Statistics
Lahore Board 2015
Inter Part-I
Time: 20 Min.
Objective
Marks = 17
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 in the answer-book. Cutting or fillting two or more circies will result in zero mark in that question.

Q1

• The variance of 5, 5, 5, 5 and 5 is :

(A) Zero         
(B) 25
(C) 5   
(D) 125

• If N = 40, n = 5, K= 4, then mean of hypergeometric distribution is

(A) 1
(B) 1/2
(C) 1/4
(D) 1/3

• When two dice are rolled, the number o possible outcomes are : -

(A) 6   
(B) 12
(C) 36 
(D) 48

• The frequency of a class divided by total frequency is called :

(A) Class frequency   
(B) Cumulative frequency
(C) Relative frequency
(D) Total frequency

• In a symmetrical distribution Q1=4, Q3=12, then median is :

(A) 4   
(B) 6
(C) 8   
(D) Zero

• For computing chain index number, we compute :

(A) Price relative        
(B) Link relative
(C) Weighted indices
(D) None of these

• How many methods are used for the collection of data:

(A) 1   
(B) 2
(C) 3   
(D) 4

• For a binomial distribution with n = 5 prob. (X=-2) is:

(A) 0   
(B) Greater than zero
(C) Less than zero      
(D) None of these

• If P=1/2, then binomial distribution is called :

(A) Symmetrical         
(B) Skewed
(C) Positively skewed
(D) Negative skewed

• Mean is affected by change of :

(A) Origin      
(B) Scale
(C) Both A and B      
(D) None of these

• For a random variable X, ΣP(X) is equal to :

(A) Zero         
(B) 1
(C) Greater than 1      
(D) Less than 1

• Sum of absolute deviations of the values is least, when deviations are taken from:

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

• If A and B are mutually exclusive events, then P (AՈB) is :

(A) Zero         
(B) 1
(C) 0.5
(D) 0.8

• Smoking habits of residents of a city are :

(A) Qualitative data   
(B) Quantitative data
(C) Discrete data        
(D) Continuous data

• Which of the following average is most suitable for computing chain index number:

(A) A.M.        
(B) Median
(C) G.M.        
(D) H.M.

• If X and Y are independent variables then E (XY) is equal to:

(A) E(X).E(Y)
(B) X E(Y)
(C) Y E(X)     
(D) None of these

• If Q3=20, Q1=10, the coefficient of quartile deviation is :

(A) 3   
(B) 1/3
(C) 2/3
(D) 1

Statistics
Lahore Board 2015
Inter Part-I
Time 3.10 hrs
Essay Type
Marks : 83
SECTION - I

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

• Define population and sample.
• Define descriptive statistics.
• Define geometric mean.
• Write any two qualities of a good average.
• Define mode with formula.
• The sum of deviations of 15 values from 20 is 45. Find arithmetic mean.
• If mode=15 and mean=10.5. Find median.
• Define composite index number.
• Define link relatives.
• What is consumer price index number?
• Find the current year weighted index for given data Σpnqn=2260, Σpoqn=2230.
• If Laspeyre's index number = 105.4 and Paache's index number = 103.2, find the Fisher's index number?

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

• What is meant by frequency distribution?
• Distinguish between one way classification and two ways classification..
• In a symmetrical distribution, Ql=25 and Q3=75 then find the value of median.
• The first two moments of a distribution about X=10 are 2 and 20. Find coefficient of variation.
• Define the term 'standard deviation'.
• Name the various absolute measures of dispersion.
• Given Mean=50, Median=48 and standard deviation =6 then find Karl's pearson's coefficient of skewness.
• What is meant by skewness and how it is calculated?
• Differentiate between permutations and combinations.
• What is meant by random experiment?
• If P(A)=0.30, P(B)=0.60 then find: (a) P (A/B) (b) P (A Ս B), assuming that A and B are independent?
• State only law of additions for both mutually and non-mutually exclusive events.

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

• Define random experiment.
• What is random variable?
• What is discrete random variable?
• ‘If E(X) = 1.1 and E (X2) = 2.1, find var (X)?
• ‘If E(X) =1.1, find E (3X + 5 )?
• What are 'Bernoulli trials' ?
• What is 'Binomial experiment'?
• If n = 4 , p= 1/2, find P (X = 3 )?
• Is it possible to have a binomial distribution with Mean = 5 and S.D. = 4?

SECTION-II
Note: Attempt any THREE questions.

5.(a) Compute weighted arithmetic mean:

(b) Calculate median for the given data: 4

6.(a) Find quartile deviation from the following observations:04

10, 12, 15, 25, 28, 35, 42, 20, 32, 18, 14, 5                         
                          
(b) Calculate the first four moments about X = 17.5 from the data given below: 4

7.(a) Find chain indices:

(b)When two dice are rolled, what is the probability of getting a sum of 8?4

8.(a) A continuous random variable X, which can assume between 2 and 8 inclusive, has a density function given by :4
f(x) = a(x + 3) where a is a constant
Find

• a
• (P 3 < x < 5)

(b) Given the following discrete probability dist:

Find its mean and S.D.

9.(a) If 20% of bolts produced by a machine are defective, determine the probability that out of 4 bolts chosen at random:4

• zero bolts defective,
• 2 bolts are defective?                                                                                   

(b) Three balls are drawn from a bag containing 5 white and 3 black balls. If X denote the number of white balls, then find the probability distribution of X. 4

SECTION - III (Practical Part)

Note: Attempt any THREE questions.

A. A variable 'Y' is determined from a variable 'X' by the equal Y=10-4X. Find ‘Y’when X= -3, -2, -1, 0, 1, 2, 3, 4, 5 and show that Y =10 - 4X : (5)

B. By using provisional mean, calculate variance for the values 14, 16, 23, 25, 29, 30, 35, 40.  (5)

C. Given the following information: (5)
Σpogo = 3600, Σp1qo = 4300, Σpoq1=4100, Σplq1=4890. Show that
Fisher's Ideal Price index number is the G.M. of Laspeyre's and Paasche's index                                                                
number.

D. Let 'X' has the following probability distribution : 5

Find E (X) and E (X2)

E. Four dice are tossed 96- times. Find the expected frequencies when throwing of 4, 5,or 6 is regarded as a success.5