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If θ is the angle between two regression lines with correlation coefficient γ, then

1) sin θ ≥ 1- γ2 2) sin θ ≤ 1- γ2 3) sin θ ≤ γ2 + 1 4) sin θ ≤ γ2 - 1 Solution: (2) sin θ ≤ 1- γ2 The relation between θ and correlation... View Article

If the lines of regression are 3x + 12y = 19 and 3y + 9x = 46, then r_xy will be

1) 0.289 2) -0.289 3) 0.209 4) None of these Solution: (2) - 0.289 Assume that the line of regression y on x is 3x + 12y = 19 and x on y is... View Article

In a bivariate data, ∑x = 30, ∑y = 400, ∑x² = 196, ∑xy = 850 and n = 10. The regression coefficient of y on x is

1) -3.1 2) -3.2 3) -3.3 4) -3.4 Solution: (3) -3.3 byx = [∑xy - (1 / n) ∑ x . ∑y] / [∑x2 - (1 / n) (∑x)2] = [850 - (30 × 400) / 10] / [196 -... View Article

Angle between two lines of regression is given by

1) tan-1 [bxy - (1 / byx)] / [1 - (bxy / byx)] 2) tan-1 [byx . bxy - 1] / [(byx + bxy)] 3) tan-1 [bxy - (1 / byx)] / [1 + (bxy / byx)] 4)... View Article

The correlation coefficient of two variables x and y are 0.8. The regression coefficient of y on x is 0.2, then the regression coefficient of x on y is

1) 3.2 2) -3.2 3) 4 4) 0.16 Solution: (1) 3.2 Given correlation coefficient (r) = 0.8 byx = 0.2 ∴r2 = bxy . byx bxy = r2 / byx = [0.8 ×... View Article

The two regression lines were found to be 4X – 5Y + 33 = 0 and 20X – 9Y – 107 = 0. Find the coefficient of correlation between X and Y.

1) 0.6 2) 0.16 3) 0.3 4) 0.7 Solution: (1) 0.6 4X – 5Y = -33 … (1) 20X – 9Y = 107 … (2) (1) × 5 ⇒ 20X – 25Y = - 165 20X – 9Y = 107... View Article

Two numbers within the brackets denote the ranks of 10 students of a class in two subjects (1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2), (10, 1), then rank correlation coefficient is

1) 0 2) -1 3) 1 4) 0.5 Solution: (2) -1 On relating the difference of ranks between the pairs 1 & 10 , 2 & 9 , 3 & 8 , 4 &... View Article

The correlation coefficient between x and y from the following data ∑x = 40, ∑y = 50, ∑xy = 220, ∑x² = 200, ∑y² = 262, n = 10 is

1) 0.89 2) 0.76 3) 0.91 4) 0.98 Solution: (3) 0.91 r = rxy = [cov (x, y)] / (Sx * Sy) Cov (x, y) = [∑xy / n] - mean of “x” . mean of “y”... View Article

If x₁, x₂ ….. x_n are n observations such that ∑x_i² = 400 and ∑x_i = 80. Then a possible value of n among the following is

1) 12 2) 9 3) 18 4) 15 Solution: (3) 18... View Article

If 𝜎 is the standard deviation of a random variable x, then, the standard deviation of the random variable (ax + b) / c, where a, b ϵ R is

1) a∑ + b 2) |a / c| 𝜎 3) |a|∑ + b 4) a2 ∑ Solution: (2) |a / c| 𝜎 Let y = (ax + b) / c... View Article

For the arithmetic progression a, (a + d), (a + 2d), (a + 3d),…, (a + 2nd), the mean deviation from mean is

1) [n (n + 1) d / (2n - 1)] 2) [n (n + 1) d / (2n + 1)] 3) [n (n - 1) d / (2n + 1)] 4) [(n + 1) d / (2)] 5) [n (n - 1) d / (2n - 1)]... View Article

The standard deviation of n observations x₁, x₂ ….. x_n is 2. If ∑_i=1ⁿ x_i = 20 and ∑_i=1ⁿ x_i² = 100, then n =

1) 10 or 20 2) 5 or 10 3) 5 or 20 4) 5 or 15 5) 25 Solution: (3) 5 or 20... View Article

Suppose population A has 100 observations 101, 102,…200 and another population B has 100 observations 151, 152, …, 250. If V_A and V_B represents the variance of the two population respectively, then V_A / V_B is equal to

1) 9/4 2) 4/9 3) 2/3 4) 1 Solution: (4) 1 𝜎x2 = ∑di2 / n (Here deviations are taken from the mean). Since A and B both have 100 consecutive... View Article

What is the standard deviation of the following series

Measurements 0 - 10 10 - 20 20 - 30 30 - 40 Frequency 1 3 4 2 1) 81 2) 76 3) 9 4) 2.26 Solution: (3) 9 Let us assume an arbitrary mean a =... View Article

If the mean of n observations 1², 2², 3² ….. n² is 46n / 11, then n =

1) 11 2) 12 3) 23 4) 22 Solution: (1) 11... View Article

The standard deviation of the numbers 31, 32, 33, …, 46, 47 is

1) √17 / 12 2) √(472 - 1) / 12 3) 2√6 4) 4 √3 Solution: (3) 2√6 The standard deviation of 31, 32, 33, ... , 47 will be the same as those of... View Article

The standard deviation of a variable x is 10. Then, the standard deviation of 50 + 5x is

1) 50 2) 550 3) 10 4) 500 Solution: (1) 50 Variance (x) = 102 = 100 Standard deviation = √variance (50 + 5x) = √variance (5x) = √52 variance... View Article

The standard deviation for the scores 1, 2, 3, 4, 5, 6 and 7 is 2. Then, the standard deviation of 13, 24, 35, 46, 57, 68 and 79 is

1) 2 2) 4 3) 22 4) 11 5) 44 Solution: (3) 22 Let x = 1, 2, 3, 4, 5, 6, 7 and y = 13, 24, 35, 46, 57, 68 & 79 yi = 11xi + 2 ........... View Article

Complete the mean and standard deviation of the following observations of marks of 5 students of a tutorial group: Marks out of 25:8,12,13,15,22

1) 14, 4.604 2) 15, 4.604 3) 14, 5.604 4) None of these Solution: (1) 14, 4.604 Here, mean = [8 + 12 + 13 + 15 + 22] / [5] = 70 / 5 = 14 ∴... View Article

The mean of the numbers a, b, 8, 5, 10, is 6 and the variance is 6.80. Then, which one of the following gives possible values of a and b?

1) a = 3, b = 4 2) a = 0, b = 7 3) a = 5, b = 2 4) a = 1, b = 6 Solution: (1) a = 3, b = 4... View Article