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Question Bank No: 1

1. The weighted A.M. of first n national numbers whose weights are equal is

a)		$\frac{n + 1}{2}$
b)		$\frac{2 n + 1}{2}$
c)		$\frac{2 n + 1}{3}$
d)		$\frac{(2 n + 1) (n + 1)}{6}$

2. If $G_{1}$ , $G_{1}$ are G.M's of two series having n items each and G is the G.M of the ratios of the corresponding observations of two series, then G is equal to

a)		$\frac{G_{1}}{G_{2}}$
b)		log $G_{1}$ - log $G_{2}$
c)		$\frac{{logG}_{1}}{\log G_{2}}$
d)		None of these

3. Variance is independent of

a)		origin only
b)		scale only
c)		origin and change of scale
d)		None of these

4. Median can be graphically determined from

a)		Ogive
b)		Histogram
c)		Frequency curve
d)		None of these

5. The sum of squares of deviations of a set of values is minimum when taken about

a)		A.M
b)		Median
c)		Mode
d)		H.M

6. A statistical measure which cannot be determined graphically

a)		Median
b)		Mode
c)		H.M
d)		Mean

7. If S.D of a set of bservations is 28 and each observation is divided by -4, then S.D of new set is

a)		-28
b)		28
c)		7
d)		-7

8. The variance of the first n natural numbers is

a)		$\frac{n^{2} - 1}{12}$
b)		$\frac{n^{2} - 1}{6}$
c)		$\frac{n^{2} + 1}{6}$
d)		$\frac{n^{2} + 1}{12}$

9. The S.D of first n natural numbers is

a)		$\frac{n + 1}{2}$
b)		$\sqrt{\frac{n (n + 1)}{2}}$
c)		$\sqrt{\frac{n^{2} - 1}{12}}$
d)		None of these

10. If each observation of a raw data whose variance is $σ^{2}$ is increasde by $λ$ , then the variance of the new set is

a)		$σ^{2}$
b)		$λ^{2}$ $σ^{2}$
c)		$λ$ + $σ^{2}$
d)		$λ^{2}$ + $σ^{2}$

11. Which of the following, in case of discrete date is not equal to median?

a)		$4^{th}$ octile
b)		$5^{th}$ decile
c)		$2^{nd}$ quartile
d)		$3^{rd}$ quartile

12. Geometric mean of 1, 2, $2^{2}$ , $2^{3}$ , ...., $2^{n}$ is

a)		2 $\frac{2}{n}$
b)		2 $\frac{n}{2}$
c)		2 $\frac{n - 1}{2}$
d)		2 $\frac{n + 1}{2}$

13. If mode of a data is 27 and mean is 24, then median is

a)		24
b)		25
c)		26
d)		None of these

14. Mean of 100 items is 49. It was discovered taht 3 items 60, 70, 80 were wrongly read as 38, 22, 50 respectively. The correct mean is

a)		48
b)		78
c)		50
d)		80

15. A car owner buys petrol at Rs. 7.50, Rs. 8.00 and Rs. 8.50 per litre for the 3 successive years. If he spends rs. 4000 each year, then the average cost per litre of petrol is

a)		Rs. 8
b)		Rs. 8.25
c)		Rs. 7.98
d)		None of these

16. The weighted mean of first n natural numbers whose weights are equal to the squares of the corresponding numbers is

a)		$\frac{n + 1}{2}$
b)		$\frac{3 n (n + 1)}{2 (2 n + 1)}$
c)		$\frac{(n + 1) (2 n + 1)}{6}$
d)		$\frac{n (n + 1)}{2}$

17. Which of the following is not a measure of central tendency?

a)		Mean
b)		Median
c)		Mode
d)		range

18. If a student gets marks : English 80, Hindi 70, Mathematics 85, Physics 75 and Chemistry 67, and the weights of subjects are 1, 2, 1, 3, 1 respectively, then weighted A.M is

a)		74.625
b)		75.625
c)		73.625
d)		None of these

19. The A.M of 9 items is 15. If one more item is added to this series, the A.M becomes 16. The value of 10th item is

a)		23
b)		25
c)		27
d)		30

20. The mean wage of 1000 workers in a factory running in two shifts of 700 and 300 workers is Rs. 500. The mean wage of 700 workers working in day shift is Rs. 450. The mean wage of workers working in the night shift is

a)		Rs. 570
b)		Rs. 616.67
c)		Rs. 543.67
d)		None of these

21. Objective function of z = 8x + 3y subject to constraints x + y $\leq 3, 4 x + y \leq 6; x \geq 0$ is

a)		z = 400x + 500y
b)		z = 200x + 150y
c)		z = 100x + 80y
d)		None of these

22. The maximum value of z = 8x + 3y subject to constraints x + y $\leq 3, 4 x + y \leq 6; x \geq 0$ is

a)		9
b)		12
c)		14
d)		16

23. Solution set of inequations x – 2y $\geq 0,$ 2x – y $\leq - 2$ is

a)		empty
b)		infinite
c)		a set containing x-axis completely
d)		None of these

24. 'The maximum or the minimum of the objective function occurs at the corner points of the feasible region' is called the fundmental theorem of

a)		Arithmetic
b)		Algebra
c)		Calculus
d)		Extreme points

25. The optimal value of the objective function is attained at the points:

a)		given by the intersections of inequalities with x-axis only
b)		given by the intersection of inequalities with the axes only
c)		given by the corner points of the feasible region
d)		None of these

26. Objective function of a L.P.P is

a)		a constraint
b)		a function to be optimized
c)		a relation between the variables
d)		None of these

27. The solution set of 3x + 2y $\leq 6$ is

a)		half plane not containing the origin
b)		half plane containing the points lying on the line 3x + 2y = 6 and the origin
c)		xy-plane except points on the line 3x + 2y = 6
d)		None of these

28. The solution set of the inequation x + 2y $>$ 3 is

a)		half plane containing the origin
b)		open half plane not containing the origin
c)		the whole of xy-plane except points lying on the line x + 2y - 3 = 0
d)		None of these

29. Region represented by the inequations x $\geq 0, y \geq 0$ is

a)		first quadrant
b)		second quadrant
c)		third quadrant
d)		fourth quadrant

30. Solution set of the inequality x $\geq 0$ is

a)		half plane on the left of y-axis
b)		half plane on the right of y-axis excluding y-axis
c)		half plane on the right of y-axis including the points on y-axis
d)		None of these

31. If the S.D of15 items is 6 and each term is decreased by 1, then S.D will be

a)		5
b)		7
c)		9
d)		$\frac{91}{15}$

32. The variance of, $\propto, β, and ϒ is 9 then variance of 5 \propto, 5 β, 5 ϒ is$

a)		45
b)		$\frac{9}{5}$
c)		$\frac{5}{9}$
d)		225

33. The geometric mean of number 7, $7^{2}, 7^{3} ... 7^{n} is$

a)		$7^{\frac{7}{n}}$
b)		$7^{\frac{n}{7}}$
c)		$7^{\frac{n - 1}{2}}$
d)		$7^{\frac{n + 1}{2}}$

34. If the mean deviation is 12, the value of S.D will be

a)		15
b)		12
c)		24
d)		none of these

35. If the mean of the numbers 27+x,31+x,89+x,107+x,156+x is 82, then the mean of 130 +x, 126+x,68+x,50+x,1+x is

a)		75
b)		157
c)		82
d)		80

36. The mean deviation from the median is

a)		greater than that measured from any other value
b)		Less than that measured from any other value
c)		equal to that measured from any other value
d)		maximum of all observations are positive

37. The mean deviation of the numbers 3,4,5,6,7 is

a)		0
b)		1.2
c)		5
d)		25

38. If the mean of numbers 27,31,89,107,156 is 82, then the mean of 130, 126,68,50,1 is

a)		75
b)		157
c)		82
d)		80

39. The mean and S.D. of 1,2,3,4,5,6 is

a)		$\frac{7}{2}, \sqrt{\frac{35}{12}}$
b)		3,3
c)		$\frac{7}{2}, \sqrt{3}$
d)		$3, \frac{35}{12}$

40. If each observation of a raw data whose varience is $σ^{2} is multiplied by λ then the varience of the new set is$

a)		$σ^{2}$
b)		$λ^{2}$ $σ^{2}$
c)		$λ +$ $σ^{2}$
d)		$λ^{2} + σ^{2}$

41. If a variable takes the discrete values $\propto + 4, \propto - \frac{7}{2}, \propto - \frac{5}{2}, \propto - 3, \propto - 2, \propto + \frac{1}{2}, \propto - \frac{1}{2}, \propto + 5, (\propto > 0) then median is$

a)		$\propto - \frac{5}{2}$
b)		$\propto - \frac{1}{2}$
c)		$\propto - 2$
d)		$\propto + \frac{5}{4}$

42. The median of 10, 14,11,9,8,12,6 is

a)		10
b)		12
c)		14
d)		11

43. The relationship between mean, median and mode for a moderately skewed distribution is

a)		mode = median - 3mean
b)		mode = 2median - mean
c)		mode = 3median - 2mean
d)		mode = 2median - 3mean

44. The mean of 100 items is 49.It was discovered that three items which should have been 60,70,80 were wrongly read as 40,20,50 respectively.The correct mean is

a)		48
b)		82 $\frac{1}{2}$
c)		50
d)		80

45. Which of the following is not a measure of central tendency

a)		mean
b)		median
c)		mode
d)		range

46. Which of the following is not a measure of dispersion?

a)		variance
b)		mean deviation
c)		standard deviation
d)		mode

47. If the mean 3, 4, x, 7, 10, 6, then the value of x is

a)		4
b)		5
c)		6
d)		7