Inter (Part-I) Lahore Board 2013
Statistics (New Scheme) 
Paper: 1
Time Allowed: 20 Minutes
Max. Marks: 17
OBJECTIVE
Note: Four possible answers A, B, C and D to each question are given. The choice which you think is correct, fill that circle in front of that question with Marker or Pen ink. Cutting or filling two or more circles will result in zero mark in that question.

Question#1

• Which of the following averages is affected by extreme values:
  
  (A) Arithmetic mean
  (B) Median
  (C) Mode
  (D) All of these
  
  
• The distribution function of a.r.v. X, denoted by F(X), is:
  
  (A) F(x) = P (Xx)
  (B) F(x) = P (Xx)
  (C) F(x) = P (X = x)
  (D) None of these
  
  
• In a negatively skewed distribution:
  
  (A) Mean = Mode
  (B) Mean > Mode
  (C) Mode > Mean 
  (D) None of these
  
  
• The events A and B are mutually exclusive. If P(A) 0.2, P(B) = 0.4, P (A  B) is:
  
  (A) 0.08
  (B) 0.6
  (C) 0
  (D) There is not enough information
  
  
• A quantity calculated from a population is called:
  
  (A) Frequency
  (B) Statistic
  (C) Parameter 
  (D) Sample
  
  
• CPI falls in the category of:
  
  (A) A simple index    
  (B) An aggregative index
  (C) An inflationary index
  (D) Wholesale price index
  
  
• The mean of the hypergeometric destruction is:
  
  (A )
  (B)
  (C)  
  (D)
  
  
• Which of the following is not possible in a probability distribution?
  
  (A) f (x) > 0   
  (B) ∑f (x) = 1
  (C) ∑xf (x) = 2
  (D) f (x) = -0.3
  
  
• The mean and variance of the binomial distribution are:
  
  (A) np and  
  (B) np and npq
  (C) np and nq
  (D) n and p
  
  
• The average of lower and upper limits of a class is called:
  
  (A) Class mark
  (B) Class frequency
  (C) class boundary 
  (D) Relative frequency
  
  
• The range of the scores 19, 3, 140, 25, 95 is:
  
  (A) 140
  (B) 3
  (C) 137
  (D) 143
  
  
• The parameters of the binomial distribution are:
  
  (A) n and p     
  (B) p and q
  (C) np and nq 
  (D) np and npq
  
  
• Which of the following formulas is a price index panther?
  
  (A)
  (B)
  (C)
  (D) All of these
  
  
• Which of the following cannot be probability of an event?
  
  (A) 0 
  (B) 1
  (C) 0.32 
  (D) 1.05
  
  
• The modal letter of the word "STATISTICS" is:
  
  (A) No mode  
  (B) S
  (C) T   
  (D) S and T
  
  
• If var (X)= 9, then S.D. (2X + 4) is:
  
  (A) 36       
  (C) 18 
  (D) 6
  
  
• Cumulative frequency curve is also called:
  
  (A) Histotrigram 
  (B) Histogram
  (C) Ogive
  (D) Frequency curve

Statistics (New Scheme)
Paper: I
Time: 3:10 Hours
Marks: 836.)
SUBJECTIVE
(Section –I)

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

• Define population and sample.
• Write sources of secondary data.
• Define quartiles.
• Describe empirical relation between mean, median and mode.
• For a certain distribution, if ∑(X -15) = 5 , E (X - 18) = 0 and ∑ (X -21) = -21, then what is the value of mean and why?
• Write any two properties of arithmetic mean.
• If mean = 20, median = 18, find mode for a set of data?
• Differentiate between fixed base method and chain base method.
• Define unweighted index number.
• Define volume (quantity) index number.
• Define link relative and how we calculate it.
• If Fisher's Ideal Index = 117.84 and Laspeyre's Index = 117.9, then what will be Paashe's Index?

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

• Differentiate between historigram and histogram.
• Enlist the main parts of a table.
• Define the range. How will you calculate it for grouped data?
• Given that Q1 = 89 and Q.D. = 10.875, then find the value of Q3.
• Define variance and give its atleast two formulas.
• For a set of ungrouped values, the following sums are found: n= 15 , ∑x = 480 ∑x2 = 15735, find the C.V.
• For a certain distribution mean = 40, median r=41 and coefficient of skewness = -0.25, find the value of S.D.
• var (x) = 5 and var (y) = , then find var(2x 3y)?
• Define set and a subset.
• What do you understand by random experiment?
• If A and B are two independent events, such that P (A) = 0.2 and P (B) = 0.15, then evaluate :
  (i) P (A ∩ B)
  (ii) P (A/ B).
• Write the sample space, when three fair coins are tossed.

4. Write short answers to any SIX (6) questions:(12)

• Describe the properties of a probability distribution (Discrete).
• Write down the properties (any two) of mathematical expectation.
• If E (X) = 3 and E (X2) = 12, then find variance and S.D. of X?
• Write down the properties of a random experiment.

• Find the value of C =?
• Define binomial random experiment.
• In binomial distribution n = 5 and P = 0.2, find coefficient of variation.
• If N = 10, K = 5, n = 3, find P (X < 1) = ?
• Write down the formula of variance of hypergeometric distribution.

(Section — II)

Note: Attempt any THREE questions.
Question#5
(a) The deviations 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 and 0.4 Find out lower quartile of X. 4
(b) Consider the following data:

Compute harmonic mean.

Question#6
(a) Compute the variance from the following data:  4

b) If q2 = 26.01 , q3 = 38.29 , q1 = 13.73, find coefficient of skewness?  4

Question#7
(a) Compute Fisher's Ideal Price Index Number for the year 2001 taking 2000 as base year: 4

a) A fair coin is tossed four times. Find the probability that there will appear:
(i) At least 2 heads.
(ii) At most 2 heads. 
(b) Determine the probability distribution for the number of white beads among 5 beads drawn at random from a box, containing 4 white and 7 black beads. 4

(Section — III)
( Practical)

10. Attempt any THREE questions:
(A) Calculate median both by graph and formula from the given data: 5

B) Calculate quartile deviation for the data given below: 5

(C) Construct the index number for 1963 assuming 1953 as base period by: 5
(i) Laspeyre's formula
(ii) Paasche's formula.

(D) Out of 800 families with 5 children each, how many would you expect to have:
(i) 3 boys
(ii) 5 girls
(iii) 5 boys(E) Five balls are drawn from a box containing 4 white and 7 black balls. If X denotes the no. of black balls selected, find the probability distribution of X? 5