Faisalabad Board 2014
Paper Statistics Part – I
Time 20 Minutes
(Objective part)
mark : 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

• The mean deviation of the values 18, 12, 15 is:
  
  (a) zero
  (b) 3
  (c) 6
  (d) 8
  
  
• If X and y are independent random variables then S.D (x –y) will be:
  
  (a) S.D (x)
  (b) S.D(x) + S.D(y)
  (c)
  (d)
  
  
• The index number for base year is always taken as:
  
  (a) 50
  (b) 100
  (c) 150
  (d) 200
  
  
• Simple index number involves commodity.
  
  (a) One
  (b) Two
  (c) Three
  (d) Four
  
  
• Any subset of the sample space is called:
  
  (a) Nothing
  (b) Zero
  (c) Events
  (d) none of these
  
  
• A set consists of more than one sample points M called:
  
  (a) Simple event
  (b) Compound event
  (c) Empty set
  (d) None of these
  
  
• Sum of dab when two dice are rolled la:
  
  (a) Discrete variable
  (b) Continuous variable
  (c) Constant
  (d) Qualitative variable
  
  
• A random variable may be discrete or:
  
  (a) Experimental 
  (b) Continuous
  (c) Fixed 
  (d) Discontinuous
  
  
• Mean of binomial distribution?
  
  (a) nq
  (b) npq
  (c) 
  (d) np
  
  
• Which is true in binomial distribution?
  
  (a) Mean > variance 
  (b) Mean < variance
  (c) Mean = variance
  (d) None of these
  
  
• Binomial distribution hat:
  
  (a) Three parameters
  (b) One parameter
  (c) Two parameters
  (d) None of these
  
  
• The word Statistics comes from the Latin word:
  
  (a) Status
  (b) Statistik
  (c) Statista
  (d) Statistique
  
  
• In a relative frequency distribution, the total of the relative frequencies is:
  
  (a) 100
  (b) One
  (c) Σ
  (d) ΣX
  
  
• The measure of central tendency listed below is:
  
  (a) Range
  (b) Mean
  (c) Variance
  (d) Moments
  
  
• The sum of deviations is zero when the deviations are taken from.
  
  (a) Mean
  (b) Median
  (c) Mode
  (d) G.M
  
  
• Which is least if x = 100?
  
  (a) Σ (x – 200)²
  (b) Σ (x-100)²
  (c) Σ (x-50)²
  (d) Σ (x-150)²
  
  
• A measure of dispersion is always:
  
  (a) Zero
  (b) Positive
  (c) Small
  (d) One

Subject Part
Marks: 68
SECTION

2. Write short answers of any Eight Parts.(8*2=16)

• what is meant by primary data?
• Define inferential statistics.
• Define the term median.
• Write the properties of arithmetic mean. (any two)
• Given u = x -  , Σ  = 100 ,  Σ  = 200. Find  .
• Given I  = 200,    m  = 25,    1 = 20,  2 = 20,  h  =  10, find mode
• Define index number.
• Explain the fixed base method.
• Given N = 5,  Σ    x  100 =  510 , find price index by average of relative method.
• Define the term weighted index.
• Given ΣP0 qn  = 1000 and ΣPn qn  =  1360 , find current year weighted index.
• Define geometric mean with formula.

3. Write short answers of any Eight Parts.(8*2=16)

• What is histogram?
• Name any four parts of a statistical table.
• What is relative dispersion?
• What are the names of measures of absolute dispersion?
• Find the range of 1-, -3,  0, 2, 3
• What is mean deviation?
• Differentiate between inter quartile range and quartile deviation.
• What are values of ẞ1, and ẞ2 in a symmetrical distribution?
• What are combinations?
• What is a sample space?
• Give the addition law for two mutually exclusive events.
• What are exhaustive events?

4. Write short answers of any Six Parts.(6*2=12)

• What is continuous random variable?
• What are the random numbers?
• What are the properties of probability density function?
• Define random variable.
• Write down the properties of discrete probability distribution.
• In a binomial distribution n = 7, p = 0.7, find coefficient of variation.
• Define hypergeometric experiment.
• If x is a binomial random variable, find p(x = 3) = ? when n = 3, p = ½.
• In binomial distribution mean = 6, variance = 4. Find its parameters.

Section II

Attempt any three question .each question carries 8 Marks
Questiopn#5
(a) The mean and geometric mean of three numbers are 34 and 18 respectively. Find all three numbers when geometric mean of first two number is 10.
(b) Compute the median of the following distribution:

Questiopn#6
(a) find standard deviation from the data given below:

(b) Given Σ  = 120, Σx  = 296, mode = 2.94 and second moment about mean = 1.48. calculate coefficient of skewness.

Questiopn#7
(a)        Find laspeyer’s price index number taking 1980 as base:

Questiopn#8
(a) Given the discrete probability mass function mass function
P(x)   =   for x 0, 1, 2, 3, 4. Find the probability distribution and calculate E(x).
(b) A continuous random variable x having values between 0 and 4 has a density function given by (x) = (1/2) -  ax where a is a constant. Find
(i) a 
(ii)  p(1 < x < 2)

Questiopn#9
(a) In binomial distribution n = 5 and p(x =0) = p(x = 1). Find
(i) (p)      
(ii) mean and variance.
(b) A bag contains 4 red and 3 white balls. If 3 balls are drawn at random by without replacement method. Construct probability distribution of white balls.

Section – III

10. Note attempt any three question
(A) Find mode:

(B) Compute quartile deviation and its coeffient:

(C) Calculate the index number for 1990 on the basis of 1978:

(D) fir a binomial distribution if n = 5, p = 0.4 and N = 200.
(E) A bad contains ten items, seven good and three defective A sample of four items is to be selected. Compute the probability distribution for the number of defectives. Also find mean and standard deviation.