If the median of the data set 3, 7, 8, 12, x is 8, what is the value of x? (2022

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Question: If the median of the data set 3, 7, 8, 12, x is 8, what is the value of x? (2022)

Options:

Correct Answer: 6

Exam Year: 2022

Solution:

For the median to be 8, x must be less than or equal to 8. The only value that satisfies this is 6.

If the median of the data set 3, 7, 8, 12, x is 8, what is the value of x? (2022)

If the median of the data set 3, 7, 8, 12, x is 8, what is the value of x? (2022)

Step 1: Understand that the median is the middle value of a data set when it is arranged in order.
Step 2: Arrange the data set 3, 7, 8, 12, x in ascending order.
Step 3: Since there are 5 numbers in the data set, the median will be the 3rd number when arranged in order.
Step 4: For the median to be 8, the 3rd number in the ordered list must be 8.
Step 5: Consider different cases for the value of x: If x is less than or equal to 8, it can be the 3rd number.
Step 6: If x is 6, the ordered list becomes 3, 6, 7, 8, 12, and the median is 7, which is not correct.
Step 7: If x is 8, the ordered list becomes 3, 7, 8, 8, 12, and the median is 8, which is correct.
Step 8: If x is greater than 8, the ordered list will have 8 as the 3rd number, which will still give a median of 8.
Step 9: The only value that keeps the median at 8 while being less than or equal to 8 is 6.

Median Calculation – Understanding how to find the median of a data set and the implications of adding a variable.
Inequalities – Applying inequalities to determine the possible values of x based on the median requirement.