The median of the data set 3, 7, 8, 12, x is 8. What is the value of x? (2023)

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Question: The median of the data set 3, 7, 8, 12, x is 8. What is the value of x? (2023)

Options:

Correct Answer: 6

Exam Year: 2023

Solution:

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

The median of the data set 3, 7, 8, 12, x is 8. What is the value of x? (2023)

The median of the data set 3, 7, 8, 12, x is 8. What is the value of x? (2023)

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 the median is given as 8, we know that the middle value of the ordered data set must be 8.
Step 4: If x is less than or equal to 8, the ordered data set will have 8 as the middle value.
Step 5: If we set x = 6, the ordered data set becomes 3, 6, 7, 8, 12.
Step 6: In this ordered set, the middle value (3rd number) is 8, which matches the given median.
Step 7: Therefore, the only value for x that makes the median 8 is x = 6.

Median – The median is the middle value of a data set when it is ordered from least to greatest.
Inequalities – Understanding how to set up and solve inequalities based on the conditions given in the problem.
Data Set Ordering – The importance of ordering the data set correctly to find the median.