum from
  
  (A) Mode   
  (B) Median
  (C) G.M     
  (D) Arithmetic Meal
  
  
• The first moment about mean is
  
  (A) Variance
  (B) Zero
  (C) 1
  (D) Standard deviation
  
  
• For Meso Kurtic distribution b₂ is
  
  (A) >3
  (B) <3
  (C) 0
  (D) =3
  
  
• Link Relative is equal to
  
  (A) pⁿ/ pox100
  (B) pⁿ/ pn-1x100
  (C) p^O/ pnx100
  (D) pⁿ/ pn+1x100
  
  
• Index no. for base period is equal to
  
  (A) I             
  (B) 0           
  (C) 100
  (D) 10
  
  
• When two coins arc tossed the no. of all possible outcomes
  
  (A) 2
  (B) 8
  (C) 16
  (D) 4
  
  
• The Prob. of red card out of 52 cards is
  
  (A) 1/4
  (B) 1/2
  (C) 4/52
  (D) Zero
  
  
• A random variable is also called
  
  (A) Constant
  (B) Chance variable
  (C) Stochastic varied)
  (D) Both B & C
  
  
• If E(X)=4 then mean
  
  (A) 0
  (B) 1
  (C) 16
  (D) 4
  
  
• Parameters of binomial distribution are
  
  (A) n.x
  (B) n,P
  (C) P,q      
  (D) n,P,q
  
  
• Mean of hyper geometric distribution is
  
  (A) NK
  (B) Nk/ N2
  (C) n2K2 / N
  (D) nK / N
  
  
• In binomial distribution
  
  (A) Mean= variance 
  (B) Mean > variance
  (C) Mean = S.D
  (D) Mean < variance

Max. Marks 83
Statistics
(Subjective)
Time Allowed: 3.10 Hours
2. Answer briefly any Fight parts from the followings:-  8x2=16

• Define variable and constant.
• Define harmonic mean.
• Write down two properties of arithmetic mean.
• Define variable and constant.
• Find median of 0,-1,-3,-2,3,4
• If mode=25 and median = 28, find the approximate value of mean
• Define percentiles.
• Write down different types of index numbers
• Define simple and composite index numbers
• Write down the methods to compute consumer price index numbers.
• Given Laspeyre's price index number =120 and Paasche's price index nurnber= 119.6 Find Fisher's price index number.\
• Given Σw=20 and ΣwI=1820. Find consumer price index number by weighted average of price relatives method.

3. Answer briefly any Fight parts from the followings:-           8x2=16

• Define classification
• What is Historigram
• What do you understand by dispersion
• Given that Q1=89 and Q.D = I 0.875, then find the value of Q₃.
• Define mean deviation.
• Sum of squares of deviation from mean of 12 items is 192. Find standard deviation.
• The mean of 5 items is 6 and their S.D is √8. Find ΣX and ΣX²
• Define moments ratio ß,. For what purpose it is computed?
• Define the terrn random experiment?
• Diffrentiate between simple and compound events.
  
• If A and B are.two independent events and P(A) = 2 and P(B)=- 15 then find P(AnB)
• Write statement of addition ride for mutually exclusive events.

4. write briefly any six parts from the followings: 6x2=12

• Define continuous random variable
• How many possible outcomes has a random experiment?
• If E(X)=10; E(y)=3, then find E(3X-5)= ?
  
• Define probability distribution.
  
• If    x : 0     I           2
  P(x): K    2K     3K  What will be the Kin the given probability distribution?
• What is the Binomial experiment.
• If n=4, P=0.2 then find E(x) and var (x)
• If-N=40, n=5,  k=4 then find E(x) and var (x)
• (ix) Write any two properties of Hyper geometric distribution.

Section-II

Note: Attempt say three questions. (8 x3=24)
Question#5
(a) The following distribution given below has been derived by the use of working origin.

(b) The geometric mean of two numbers is 8 and arithmetic mean is 10. Find the two numbers.

Question#6
(a) Find quartile deviation from the following un-grouped data. Also compute coefficient of quartile deviation. 3,24,5,18,6,15,7,12 and 10
(b) Given the following results. Compute combined variance
N₁=100 , S₁=2.4, X₁=12.6
N₂= 120 , S₂=4.2, X₂ =15.8
N₃= 150 , S₂= 3.7, X₂= 10.5

Question#7
(a) Find Index number of Price from the following data taking average Price of all years as the base

(b) A bag contains 5 white and 7 black balls, if 3 balls are drawn from the bag, what is the probability that
(i) All are white
(ii)All are of the same colour

Question#8
(a) The probability density function of a random variable f(x)= a(3x+2) 2≤x≤4
Find a =?          
P(2 ≤ x ≤ 2.7)=?
(b) Given the following probability distribution

Find Mean and variance of X?

Question#9
(a) If 20% of the bolts produced by a machine are defective. Determine the probability that out of 4 bolts chosen at random
(i) 0
(ii) 2 bolts are defective
(b) Given that x is a hyper geometric random variable with N=8, n=3 and K=5 Find P(X ≤ 3)= ?

(Section-III)

10- Attempt any three Parts.
A. Find Harmonic mean for the foliowioat data

B. Find Quartile deviation and co-efficient of quartile deviation from the following data

C. From Given information find Index No. by Laspyer’s formula when 2002 is base year

D. Find the complete binomial dist. With parameter n=8, P= 2/3.
E. A committee of size 5 is to be selected at random from 3 women and 5 men. Find the expected number of women in the committee.