Gujranwala Board
(Inter Part -I) 2013
Statistics (Obj. Type)
Total Marks: 17
Time Allowed: 20 Min.

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 with marker or pen on the Answer, Book provided. Cutting or filling two or more circles will result in zero mark in that question. Attempt as many questions as given in objective type question paper and leave others blank.

• In hyper geometric distribution, N = 6, n = 2, K = 3, then mean is
  
  (A) 2
  (B) 3
  (C) 1
  (0) 4
  
  
• Binomial dist. has parameters
  

(A) one
(B) two
(C) three
(D) four

• If X and Y are random variables, then E(X Y) is
  
  (A) E(X) E(Y)
  (B) E(X) - E(Y)
  (C) X-E(Y)
  (D) E(X) -Y
  
  
• If A and B are mutually exclusive events, then P(A∩B) is
  
  (A) zero
  (B) 1
  (C) 0.5
  (D) 0.8
  
  
• Link Relative is equal to
  
  (A) x 100
  (B) x 100
  (C) x 100
  (D) x 100
  
  
• 6, Second moment about mean is
  
  
• (A) 0
  (B) 1
  (C) Variance
  (D) S.D
  
  
• The median of -35 0, -5 is
  
  (A) -3
  (B) 0
  (C) -5
  (D) does not exist
  
  
• Registration is the source of
  
  (A) primary data
  (B) secondary data
  (C) ogive
  (D) histogram
  
  
• If V is a constant, then – is equal to
  
  (A) a₁ + a₂ + a₃ + a₄ + a₅
  (B) a
  (C) 5a
  (D) none
  
  
• The binomial dist. is symmetrical when
  
  (A) p = q
  (B) P<g
  (C) p > q
  (D) np > npq
  
  
• If C is a non random variable, then E(C) is
  
  (A) C
  (B) 0
  (C) 1
  (D) X
  
  
• For symmetrical dist. u3 is
  
  (A) zero
  (B) 1
  (C) 3
  (D) 4
  
  
• How many basic types of index number are there ?
  
  (A) 2
  (B) 3
  (C) 4
  (D) 5
  
  
• Tossing two dice possible samples are
  
  (A) 36
  (B) 12
  (C) 6
  (D) 2
  
  
• If X and Y are independent, then Var (X – Y) is equal to
  
  (A) Var(X) Var(Y)
  (B) Var(X)- Var(Y)
  (C) Var(X + Y)
  (D) Zero
  
  
• The G.M. of negative value is
  
  (A) Zero
  (B) negative
  (C) Positive
  (D) Not possible
  
  
• Statistical laws are true
  
  (A) on the average
  (B) always
  (C) in the tong run
  (D) A and C

«Gujranwala Board»
(Inter Part - I) 2013
Statistics (Sub. Type)
Total Marks: 83
Time Allowed: 3:10 hrs.

Section-I

2. Write short answers to any EIGHT (8) questions : 16

• Differentiate between parameter and statistic.
• Define statistics in plural sense.
• Define harmonic mean.
• Average of 5 values is 70. Find the sum of values.
• For a frequency distribution of a variable X, it is given that X = 10+ 5 u, ∑f = 125 and ∑fu= - 45. Find the value of mean.
• Find median of -1, -3, 3, -2 and 5.
• A distribution consists of 3 components with respective size 45, 40 and 65 along with
• their means 2, 2.5 and 2. Compute the combined mean.
• What do you understand by base period?
• If Laspeyre's index number = 105.4 and Paasche's index number = 103 .2, then find the Fisher's index number.
• Define weighted index number.
• Given Mpᵒqᵒ = 352 ∑pᵒq1 = 422 Epᵒq1 =
• 402 ∑p1q1 = 481, then find (a) base year weighted index number (b) current year weighted index number.
• What is the relationship between Laspeyre's, Paasche's and Fisher's ideal index numbers.

3. Write short answers to any EIGHT questions: 16

• What is different method of presentation of data?
• What is meant by frequency distribution?
• Define semi-inter quartile range.
• If Var(X) = 16, then find variance of (a) 3x (b) 3x - 10
• If S.D. = 3 of a set of data, then what will be the variance?
• If co-efficient of skewness is zero i.e. SK = 0, then what will you say about mean, median and mode?
• If variance is 5 and third moment about mean is -12.8, find b1 and discuss the distribution.
• What does kurtosis mean?
• Define factorial with example.
• What is the answer of 4 and
• What is the range of probability?
• Find the probability of '6 and 4', when a fair die is rolled.

4. Write short answers to any SIX questions: 12

• Explain random number.
• What is continuous random variable?
• Write down the properties of distribution function.
• Find E(X) , E() from the following data :X = 0 1 2 ,P(X)=
• What is discrete random variable? Is it possible to have binomial distribution with u = 10 and ⱺ = 4 ?
• Write any two properties of binomial distribution.
• In hyper geometric distribution N = 40. n = 5,K = 4. Find mean and variance.
• Find any two properties of hypergeornetric distribution.
  
  

  (SECTION - II)

Q.5
(a)The deviations from 25.5 o 15 different values are:
 -15.4 -1.9, 6.2, 13.7, 24.6, 25.5, 3.8, -7.9
-13.6 21.1, 16.4, 18.7. -14.3, -9.8 and 4.9.

• What are their respective chances of winning?
• What is the probability that B or C wins?

Q.8
(a) Determine value of C so the function can serve as a probability function of random variable:

• C y for y = 1, 2, 3, 4
• (I - C) for y = 0, 1, 2

(b) Calculate mean and variance of the following probability distribution:

• (a) An event has probability P = Find complete binomial dist. for n = 5
• (b) A box contains 5 red and 10 white marbles. If 8 marbles are chosen at
• random without replacement, determine the prob.
  (i) 4 are red (ii) all are white

(SECTION - III Practical)

Attempt any THREE parts of the following
Q.10
(a) Find the value of mode from the data:
Marks: 10-14 15-19 20-24 25-29 30-34
F: 2 4 8 6 3
(b) Find mean deviation from following data:
Group: 2-4 4—S 6-8 8-10 10-12
Freq : 10 20 30 20 10
(c) Find price relatives for the following data taking
(i) 1990 as base year
(ii) Average of first five years as base