Find the value of \( x \) that makes the median the given number.
Given: 2, 5, 4, 9, 7, \( x \); median = 5
Answer (2)
The goal is to find the value of x that will make the median of the dataset equal to 5. The given dataset is 2, 5, 4, 9, 7, x ; to find the median when x is included, we must first order the dataset from least to greatest and then find the middle number(s). Since there are six numbers, the median will be the average of the third and fourth numbers once arranged.
First, order the numbers without x : 2, 4, 5, 7, 9.
The median is 5, which means that, in order, x has to be less than or equal to 5 to not disturb the third and fourth positions.
x could be any value less than or equal to 5.
If x is 5, the dataset would be 2, 4, 5, 5, 7, 9 and the median is still 5. If x is less than 5, for example: 3, then the dataset would be 2, 3, 4, 5, 7, 9 with the median again being the average of the third and fourth numbers, which is (4+5)/2 = 4.5, which does not equal the given median of 5. Therefore, the only value for x that makes the median 5 is 5.
The value of x that makes the median of the dataset 2, 5, 4, 9, 7, x equal to 5 is 5 itself. By including 5 among the numbers, we ensure the average of the 3rd and 4th positions remains 5. Values less than 5 would lower the median below 5.
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