### Statistics Class 10th Mathematics Tamilnadu Board Solution

##### Question 1.The range of the first 10 prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 isA. 28B. 26C. 29D. 27Answer:Range R = xmax - xminR = 29 - 2 = 27So the correct option is D.Question 2.The least value in a collection of data is 14.1. If the range of the collection is 28.4, then the greatest value of the collection isA. 42.5B. 43.5C. 42.4D. 42.1Answer:Given xmin = 14.1, R = 28.4Range R = xmax - xmin28.4 = xmax - 14.1 xmax = 42.5So the correct option is A.Question 3.The greatest value of a collection of data is 72 and the least value is 28. Then the coefficient of range isA. 44B. 0.72C. 0.44D. 0.28Answer:Given xmax = 72, xmin = 28Coefficient of range s = = So the correct option is C.Question 4.For a collection of 11 items, , then the arithmetic mean isA. 11B. 12C. 14D. 13Answer:N = 11AM So the correct option is B.Question 5.For any collection of n items, =A. B. C. D. 0Answer: can be rewritten as We know that so Also, because is just a constant term.Substituting these in , we get = 0So the correct option is D.Question 6.For any collection of n items, =A. B. C. D. 0Answer:We know that so Substituting this in the question, we have So the correct option is C.Question 7.If t is the standard deviation of x, y. z, then the standard deviation of x + 5, y + 5, z + 5 isA. B. t + 5C. tD. x y zAnswer:It is a direct consequence of the theory of standard deviation that, the same constant term added to the terms in a set of data doesn’t change the value of standard deviation.So the correct answer is t and correct option is C.Question 8.If the standard deviation of a set of data is 1.6, then the variance isA. 0.4B. 2.56C. 1.96D. 0.04Answer:Variance = SD2So Variance = 1.62 = 2.56Therefore, the correct option is B.Question 9.If the variance of a data is 12.25, then the S.D isA. 3.5B. 3C. 2.5D. 3.25Answer:Variance = SD2Or SD = SD = 3.5So the correct option is A.Question 10.Variance of the first 11 natural numbers isA. B. C. D. 10Answer:Variance of first n natural numbers is given by V = 10So the correct option is D.Question 11.The variance of 10, 10, 10, 10, 10 isA. 10B. C. 5D. 0Answer:Standard deviation of a constant set of data is 0.We know that Variance = SD2 Variance = 0So the correct option is D.Question 12.If the variance of 14, 18, 22, 26, 30 is 32, then the variance of 28, 36,44,52,60 isA. 64B. 128C. 32√2D. 32Answer:Two data sets are given.Set A : 14, 18, 22, 26, 30 with V = 32Set B : 28, 36, 44, 52, 60 with V = ?We notice that each data entry in set B is twice the corresponding data entry in set A. SD of set B = 2 × SD of set A.We know that Variance = SD2 Variance of Set B = 22 × Variance of Set A.= 4 × 32 = 128.So the correct option is B.Question 13.Standard deviation of a collection of data is 2√2. If each value is multiplied by 3, then the standard deviation of the new data isA. B. 4√2C. 6√2D. 9√2Answer:SD of set B = n × SD of set A, where n is the data multiplierHere, n = 3.So, SD of set B = 3 × SD of set A = 3 × 2 = 6 So, the correct option is C.Question 14.Given and n = 12. The coefficient of variation isA. 25B. 20C. 30D. 10Answer:Insufficient data.Question 15.Mean and standard deviation of a data are 48 and 12 respectively. The coefficient of variation isA. 42B. 25C. 28D. 48Answer:CV = CV = So, the correct option is B.

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