FAISALABAD BOARD 2013
PAPER STATISTICS PART-I
Time: 20 Minutes
(Objective Part)
Marks: 17
Note: Four Answers are given against each column A, B, C &D. Select the write answer and only separet answer sheet, fill the circle A, B, C or D with pen or marker in front of that question number.

Question#1

• A part of the population selected for study is called:
  
  (a) Variable
  (b) Data
  (c) Sample
  (d) Parameter
  
  
• The class boundaries can be taken when the nature of variable is:
  
  (a) Discrete
  (b) Continuous
  (c) Qualitative
  (d) Discrete and continuous
  
  
• Total angle of the pie chart is:
  
  (a) 45°
  (b) 90°
  (c) 180"
  (d) 360°
  
  
• The sum of square of the deviation about mean is:
  
  (a) Zero
  (b) Maximum
  (c) Minimum
  (d) All of these
  
  
• The middle value of an ordered series is called:
  
  (a) Median
  (b) 5th decile
  (c) 50th percentile
  (d) All of these
  
  
• The range of the scores 29, 3, 143, 27, 99 is:
  
  (a) 140
  (b) 143
  (c) 146
  (d) 70
  
  
• Standard deviation is always calculated from:
  
  (a) Mean
  (b) Median
  (c) Mode
  (d) Lower quartile
  
  
• If mean = 20, mode = 16 and standard deviation = 2, then coefficient of skewness is:
  
  (a) 1
  (b) 2
  (c)  4
  (d)-2
  
  
• Index number are expressed in:
  
  (a) Ratio
  (b) Square
  (c) Percentage
  (d) Combination
  
  
• In fixed base method, the base period should be.
  
  (a) For away
  (b) Abnormal
  (c) Unreliable
  (d) Normal
  
  
• The probability of an event cannot be:
  
  (a) Equal to zero
  (b) Greater than zero
  (c) Equal to one
  (d) Less than zero
  
  
• If three coins are tossed then possible outcomes are called:
  
  (a) 8
  (b) 3
  (c) 1
  (d) None of these
  
  
• In discrete probability distribution the sum of all the probabilities is always equal to:
  
  (a) Zero
  (b) One
  (c) Minimum
  (d) Maximum
  
  
• E (XY) is equal to:
  
  (a) E(X) E(Y)
  (b) E(X) ± E(Y)
  (c) E(X+Y)
  (d) None of these
  
  
• Nature of the binomial variable 'X' is:
  
  (a) Quantitative
  (b) Qualitative
  (c) Discrete
  (d) Continuous
  
  
• The binomial probability is symmetrical when:
  
  (a) P = q
  (b) P < q
  (c) P > q
  (d) np > npq
  
  
• The hypergeometric distribution has:
  
  (a) One parameter
  (b) Two parameter
  (c) Three parameter
  (d) Four parameter

Time: 2:40 Hours
(Subjective Part)
Marks: 68
SECTION-I

• What is statistics?
  
• Define secondary data.
  
• What is quartile?
  
• Define mode.
  
• Define arithmetic mean.
  
• What is the sum of deviations from mean?
  
• Write any two merits of geometric mean.
  
• Define composite index number.
  
• What is link relative?
  
• Write down the formula for household budget method.
  
• What is consumer price index number?
  
• What is the name of Paasche's Index number?

3. Write short answers of any Eight Parts.16

• What is tabulation?
• What is histogram?
  
• Give two properties of variance.
  
• Find the range of data given as C, C, C, C, and C.
  
• Define quartile deviation.
  
• Define moments about zero.
  
• In normal distribution what are values of β1 & β2
  
• Define range.
  
• Define probability.
  
• What is random experiment?
  
• Define sure and impossible events.
• Define Venn diagram.

4. Write short answers of any Six Parts. 12

• Define a random variable.
  
• Define probability distribution.
  
• Enlist 2 properties of expectation.
  
• What does p.d.f. stand for?
  
• What are the properties of distribution function?
  
• What is binomial experiment?
  
• Write down any two properties’ of binomial experiment.
  
• Define hypergeometric distribution.
  
• Write down mean and variance of hypergeometric distribution.

SECTION -II

Attempt any THREE questions Each questions carries 8 marks
Question#5
(a) The reciprocal of 11 value of x are give below. 4 0.0500, 0.0454, 0.0400, 0.0333, 0.0285, 0.0232, 0.0213, 0.02000, 0.0182, 0.0151, 0.0143.Calculate harmonic mean and arithmetic mean of 'X'.
(b) The arithmetic mean and geometric mean of three numbers are 34 and 18 respectively. Find all the three numbers, when the geometric mean of first two numbers is 9. 4

Question#6 
(a) Find M.D. using mode as average from the following data: 4

(b) In a certain distribution first four moments about 5 are 2, 20, 40 and 50. Calculate β1, and discuss the shape of distribution. 4

Question#7
(a) Compute Fisher's price index number for 1967 using 1964 as base for the following data:

(b) The probability that a man will be alive in 25 years is   and his wife will be alive in 25 year is   Find the probability that: 4
(i) Both will be alive in 25 years
(ii) only the man will be alive in 25 years.

Question#8
(a) A continuous random variable X has probability density function f(X) = cx for 0 ≤ x ≤ 2. Find
(i) C
(ii) probability that x < 1:5.
(b) Let x be a random variable with probability distribution as follows:

Find mean and varience.

Question#9
(a) If x is the number of successes with probability of success as  in each of 5 independent trials, then find. 4
(i) P(x=0)
(ii) P(x ≤ 3)
(b) A machine produces 7 good and 3 defective items. Two items are selected randomly without replacement. Find the probability out of these two (i) none is defective (ii) both are defective.4

SECTION -III
(Practical)

10. Attempt any THREE parts. Each part carries 05 marks.
(A) Find arithmetic mean by short cut formula:

(B) Calculate standard deviation from the following data:

(C) Given the following information:

Compute Fishers index number taking 2008 as base year.
(D) A die is tossed 4 times. Appearance of 5 or 6 is regarded as success. Find probability distribution of successes.
(E) A man draws 2 balls from a bag containing 3 white and 5 black balls. If he is to receive Rs. 70 for each white ball which he draws and Rs. 7 for every black ball. Find is expectation.