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Question-5, , If the mean of the following data is 21.5, find the value of k:, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , xi 5 15 25 35 45, fi 6 4 3 k 2, Solution:, Xj fj Xif, 5 6 30, 15 4 60, 25 3 75 h, 35 k 35k, 45 2 90, Total 15+k 255 + 35k, > xiff, Mean =, 2 fi, , 15 +k PS, 21.5 (15 +k) = 255 + 35k, , 21.5 x15 + 21.5k = 255 + 35k, 35k - 21.5k = 322.5 - 255, 13.5k = 67.5

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Question-7, , The median of the observations 11, 12, 14, 18, x +2, x + 4, 30, 32, 35, 41, arranged in ascending order is 24. Find the value of x., , Solution:, The number of observations = n = 10. Since nis even,, , - a iont (2+ i, Median = 5 bsevation 3 1 pdbservatin, , £, >24= (3 pocavation +(e pocarvatio n = meskes = 246, ny + ns :, , >x=21., , Question-8, , Find the median of the following data: 19, 25, 59, 48, 35, 31, 30, 32, 51. If, 25 is replaced by 52 and 19 by 29, what will be the new median?, , Solution:, Arranging the data in ascending order: 19, 25, 30, 31, 32, 35, 48, 51, 59., The number of observations n = 9 (odd), , “, Median = (24+) observation = 5" observation = 32., , , , Hence Median = 32. bd, , If 25 is replaced by 52 and 19 by 29, the new observations in ascending, order are :, , 29, 30, 31, 32, 35, 48, 51, 52, 59., , .". New Median = 5" observation = 35.