Statistics (New Scheme)
 Gujranwala Board Inter Part I
Time:20 Minutes
Objective Type
Max. Marks: 17
Note: You have four choices for _each objective type question as A, B, C and D. The choice you think is correct, till that circle in front of question, number. Be marker or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question. Attempt as many questions as given in objective type question paper and leave others blank.

• A specific characteristic of a population is called.

(a) Statistic'
(b) parameter
(c) variable 
(d) Sample

• Histogram is a graph of:

(a) Frequency distribution
(b) tune series
(c) qualitative data
(d) ogive

• Ogive is a graphical representation of:

(a) Frequency distribution
(b) raw data
(c) Cumulative frequency representation
(d) historigram

• It is important to array the data before calculating;

(a) mean
(b) median
(c) mode
(d) geometric mean

• In a symmetrical distribution:

(a)  
(b)  
(c) A.M. = G.M = H.M
(d) AM = Med =Mode

• The range of the values -2, -4, -6 and -8 is:

(a)-6
(b)6
(c)-10
(d) -4

• The mean deviation is minimum when deviations arc taken from:

(a) mean
(b) median
(c) mode
(d) zero

• The standard deviation of values -2, -2, -2, is:

(a) -2
(b) 2
(c) zero
(d) -1

• An index that measures the change for a fixed time period is called:

(a) Chain base method
(b) fixed base method
(c) Simple aggregative method
(d) cost of living method

•  x 100 is called:

(a) simple index
(b) weighted index
(c) simple aggregative index
(d) price relative

• The events having no element in common are called:

(a) Equally likely events
(b) exhaustive events
(c) Mutually exclusive events
(d) independent events

• Arrangement of things without regard to order is called:

(a) combination
(b) permutation
(c) arrayed dat
(d) raw data

• Var(x) is equal to:

(a)
(b)
(c)  
(d)

• The expected value of a random variable is equal to its:

(a) Mean
(b) median
(c) mode
(d) variance

• The parameters of binomial distribution are:

(a) n. p and q
(b) n and q
(c) n and p
(d) p and q

• The binomial distribution is negatively skewed if:

(a) p 
(b) p= 
(c) p 
(d) p=1

• In a hyper geometric distribution:

(a) Mean > variance
(b) mean < variance
(c) Mean=variance
(d) mean =zero

Statistics (New Scheme)
 Gujranwala Board 2015
Inter Part I
Paper I
  Time: 3:10 Hours
Subjective Type
Max. Marks: 83
 (SECTION-I)

Q.No.2 Write short answers to any EIGHT questions:     (2x8=16)

• Define primary data.
  
• Define continuous variable.
  
• Define the term harmonic mean.
  
• If =10,  =15,  =18, ==12, find 
  
• Define percentiles.
  
• If mean = 75, mode = 70. Find median.
  
• Define weighted mean.
  
• If = 480 and = 410, then find current year weighted index No.
  
• What is base period?
  
• Write down any two uses of index numbers.
  
• Which averages are used in index numbers?
  
• Write down some names of consumer items.

Q.No.3 Write short answers to any eight questions:

• Define tabulation.
  
• Differentiate between ungrouped and grouped data.
  
• Define absolute measure of dispersion.
  
• Enlist the relative measures of dispersion.
  
• Define mean deviation.
  
• Write any two properties of standard deviation.
  
• Differentiate between positive skewness and negative skewness.
  
• The mean of a certain distribution is 3 while its second moment about mean is 64. Find its S.D.
  
• Define combination.
  
• Define equally likely events.
  
• Differentiate between mutually exclusive and not = mutually exclusive events.
  
• If A and B are two independent events, such that P(A) = 0.2  and  P(B) = 0.15. then find P(AuB).

Q.No.4 Write short answers to any SIX questions: (2x8=16)

• What is random variable?
  
• Define continuous random variable.
  
• Define discrete probability distribution.
  
• Give E(x) =10, find E(y) if y = 3x + 7.
  
• Define mathematical expectation.
  
• Define binomial probability distribution.
  
• In binomial distribution n = 3, p= , find p(x  2).           
  
• What are properties of hyper geometric experiment?
  
• In binomial distribution np =  and npr , find its parameters.                                 

(Section-II)

Q.No.5 (a) Reciprocals-of 'X' are given below:                                                                                                                     
0.0267, 0.0235, 0.0211, 0.0191, 0.0174, 0.0160, 0.0148.  Calculate H.M of X.
(b) The following distribution shows the number of orders for Groceries received each week in a particular year by a village shop.

Find  (i) Mode  (ii) Median

Q.No.6 (a) Find the Karl Pearson's co-efficient of skewness for the data given (4)

(b) The first three moments about the value 4 are I, 4 and 10.ls the distribution symmetrical. Positively skewed or negatively skewed?

Q.No.7.(a) Construct index numbers for 1963 assuming 1953 as base period by
(i) Laspeyre's formula
(ii) Paasche's formula
Commodities       1953              963
Price              Quantity               Price          Quantity
A                           2                   50                 10                   40
B .                         3                   10                  8                     5
C                           4                   5                    4                     5
(b) A class contains 0 men and 20 women, out of which half men and half women have brown eyes. Fine the probability that a person chosen random is a man or has brown eyes.

Q.No.8 (a) A continuous random variable x having values between 0 and 4 has the probability density function given by f(x)=ax
Find  (i) a     (ii) P(1 < x < 2)
(b) If f(x) =     for X = 2,3,4,5,……...., 12. Then find mean and variance of random variable X.
Q.No.9 (a) An event has the probability p =   . Find the complete binomial distribution, for n = 5.
(b) A committee of size 3 is selected from 4 men and 2 women. Find the probability distribution by the hyper geometric experiment for the number of men in the committee.

(SECTION-III
(PRACTICAL)

Q.No.10 (a) Find the value of mode from the given data:  

(b) Calculate mean deviations about me n from the following data:

X:              3          5           7             9          11
P(x)           1         0.2         0.4        0.2         0.1
(c) An event has the probability P =  . Find the complete binomial distribution for n = 4. Find mean and variance.