Inter (Part-I) Bahawalpur 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.

• A characteristic which varies from one object to another object is called

(A) Variable
(B) Constant
(C) Coefficient
(D) Exponent

• Total of Relative Frequency is called

(A) One
(B) Two
(C) Half
(D) Quarter

• Harmonic Mean can not be computed if any value in the data is:

(A) > 0
(B) < o
(C) = 0
(D) = 1

• The most popular value of the data is called :

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

• Q₂ = Q₅ = P50 = ?

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

• The variance of 12 , 14 , 16 , 18 , 20 is 8 then the Variance of 10 , 12 , 14 , 16 , 18 is

  (A) 6
  (B) 8
  (C) 10 
  (D) 0

• For Symmetrical Distribution:

(A) ß₁ > 0
(B) ß₁ < 0
(C) ß₁ = 0
(D) ß₁ = 3

• The Mean Deviation is least when Deviation are taken from :

(A) Mean
(B) Median
(C) Mode
(D) Origin

• In a fixed base method which period is always taken as 100 :

(A) Preceding 
(B) Following 
(C) Base
(D) Current

• Consumer Price Index Number may be obtained by:

(A) Laspeyre's Formula
(B) Paasche's Formula
(C) Fisher's Formula
(D) Link Relative

• The Probability of an event always lies between

(A) - 1 and 0
(B) - 1 and 1
(C) 0 and 1
(D) 1 and 2

• The Probability of drawing a Icing from 52 playing cards is

(A) 4/ 52
(B) 3/52
(C) 2/52
(D) 13/52

• If x and y are two independent variable then E(xy) = :

(A) E (x) E (y)
(B) E (x) + E (y)
(C) E (x) - E (y)
(D) Zero

• E ( x - µ)² = : 

(A) Zero
(B) S.D
(C) Variance
(D) M . D.

• A Binomial Distribution has variance:

(A) nq
(B) np 
(C) npq
(I)) √npq

• In Binomial Distribution P=1/2 then m₃ is:

(A) = 0
(B) < 0
(C) > 0
(D) Mean

• Hypergeometric Distribution has parameters :

(A) n, p
(B) n, p,q
(C) N, n, k
(D) n , k

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

Section I

Q.2. Attempt any eight parts.

• Define Parameter and Statistic.
• Define Discriptive and Inferential Statistics.
• Define Harmonic Mean.
• Write two properties of Arithmetic Mean.
• For a certain distributionI Σ (x-15)²=868, Σ(x-16)²=720, Σ(x-20)²=982 
• What is the value of Mean and Why?
• Distinguish between an Uri-weighted Index Number and a Weighted Index Number.
• Calculate G.M. for 0,2,4,6,10.
• Find the Mode and Median of the letter Statistics.
• Define Link Relative.
• Write the formula for Fisher's Index Number.
• Given Σp_oq_o=1500 and Σp_nq_o=2040 find Base Year Weighted Index.
• Write down two formulae of Consumer Price Index Number.

Q.3. Attempt any eight parts.  

• Explain the term Classification.
• Define Absolute Measure of Dispersion.
• If Range = 48, Interval (h) = 5 find no. of classes (m) = ?
• If Mean = 8 , Mean Deviation = 4•8 find Coefficient of Mean Deviation.
• What is the difference between Positive and Negative Skewness?
• If P(A) = 0.7 and P(B) = 0.5 find P(A Ո B) where A and B are Independent Event.
• If S.D.(x) = 3, find S.D.(5x + 2 ).
• 1^st three Moments about mean are: µ₁ = 0, µ₂ = 8, µ₃ = 0 find B.
• Define Moments.
• Define Mutually Exclusive Events.
• Define Random Experiments.
• Define an Event.

Q.4. Attempt any six parts.    

• Define a continuous Random Variable.
• Define Expectation of a Random Variable.
• Write down any two laws of Expectations.
• What is the Sample Space of a Random Variable?
• Define Hypergeometric Experiment.
• Given N=10, n=2 and K= 3 find P (x = 0)
• What are Parameters, Mean , Variance and Standard Deviation of Binomial Distribution?
• State the formula used to find out the probabilities of a Hypergeometric Distribution.
• What are the properties associated with a discrete random variable?

Section-II

Question #5
(a) The Frequency Distribution given below has been obtained from use of working origin. (4)

If D = x-18, find Mean and H.M.

(b) Compute Median, Mode , Quartiles for Number of Children. 4

Question #6
(a) Calculate Mean Deviation and Coefficient of Mean Deviation about Mean from the following data. 4

(b) The Mean of 200 items is 48 and their Standard Deviation is 3.Find the Sum of Squares of all these items. 4

Question #7
(a) Given Σp_oq_o = 352; Σp₁q₁=481, Σp₁q_o=422; Σp_oq₁=402 find 4
(i) Base Year Weighted Index Number
(ii) Current Year Weighted Index Nubmer.
(b) 52 Cards are equally distributed among 4 players. What is the probability that a player has 5 Club Cards? (4)

Question #8
(a) In a Summer Season, a dealer of Desert Room Cooler can earn Rs. 800per day if the day is very hot and can earn Rs. 200 per day If it is fair. And loses Rs.50 per day if it is cloudy. Find his mathematical expectation if the probability of the day being very hot is 0.40 and for being cloudy is 0.35?
(b) A continuous random variable ' x' having values between 0 and 4 has a density Function given by f(x) = ½ - a.x; where ' a ' is any constant. Find (i) a (ii) P(1≤x≤2)

Question #9
(a) A fair coin is tossed 5 times.Pihat is the probability of getting : (4)
(i) at least two heads
(ii) at the most two heads.
(b) A committee of siz 3 is selected at random from 4 men and 2 women. Find the Probability Distribution for the number of men on the committee.

Attempt any three Parts Section-III ( Practical Part )

Question #10
(a) Calculate Geometric Mean from the Data given below. (5)

(b) Find Coefficient of Variation from the Data given below. (5)

(c) Calculate Price Index Number by Paasche's Method from the following data. (5)

(d) Find the complete Binomial Distribution for (1/2 + 1/2)⁵, Also find Mean and Standard Deviation.

(e) A committee of size 5 is selected from 5 men and 6 women. Find the Complete Probability Distribution for number of men in the committee. (5)