# Median of a data arranged in ascending order 7, 10, 15, x, y, 27, 30 is 17 and when one more observation 50 is added

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Median of a data arranged in ascending order 7, 10, 15, x, y, 27, 30 is 17 and when one more observation 50 is added to the data the median has become 18. Find x and y.

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The given data in ascending order is 7, 10, 15, x, y, 27, 30

Median = (n+1/2)th term = (7+1/2) = 4th term = x

∴ x = 17 by problem

When 50 is added, the data becomes 7, 10, 15, 17, y, 27, 30, 50

Median = $\frac {((\frac n2) + (\frac n2+1))}{2}$ terms

18 = 17 + y/2 (by problem)

17 + y = 36 y = 36 – 17 = 19