If the set {10, 5, 9, x} has a median of 7, which of the following cou

Theory

➡ Median is the middle value of the set.
➡ In case of even number of numbers in the set: Median is the mean of the two middle numbers (after the numbers are arranged in the increasing / decreasing order)

The set {10, 5, 9, x} has a median of 7, which of the following could not be a possible value of x

Let's take each option and check what is the median

A. 1
Set becomes {10, 5, 9, 1}, in ascending order it becomes {1, 5, 9, 10}
Median = Mean of middle two values = \(\frac{5+9}{2}\) = \(\frac{14}{2}\) = 7 => POSSIBLE

B. 3
Set becomes {10, 5, 9, 3}, in ascending order it becomes {3, 5, 9, 10}
Median = Mean of middle two values = \(\frac{5+9}{2}\) = \(\frac{14}{2}\) = 7 => POSSIBLE

C. 4
Set becomes {10, 5, 9, 4}, in ascending order it becomes {4, 5, 9, 10}
Median = Mean of middle two values = \(\frac{5+9}{2}\) = \(\frac{14}{2}\) = 7 => POSSIBLE

D. 5
Set becomes {10, 5, 9, 5}, in ascending order it becomes {5, 5, 9, 10}
Median = Mean of middle two values = \(\frac{5+9}{2}\) = \(\frac{14}{2}\) = 7 => POSSIBLE

E. 7
Set becomes {10, 5, 9, 7}, in ascending order it becomes {5, 7, 9, 10}
Median = Mean of middle two values = \(\frac{7+9}{2}\) = \(\frac{16}{2}\) = 8 => NOT POSSIBLE

So, Answer will be E.
Hope it helps!

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