HSC Statistics 1st Paper Model Question-2

Time : 3 hrs.                                                                                                                         Marks. 75

1.         a)         Define statistics. Discuss its characteristics, object and limitations.

            b)         What do you mean by frequency distribution? Discuss the method of construction of a

            frequency distribution.

Or,       a)         What do you mean by central tendency? What are the criteria of a good measure of central

            tendency? Which one is the best and why?                                                                            2+3+1=6

            b)         For two positive number show that    (i)  AM ³ HM.                                                3+2

                                                                                    (ii)  G.M ³

            (c)        3 is deducted from each value of a data set and each obtained value is divided by 5, the   arithmetic mean of the new set is found to be 4. find the arithmetic.                                                     4

2.         a)         What do you mean by dispersion? Discuss different measures of dispersion.                   1+6=7

            b)         For two positive number show that SD = MD = ^R/₂                                                              4

            c)         Prove that mean deviation is least when it is measured from median.                                   4

Or,       a)         Define moments. Distinguish between central moments and raw moments.

            b)         For usual notations prove that m4 = m4¹ - 4m3¹m₁¹ + 6m₂¹ m₁² - 3m₁⁴_.

            c)         Find the 2nd central moments of 1st n natural numbers.

3.         a)         Define correlation. Discuss the classification of correlation.                                1+2=3

            b)         What is Scattered diagram? How the concept of correlation can be expressed with the help of             scatter diagram.                                                                                                                             1+5=6

            c)         Prove that   - 1 £ r £ 1

            d)         Coefficient of correlation is a pure number -Explain.                                                 3

Or,       a)         What is trend? Discuss moving average method.

            b)         What do you mean by time series analysis? What are the model of a time series.

            c)         Discuss the rote of Bureau of statistics in publishing statistics in Bangladesh.

4.         What is rank correlation? Show that  ò 1 -.

Or,       Prove that        (i)        ( xi -a )² >     ( xi - x)².

                                    (ii)        ( xi - x )²  =   xi² - nx ^-2

5.   Show that, Standard deviation of the three numbers x₁, x₂ and x₃ is 6=

Or,       Find the arithmetic mean and standard deviation of the 1st n natural numbers whose frequencies are

            equal to the corresponding numbers.

6.         Show that  b₂ ³  b₁ +1.

Or,       (i)         Calculate S.D and M. D of -3a - 2a, a, 0, a, 2a, 3a.

            (ii)        The mean and variance of two numbers are 7 and 1 respectively. Find the values.

7.         What is histogram? Write the method of calculating mode from histogram.

Or        What do you mean by skewness and kurtosis? Explain their characteristics and measure.

8.         What is regression Co- efficient? Discuss its characteristics.

Or        Estimate a linear regression line of dependent variable y on independent variable x by the method of             least square.    

9.         The regression equation of. y on x is 4x - 5y = 33 =0 and the regression equation of x on y is

            20x -9y -107 = 0. The S. d of x is 6. Find mean of x and y, S.d of y and ray.

Or,       Show that        (i)  r =

                                    (ii)  ³ r.  ( where symbols are usual).