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InterviewSolution
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The numbers 52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 have been arranged in an ascending order and their median is 55. Find the value of x and hence find the mode of the given data. |
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Answer» We know that Number of observations = 9 By arranging the numbers in ascending order We get 52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 So we get Median = [(n + 1)/2]th value By substituting the values Median = [(9 + 1)/2]th value We get Median = 5th value = 2x + 1 It is given that median = 55 We can write it as 2x + 1 = 55 On further calculation 2x = 54 By division x = 27 By substituting the value of x 2x + 1 = 2(27) + 1 = 55 So we get 52, 53, 54, 54, 55, 55, 55, 56, 57 We know that 55 occurs the maximum number of times so the mode is 55. |
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