HSC Statistics 1st Paper Model Test-2

Class – XII

Subject : Statistics 1st Paper

Time : 3 hrs.                                                                                                                                         Marks. 75

[ N.B. The figures in the right margin indicate full marks.]

1.	(a)  Discuss the meaning of statistics. Discuss the function of statistics.	2+4=6
Or,	(b)  What is classification and tabulation? Discuss the basis of classification and tabulation?	4+
Or,	(a)  Define measures of central tendency? Describe its different measures.	2+5=7
	(b)  Write down the properties of arithmetic mean.	3
	(c)  In your view, which average is the best and why?	3
	(d)  Two variables x and y are connected by the equation  y = 4x +3. If mean of x is 15. Find the mean of y.	2
2.	(a)  What do you mean by measures of dispersion?	1
	(b)  Distinguish between the absolute and relative measures of dispersion.	3
	(c)  Under what situation does standard deviation take the least value.	3
	(d)  If the mean and the standard deviation of n non-negative observations are  and 6 respectively then prove that ³ 6.	4
	(e)  The mean and variance of two numbers are 10 and 4 respectively. Find the numbers and C.V.	4
Or,	(a)  Define moments. Show that,	1+3=4
	(b)  What is Skewness? Describe different types of skewness with their figures.	1+4=5
	(c)  Write down the properties of moments.	3
	(d)  1st three moments about 3 are -1, 5, and 9. Find CV. and 3rd central moments.	3
3.	(a)  What do you mean by correlation and Co-efficient of correlation.	3
	(b)  Write down the properties of co-efficient of correlation.	3
	(c)  What is scatter diagram? Discuss the various natural of correlation through scatter diagram.	6
	(d)  If the correlation co-efficient between x and y is r. Find the co-efficient of correlation between ( 3x -1) & ( 2y -1).	3
Or,	(a)  Define time series. Discuss its components.	1+6=7
	(b)  Write down the name of statistical publications of Bangladesh. Discuss any of them.	2+3=5
	(c)  Write a short note on Bangladesh Bureau of statistics.	3
4.	What do you mean by median. How do you locate median graphically.
Or,	Show that :  S ( xi -a )2 >  S ( xi - )2 where a ¹
5.	Find the mean and standard dedication of the 1st n natural numbers whose frequencies are equal to their corresponding numbers
Or,	The daily mean wages of 50 labourer was calculate as taka 90. But later on, it was found that the wages of two labours were misred as taka 49 and taka 98 instead of taka 94 and taka 89. What is the actual mean wages of labour.
6.	What is rank correlation? show that  ¦ = 1 -
Or,	The regression equation of  y on x is 4x -5y + 33 =0 and the regression equation of x  y is 20x -9y -107 =0. If the standard deviation of x is 6. find the mean of x and y. Standard deviation of y and correlation co-efficient.
7.	What do you mean by symmetrical distribution? Prove that 5th central moment is independent of origin but not of scale.
Or,	Prove that both  are independent on the change of origin and scale where the symbols have usual meanings.
8.	What do you mean by weighted arithmatic mean? Discuss its importance in statistics.
Or,	prove that. (i)              (ii)
9.	Show that the mean and median are equal for n natural numbers.
Or,	Justify your answer       (i)   Moments can be negative. (ii)  Arithmatic mean is influenced by extreme values.