Inter (Part-I) Lahore Board 2014
Statistics
Part I (Objective Type)
Time Allowed: 20 Minutes 
Max. Marks: 17

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. Use marker or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question.

Question #1
Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• The observation which occurs maximum number of times is called:

(A) Mean
(B) Median
(C) Mode
(D) H.M.

• A discrete probability function f(x) is always :

(A) Non-negative
(B) Negative
(C) One
(D) Zero

• Coefficient of Quartile Deviation is :

(A)
(B)
(C)
(D)

• Two events A & B are mutually exclusive if :

(A) A∪B =
(B) A∩B =
(C) A∩B=S    
(D) A∪B =1

• The branch of Statistics which deals with procedures of drawing inferences about the population on the basis of sample information is called :

(A) Descriptive Statistics
(B) Inferential Statistics
(C) Applied Statistics
(D) Theoretical Statistics

• If all the values are not of equal importance, the index number is called:

(A) Weighted 
(B) Unweighted
(C) Simple
(D) None of these

• In a hypergeometric experiment, the probability of each Outcome  _______     from trial to trial :

(A) Remains constant
(B) Changes
(C) Depends on N
(D) Depends on n

• The total area under the curve of a continuous probability density function is always equal to:

(A) 0
(B) t
(C) -1
(D)

• For binomial distribution :

(A) Mean <Variance  
(B) Mean > Variance
(C) Mean < Variance 
(D) Mean = Variance

• In a percentage frequency distribution, the total of percentage frequencies is :

(A) 1
(B) 100
(C) Ef 
(D) Ex

• For symmetric distributions :

(A) Mean < Median.< Mode
(B) Mean > Median >. Mode.
(C) Mean < Mode < Median
(D) Mean = Mode = Median

• The binomial distribution has  _______     parameters :

(A) 0
(B) 1
(C) 2
(D) 3

• The general purchasing power of the currency of a country is determined by :

(A) Retail price index
(B) Volume index
(C) Composite index 
(D) Wholesale price index

• If A is an empty set and S is the sample space then :

(A) P(A∪S) =1
(B) P(A∩S) = 0
(C) P(A∩S) =1
(D) P(A) = P(S)

• Arithmetic mean for Xi and X, :

(A)
(B)
(C)
(D)

• The value of standard deviation changes by a change of :

(A) Origin
(B) Scale
(C) Algebraic sign
(D) Both A and B

• Suitable average for averaging to shoe sizes is :

(A) Mean
(B) Median
(C) Mode
(D) Geometric mean

Inter (Part-II) Lahore Board 2014
Statistics
Part II(Subjective)
Time Allowed: 2.10 Hours 
Max. Marks: 83 

Section I

2. Write short answers to any EIGHT (8). Questions •                     16

• Define Statistics.
• What is Primary data?
• What is central tendency?
• Define Median.
• Give two properties of Arithmetic Mein.
• If variance of the value of "X" is 25, what is the standard Deviation of X?
• Explain the moments about mean.
• Distinguish between positive and negative skewness with diagrams.
• What do you mean by non-mutually exclusive events?
• Differentiate between simple event and compound event.
• Given P(A) = 0.3 . P(B) = 0.4 and P (A and B) = 0.20. Are A and B statistically independent?
• What is meant by dependent events?

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

• Define mathematical expectation.
• Enlist two properties of expectation.
• Given X = 0, 1,2 and P(x) = 9/16,6/16,1/16, find variance of X.
• Define random experiment.
• Define probability density function.
• Define binomial distribution.
• What is Bernoulli trial?
• What are the properties of hyper geometric distribution?
• Find the number of trials of a binomial distribution which has mean =12 and S.D = 2

(SECTION-II)
Note: Attempt any THREE questions.

Question #5
(a) Find the Arithmetic Mean from the following data

	-2	-1	0	1	2	3
F	5	8	15	20	12	4

(b) Find  the H.M from the data given below:

Question #6
(a) Calculate first four moments about Mean for the following set .      45. 32, 37, 46, 39, 36. 41. 48 and 36.
(b) The ungrouped data is given below: 2,5,6,6,8,9,12,13,16,23 Calculate the Mean Deviation from mean.

Question #7
(a) The price in Rs. per maund of coal sold during the years 1953-58 are given below :

Using 1956 as base find price relatives corresponding to all the given years:
(b) Determine the probabilities for each of the following events:
(i) A sum 8 appears in a single toss of a pair of dice
(ii) Two dice show the same number.

Question #8
(a) A continuous random variable X has a density function :         f (x)= for X=2to X=4= 0 otherwise
Find = (i) P (X < 3.5)       (ii) P (2.4 < X <3.5.)
(b) For the following probability distribution of random variable,X, find the mean and variance:  

Question #9
(a) If 20% of bolts produced by a machine are defective, determine the probability that out of 4 bolts chosen at random :   (1) Zero,   (ii) 2 bolts are defective.     
(b) Given that X is a hypergeometric random variable with N= 8 , n = 3 and K = 5 , compute P ( X < 3 ) 

Attempt any three Parts Section-III ( Practical Part )

(A) Find Mode from following data : 

(B)Find variance from following data

(C)The following data shows average price for wheat, riceand barley :       

Taking 1980 as base year, construct Price Index No. by weighted average of relative method for the year 1981 using weights 20 for wheat,. 12 for rice and 4 for barley.
(D) If f (x)= for X=2,3,4------12

(E) Five mean are tossed 96 times. Find expected frequencies when throwing of a 4,5,6 is regarded as success.