How many values of x make the mean and median of a set of numbers equal?

Thread starter math_grl
Start date Aug 9, 2011
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Average Median

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The discussion revolves around finding the values of x that make the mean and median of the set of numbers 4, 5, 7, 9, and x equal. The mean, represented as f(x), is calculated to be (25 + x)/5, while the median, g(x), depends on the value of x. Initially, two values of x (0 and 10) were identified, but it was later confirmed that there are actually three values that satisfy the condition, with the third being 25/4. The conversation highlights the importance of understanding how the mean and median can change based on the inclusion of different values. Ultimately, the problem illustrates the relationship between these two statistical measures in a set of numbers.

Aug 9, 2011

math_grl

Let f(x) be the mean of five numbers: 4, 5, 7, 9 and x. Let g(x) be the median of the same numbers.
For how many values of x, a real number, is f(x) = g(x)?

I only got 2. x = 0, 10

There are 3 though. Perhaps someone can help me find the other one.

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Aug 9, 2011

math_grl

nevermind i found it. 25/4 was the last one.

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