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If x₁, x₂ ….. x₁₈ are observations such that ∑_j=1¹⁸ (x_j – 8) = 9 and ∑_j=1¹⁸ (x_j – 8)² = 45, then standard deviation of these observations is

1) √81 / 34 2) 5 3) √5 4) 3/2 Solution: (4) 3/2 Standard deviation = √{∑j=118 (xj - 8)2 / n} - {∑j=118 (xk - 8) / n}2 = √(45 / 18) - (9 /... View Article

If the coefficient of variation is 45% and the mean is 12, then its standard deviation is

1) 5.2 2) 5.3 3) 5.4 4) None of these Solution: (3) 5.4 Since the percentage of coefficient of variation is given by = [Standard deviation /... View Article

The mean deviation from the mean of the set of observations -1, 0, 4 is

1) 3 2) 1 3) -2 4) 2 Solution: (4) 2 Find the mean of the data : (- 1 + 4 + 0) / 3 = 3 / 3 = 1 Find the distance between each data and mean.... View Article

If the variance of 1, 2, 3, 4, 5,…, 10 is 99 / 12, then the standard deviation of 3, 6, 9, 12,…30 is

1) 297 / 4 2) (3 / 2) √33 3) (3 / 2) √99 4) √99 / 12 5) 3 √3 / 2 Solution: (2) (3 / 2) √33 The variance of 1, 2, 3, 4, 5,..., 10 is 99 /... View Article

If the variable takes the values 0, 1, 2,…,n with frequencies proportional to the binomial coefficients C(n, 0), C(n, 1), C(n, 2),…, C(n, n) respectively, then the variance of the distribution is

1) n 2) √n/2 3) n/2 4) n/4 Solution: (4) n / 4 Here, μ1’ = [n . 2n-1] / 2n = n / 2 μ2’ = (1 / 2n) ∑0n {(r - 1) + r} nCr = (1 / 2n) ∑0r r... View Article

Statement I: The variance of 1st n even natural numbers is n² – 1 / (4). Statement II: The sum of 1st n natural number is [n (n + 1)] / 2 and the sum of the 1st n natural numbers is [n (n + 1) (2n + 1)] / 6.

1) Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statement I 2) Statement I is correct, Statement II... View Article

If the mean deviation of number 1, 1 + d, 1 + 2d…., 1 + 100d from their mean is 255, then d is equal to

1) 10.0 2) 20.0 3) 10.1 4) 20.2 Solution: (3) 10.1... View Article

For two data sets, each of size 5, the variance is given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

1) 5/2 2) 11/2 3) 6 4) 13/2 Solution: (2) 11/2 𝜎x2 = 4 and 𝜎y2 = 5 = 4 ∑xi / 5 = 2 ⇒∑xi = 10; ∑yi = 20 𝜎x2 = [(1 / 5) ∑xi2] - , 𝜎y2 = [(1... View Article

If the value observed are 1, 2, 3…, n each with frequency l and m is even, then the mean deviation from mean equals to

1) n 2) n/2 3) n/4 4) None of these Solution: (2) n / 2 The mean of the observation 1,2,.....,n... View Article

Mean deviation of 6, 8, 12, 15, 10, 9 through mean is

1) 10 2) 2.33 3) 2.5 4) None of these Solution: (2) 2.33 The observations are 6, 8, 12, 15, 10, 9 - 6 observations. Let the mean of given... View Article

The coefficient of variation of two distributions are 50% and 60%, and their arithmetic means are 30 and 25, respectively. The difference in their standard deviation is

1) 1 2) 1.5 3) 2.5 4) 0 Solution: (4) 0 CV1 = 50, CV2 = 60 Mean1 = = 30 Mean2 = = 25 Coefficient of variation1 = [𝜎1 / ] * 100 50 = [𝜎1... View Article

If the standard deviation of 3, 8, 6, 10, 12, 9, 11, 10, 12, 7 is 2.71, then the standard deviation of 30, 80, 60, 100, 120, 90, 110, 100, 120, 70 is

1) 2.71 2) 27.1 3) (2.71)√10 4) (2.71)√2 5) 0.271 Solution: (2) 27.1 The standard deviation is dependent on the scale. If the values in the... View Article

A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 g and a standard deviation is 2 g. Later, it was found that the measuring scale was misaligned and always under-reported every fish weight by 2 g. Find the correct mean and standard deviation (in gram) of fishes.

1) 28, 4 2) 32, 2 3) 32, 4 4) 28, 2 Solution: (2) 32, 2 Correct mean = Old mean + 2 = 30 + 2 = 32 As standard deviation is independent of... View Article

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are

1) 2 and 9 2) 3 and 8 3) 4 and 7 4) 5 and 6 Solution: (3) 4 and 7 Let observations of a & b ∴ [(1 + 2 + 6 + a + b) / 5] = 4.0 ∴ 9 + a +... View Article

All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

1) Mean 2) Median 3) Mode 4) Variance Solution: (4) Variance The variance and standard deviation don’t change even after the addition of... View Article

The sum of the deviations of the variates from the arithmetic mean is always

1) +1 2) 0 3) -1 4) real number Solution: (2) 0 The sum of the deviations of a given set of observations from their arithmetic mean is... View Article

The mean of four observations is 3. If the sum of the squares of the observations is 48, then their standard deviation is

1) √7 2) √2 3) √3 4) √5 Solution: (3) √3 Mean = 3 and number of observations = 4 = √(∑xi2 / n) - (mean)2 = √12 - 9 = √3... View Article