Statistics (PART 1)
Rawalpindi 2013
Marks = 17

1. Encircle the right option

• Binomial distribution has parameters
  
  (A) 2
  (B) 3
  (C) 1
  (D) Zero
  
  
• Mean of the binomial distribution is
  
  (A) nq
  (B) npq
  (C) pq
  (D) np
  
  
• The parameters of hypergeometric distribution are
  
  (A) N.n.k
  (B) n.q
  (C) pq
  (D) n.p
  
  
• A portion of the population selected for study is called
  
  (A) Parameter
  (B) Statistic
  (C) Population
  (D) Sample
  
  
• The science of collecting, organization and analyzing the data is called
  
  (A) Statistics
  (B)Parameter
  (C) Population
  (D) Mathematics
  
  
• A line chart of a cumulative frequency distribution is called a(n)
  
  (A) Ogive
  (B) Histogram
  (C) Bar chart
  (D) Frequency Polygon
  
  
• If y = 3x, +5. then y is equal to
  
  (A) 3x
  (B) 3x + 5
  (C) x
  (D) x+5
  
  
• Mode of 2. 10 and 7 is
  
  (A) 10
  (B) 2
  (C) 7
  (D) None
  
  
• Mean deviation is minimum when it is calculated from
  
  (A) Mean
  (B) Median
  (C) Mode
  (D) Geometric mean
  
  
• The variance of a constant is
  
  (A) a
  (B) a²
  (C) zero
  (D) None
  
  
• The second central moment of a data is equal to
  
  (A) Zero
  (B) Mean
  (C) Range
  (D) Variance
  
  
• Link relatives can be obtained dividing p, by
  
  (A) P₀
  (B) P _n-1
  (C) q₀
  (D) q_n-1
  
  
• Index for base period is always taken as
  
  (A) One
  (B) Zero
  (C) 200
  (D) 100
  
  
• If two dice are rolled, the possible out comes are
  
  (A) 12
  (B) 16
  (C) 36
  (D) 18
  
  
• The probability of drawing any Ace card is
  
  (A) 1/13
  (B) 1/14
  (C) 4/13
  (D) 1/52
  
  
• If a is a constant. then E((A) is equal to
  
  (A) Zero
  (B) a²
  (C) 1
  (D) a
  
  
• For a random variable X; ∑ P(X) is equal to
  
  (A) Zero
  (B) 1
  (C) 100
  (D) 200

2. Answer any eight par. 16

• Define primary data.
• Expand the following Xi - Yi).
• Explain general relationship between A.M.. G.M. & H.M.
• Write down empirical relation between mean, median and mode.
• Define Harmonic mean.
• Write any two demerits of Arithmetic Mean (A.M).
• Define percentiles.
• Define simple index number.
• Give two uses of index number.
• State time reversal test.
• What is the relationship among Laspeyr's, Paasche's and Fisher Ideal index number?
• Write down the Paasche's formula for price index and quantity index.

3. Answer any eight parts. 16

• What is an Ogive?
• Define relative frequency distribution.
• Name the distribution if β1 = 0 and β2 = 3.
• Write down any two properties of Mean deviation.
• Define skewness.
• Write down the Bowley's and Karal Pearson formula of skewness.
• Write down any two properties of variance.
• Give an example of simple and compound event.
• Define mutually exclusive event.
• When does probability becomes negative?
• How many possible permutations can be formed from the word 'STATISTICS'?
• For symmetrical distribution (S.(D) = 2, What is the value of m₄?

4. Answer any six parts. 12

• Define "Random experiment".
• What is “Random variable"?
• What are "Random Numbers"?
• If E(X) =1.1 and E(X) = 2.1, find var(X) .
• If E(X) =1.1 find E(3X + 5)
• What are "Bernouli trials"?
• Define 'Binomial experiment".
• What is "Hypergeometric experiment"?
• Write down the formulae for computing mean and variance of hypergeometric distribution

Answer any three questions. 24

Question#5
(A) The deviation from X = 22.5 of different values of 'X' are: -12. -8.5, -3.0, 0, 2.5, 6.6, 9.2. 1.6, 0.5,0.4 Find median of 'X' values.
(B) Mean value of 20 items is 45. If one of these values was wrongly taken as 64 instead of 46. find the corrected mean.
Question#6
(A) Calculate the standard deviation for the following frequency distribution.

(B) Given that


Find the first four moments about mean.

Question#7
(A) Find Index number from the following data by using 1977 as base:

(B)A bag contains 14 identical balls. out of which 4 are red. 5 black and 5 white balls. If 3 balls are drawn from the bag. find the probability that
(i) 3 are red 
(ii) At least 2 are white.

Question#8
(A) A continuous random variable X can assume values between X = 2 and X = 5 and has a density function  , Find
(i)   P(3 < X <4)
(ii) P(X  4)
(B)A random variable X has the following distribution:

Find
(i) E(X)
(ii) Var (X) and Show that
(iii)  E(5X + 8) = 5E(X)+8

Question#9
(A) Out of 800 families with 5 children each, how many would you expect to have
(i) 3 boys
(ii) Noboy, assuming equal probability for boy and girls?
(B)Three balls are drawn from a bag containing 5 white and 3 black balls. If X denotes the no. of black halls drawn, then find the probability distribution of X. Also find its variance.

Section-Ill
(Practical)

10. Attempt any three parts. 15

(A) For the following data find geometric mean.

(B)Calculate mean deviation about mean from the data

(C) Calculate Index number from the following data. when 1989 is base year

(D) A fair coin is tossed 5 times. what is the probability of getting: 
(i) exactly 3 heads
(ii) at least 3 heads
(iii) at most 2 heads
(E) Three bails are drawn from a box containing 4 white and 7 black balls. If "X" denotes the number of black balls drawn. then obtain the probability distribution of "X" by using the hypergeometeric distribution.