Sargodha board 2015

(Statistics)                                                                         (Inter part1)

(OBJECTIVE)

Note: Pour possible answers A, B; C and D to each question are given. The choice which you think is correct that circle in front that question with Marker or Pen ink. 'Lining or filling two or more circles 'will result in zero mat k in that question. Write the letter A, B. C or D in the column.(write correct "option) against each question also. If there k a contradiction in the bubble and hand written answer, bubble option will be considered correct.

• The word "Statistics" is the plural of.

1. Variable
2. Statistic
3. Parameter
4. None of these

• The graph of the cumulative frequency distribution is called:

1. Histogram
2. Frequency Polygon
3. Ogive
4. None of these

• If we divide the upper class and lower class limits of a particular class by 2, then we get.

1. Class Mark
2. Class Interval
3. c.f
4. None of these

• G.M of the numbers: -2, -4, 3, 0, 5 is

1. 3
2. 9
3. 2
4. Not possible

• Harmonic Mean of the numbers:- 0, 1, 3, 9, 5 is:-

1. 2
2. 5
3. -1
4. Not possible

• The variance of 7,7,7,7 is:

1. 7
2. 49
3. Zero
4. Not possible

• Var (4x +3) is:-

1. 12.Var (x)
2. 4.Var (x) + 3
3. 16.Var (x)
4. None of these

• For a set of 10 numbers ∑(x-x)² =360 then S.D will be:-

1. 36
2. 6
3. 12
4. None of these

• In chain base method, the base period is:-

1. Fixed
2. Changed
3. First year
4. None of these

•  if ∑P_n.q_n=505,  ∑P_n.q_n=425 , then: Laspeyre's index is

1. 108.8
2. 118.8
3. 128.8
4. 138.3

• The probability of a sure event is always equal to:

1. One
2. Zero
3. Negative
4. None of these

• The Probability of an event cannot be:

1. Greater than one
2. Less than zero
3. Negative
4. All of these

• If E(x) -1.1, then E(3x +5) is:-

1. 8.1
2. 8.2
3. 8.3
4. 8.4

• If Var (x)=5, Var (y) =10, then Var (2x +y) is:-

1. 10
2. 15
3. 30
4. 25

• 1n Binomial distribution, successive trials are,

1. Dependent
2. Infinite
3. Independent
4. None of these

• Binomial distribution becomes symmetrical if :-

1. p=q
2. p>q
3. p<q
4. None of these

• If in Hypergeomatric distribution, n=5 ,k=4 ,N=11  then Mean is:

1. 1.8280
2. 1.8286
3. 1.8182
4. 1.8081

 SUBJECTIVE PART

Inter part1

(Section I)

Question#2:
 Answer briefly any eight parts from the followings

• Explain any two uses of Statistics.
• Name the different sources of secondary data (Any four).
• Define Geometric mean.
• Define Harmonic mean.
• Define Median.
• If n₁ =3, n₂=2, x₁=3,  x₂=4 find  x 
• If ∑(x-15)=5, ∑(x-18)=0. ∑(x-21)=-21 What is the value of mean?
• Define Index number.
• Define Fixed Base method.
• Define Chain Base method.
• Name the methods of calculating Cost of Living Index number with formula
• Given ∑P_n.q_o=422, ∑P_n.q_o=352, find Laspeyer's Price Index number.

Question#3:
Answer briefly any Eight parts from the followings:-

• Define Class mark
• Define frequency distribution.
• Write two formulas to calculate co-efficient of skewness.
• Define dispersion.
• n=15, ∑x = 480 ∑x²=15735 find C.V
• If co-efficient of skewness is zero, what will you say about mean, median and mode?
• Define symmetry
• If mean = 25, cv= 64%, what will be the variance?
• Define Product set.
• What is the sample space, if 3 coins are teased
• Define independent events
• If A and B are two independent events such that P(A) =0.2 P(B) = 0.15, then calculate
   P(A∩B)
   P(A/B)    

Question#4:
Answer briefly any six pails from the followings

• What are the properties of a probability distribution,
• If E(x)=12 and E(x²) = 153 find Var (x)  
• Define discrete random variable.
• Write down the types of random variables.
• What do you mean by expected value of a r.v.
• Write down the properties of hypergeomatric experiment.
• Is it possible to have a binomial distribution with mean = 5 and SD = 3 and why?
• When binomial distribution is positively skewed.
• What is binomial frequency distribution?

Section II

Note: Attempt any three questions.

Question#5:

a) Find G.M for the following data.

b) Find median for the data given.

Question#6:

a)Find the co-efficient of Variation to the data.

b)The 1^st four moments of a distribution about x=2 are 1,2.5,5-5,16. Find the 1st four moments about mean.

Question#7:

a)Compute the Fisher's index number for the following data:

b)A bag contain 14-identical balls, out of which 4 are red , 5-black and 5-white balls. If three balls are drawn , find probability that

              i)3 are red
              ii)2 are white

Question#8:

a)A continuous random variable x has a density function given by. F(x)= A(x+5) where 3< x < 4. Find

             i)A
             ii)P(2<x<3)

b)Given the following probability distribution:

Verify that.  E(2x+3)=2E(x)+3

Question#9:

1. An urn contains five good and four bad eggs. Three eggs are selected without replacement. Find the probability that
2. Find the mean and variance of (q+p)3

            i) all good eggs are selected
           ii) at least one good egg is selected

 Section III   (PRACTICAL)

Note: Attempt any three Parts.

Question#10

a)Find the median from the following data.

b)Find mean deviation from mean for following data.

c)Find price relatives Inc the following data taking

1. 1990 as base year
2. Average of first five years as base.

d)Find a complete binomial distribution with parameters and  

e)Five balls are drawn from box containing 4 white and 7 black balls. If x denotes the number of black balls selected, find the probability distribution of x.