(11th CLASS — 2014)
STATISTICS
20 MINUTES
NEW COURSE)
MARKS: 17
OBJECTIVE
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 of pen to fill   the circles, Cutting or filling two c r more circles will result in zero mark in that question.

QUESTION NO. 1

• The branch of statistics which deals with collection on agreement, presentation and finding salient features of data is called

  (A) descriptive statistics
  (B) inferential statics
  (C) applied statistics
  (D) theoretical statistics

• In a relative frequency distribution; tie total of relative frequencies is

(A) 1
(B) 100
(C) ∑f
(D) ∑r

• If the data contain an extreme value, the suitable average is

(A) mean
(B) median
(C) mode
(D) GM

• Harmonic mean for x1 and x2

(A)
(B)
(C)
(D)

• The observation at the center of data ter arrangement is called

(A) mean
(B) median 
(C) mode        
(D) HM

• Quartile deviation is

(A) Qi + Q3 /2        
(B) Q1 - Q3 /2
(C) Q3 — Q1/2
(D) Q1 Q3/Q1+Q3

• SD (b x) =................

(A) lb S.D.(x)
(B) b2 S.D.(x) 
(C) SD (x)    
(D) 1/b SD(x)

• For negatively skewed distributions

(A) mean < median < mode
(B) mc an > median > mode
(C) mean < mode < median
(D) mean = median =mode

• An index number is called a simple it dex when it is computed from

(A) single variable
(B) bi — variable
(C) multivariable  
(D) All of these

• An index number calculated by Fishe 's formula is ideal because it satisfy

(A) circular test  
(B) factor revers al lest
(C) time reversal lest   
(D) all of these

• If A and B are mutually exclusive eve Its then

(A) P( = 0
(B) (= 1 
(C) P(AUB) = 0
(D) P(AUB) = 5

• If A and B are two independent event; then

(A) P(AUB) = P(A), P(B)
(B) P() 7- NA}. P(B)
(C) P(AUB) = P(A)P(B)
(D) P( = P(A) P(B/A)

• A set of numerical values assigned to a sample space is called

(A) random sample
(B) random v.triable
(C) random numbers
(D) random experiment

• Covariance of two independent random variables x and y

(A) 1
(B) 0     
(C) negative 
(D) positive

• The parameters of binomial distribute in

(A) n & P         
(B) P & q              
(C) nP & nPq
(D) nP and  

• Binomial distribution is symmetrical f

(A) p < q
(B) p > q
(C) p = q 
(D) np = npq

• The mean of hypergeometric distribu ion is

(A) nk/N
(B) Nk/n
(C) Nn/k  
(D) n+k/N

STATISTIC'S
(NEW COURSE)
(SUBJECTIVE)
SECTION
MARKS:83

QUESTION NO 2 Write short answers any Eight (8) questions of the following: (16)

• Discuss different meaning of statistics
  
• What is descriptive statistics
  
• Define harmonic mean
  
• Define quartiles
  
• Find G.M if x 1, 3 , 9 
  
• If mean=20 , Median = 18.67 , Find Mode
  
• What are the desirable properties of a good average?
  
• Explain We meaning of consumer price index number
  
• Given w = 20 25 30 and I x lO0= 100, 105 , 110 Find consumer price index number
  
• Define fixed base method
• Define chain base method
• What is the weighted index number

Question NO. 3 Write short answers any Eight (8) questions of the following: (16)

• Define frequency diminution
  
• Explain one-way classification
  
• Define coefficient of variation
• Write down the formula for Bowley's coefficient of skewness
  
• Coefficient of skewness of a distribution is 0,64, its mean is 82 and mode is 50. Find coefficient of variation
  
• Define Kurtosis          
  
• Write down the formulas of first four moments about mean
  
• If Var(x) = 25 then find S.D. (2x+5) 
  
• Define sample space
  
• What is relative frequency definition of probability  
  
• What is meant by independent events
  
• Write the statement for Multiplication Law of probability for independent events

QUESTION NO. 4 Write short answers any Six (6) questions of the following (12)

• Describe the properties of a discrete probability distribution
  
• Write down the two properties of expectation
  
• What is the expectation and variance of a constant K?
  
• What are the properties of probability density function'?
  
• Given x = 0,1 , 2 P(x) A-- 4c , 3c , c find the value of c
  
• What is the team and variance of the binomial distribution with parameters n and P
  
• What is the range of the binomial random variable?
  
• If a variable has binomial distribution as:     PXQ4-X    Pxq4-x . Find mean and variance
  
• Given N 10 , n = 4 and k = 5 find Fi(x)

SECTION-II

Note:  Attempt any Three questions from this section    (8 * 3=24)
5.(a) The following data has been obtained from a frequency distribution of a continuous variable X after making the substitution U=x-136.5/6 Show that G.M is less than A.M:             6
U   -4 -3 -2   -1    0     1    2   3
f    2   5   8   18    22    13   8   4
(b)  The ungrouped data is given: 45 30 35 40 44 32, 42 37.Calculate G.M by using
(i) Basic definition
(ii) Log formula
6.(a) Calculate coefficient of variation from the following data and interpret the result
Groups 10 — 19   20— 29     30 — 39    40-40     50-59
f      5        10         18         6         1     
(b) in a certain distribution, the first four moments about x = 5 are 2 , 20, 50 and 70 res active.
Calculate h1 and discuss the kurtosis oldie distribution 
7.(a) Compute simple index number taking 2000 as b— year from the following 
Commodities        Years      2000      2001       2002
A                             45       50          60
B                             12       15          20 
C                             20       22          25
(b) there horses A, B and C are in a race. A k twice as likely to win B and B is twice as likely to win as C
what is probability that A or C wins?

8. (a) The probability distribution of a random variable is given as X:          1    2      3        4        5
P(x):      0.1  0.3  0.39   0.2   0.01
Find the probability distribution of 3x + 5 and of 2X2is
(b) A committee of size 5 is to be selected at random from 3 women and 5 men, Find the expected number of women and variance on the committee

9.(a) Five dice are rolled 96 times. Find the expected frequencies when throwing of 4, 5 or 6 is regarded as success
(b)  Given that x is a hypergeotnetric random variable with N = S, n = 3 and k 5 Compute P (x <3)

SECTION — III   
(PRACT1CAL)

10. Attempt any three parts from A, B,C,D and E 
(A) Find Arithmetic Mean from following
Group   10 — 20 , 20 30 , 30 — 40 , 40 — 50 , 50 — 60
Freq       4        5         7        5         4

(B) 1st four moments about 17.5 are 03, 74, 45 and 12125. Find out whether the distribution is Lepto kurtic or Platy kurtic

(C) Find Index No. when year 2001 is base year
Year  2011 2002   2003   2004    2005       2006       2007       2008
Price  5 , 7.4 ,  6.9 ,  8.1 ,   10.2 ,     9.6 ,     10.5 ,       11   And also calculate chain index No.

(D) Prove that E (3x + 2) 3E(x) + 2 from foil owing probability distribution x:     1     2      3      4
P(x) 1/10 2/10   4/10   3/10

(E) A bag contains 4 white and 4 red balls Draw 4 bails by W.O.R Method. Find probability dist. of white balls
Find Mean of Prob, dist