HSC Statistics Model Question-3

Subject : Statistics 

Time : 3 hrs.                                                                                                                                     Marks. 75

1.         a)         Distinguish between Discrete and continuous variable.                                          4+5+3+3=15

           

            b)         Prove that       (i)       

                                               (ii)

            c)         Define variable and constant.

or,        a)         What are the properties of arithmatic mean? Prove any two of them.

            b)         The A.M and G.M. of two numbers are 25 and 15 respectively. Find the H.M and the numbers.

            c)         Find the arithmatic mean of the given observations 5. 10. 15 .... . ...... .....125.

2.         a)         What do you mean by measures of dispersion?                                                       2+4+5+4=15  

            b)         Distinguish between absolute and relative measures of dispersion.

            c)         If  X and  S be arithmatic mean and standard deviation respectively of n non-negative   observations the prove that 100  > C. V.

            d)        Show that standard deviation is independent of origin but depend on the change of scale.

or,        a)         What is dispersion? Discuss various measures of dispersion.

            b)         Find the variance of the n natural number.

            c)         Show that mean deviation is independent of origin but depend on the change of scale.

3.         a)         Define moment

            b)         Distinguish between central moments and row moments.

            c)         Show that.      (i)

                                                (ii)      

            d)        The first four moments about the value 4 are -1.5, 17, -30 and 108. Find the moments about the

            mean also find ₁ and  ₂

           

or,        a)         Write down the properties of moment.                                                                    3+8+4=15

            b)         Express the first row moments in times of central moments.

            c)         Show that moment is independent on the change of origin but dependent on the change of scale.

4.         Prove that  ₂  >  ₁ +1

or,        Prove that  ₂  >  ₁

5.         What do you mean by measures of skewness? State different formulac in Calculating the co-efficient of             Skewness.

or,        Show that that ₁ and  ₂ both are independent on origin and scale.

6.         The frequencies of first n natural numbers are equal to their corresponding values. Find the mean and             standard deviation of the distribution.

or,        for two observations show that,  MD= S.D ^R/₂

7.         Show that for two non-zero positive numbers A.M> G.M > H. M.

or         Prove the   (xi -a)² >.    (xi -x )² where a = x

8.         Prove that sum of the absolute deviations from the mean is equal to difference between the sum of numbers greater and the sum of numbers smaller than the media .

or,        Prove that

            (i)        G. M = Antilog (                       )

            (ii)       G =   where n₁ =n₂

9.         If the G. M of n₁ values is G₁ and n₂ values is G₂ and that of n₁ +n₂ values is G then show that

            log G =

or,        What is co=efficient of variation? Discuss its importance.