If the median of the data set 3, 5, 7, 9, x is 7, what is the value of x?

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Question: If the median of the data set 3, 5, 7, 9, x is 7, what is the value of x?

Options:

Correct Answer: 8

Solution:

For median to be 7, x must be 7 or less, hence x = 7.

If the median of the data set 3, 5, 7, 9, x is 7, what is the value of x?

If the median of the data set 3, 5, 7, 9, x is 7, what is the value of x?

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, 5, 7, 9, x in order. The median is the third number in this ordered list.
Step 3: Since the median is given as 7, we need the third number in the ordered list to be 7.
Step 4: If x is less than or equal to 7, the ordered list will be 3, 5, x, 7, 9, and the third number will be x.
Step 5: If x is equal to 7, the ordered list will be 3, 5, 7, 7, 9, and the third number will be 7.
Step 6: If x is greater than 7, the ordered list will be 3, 5, 7, 9, x, and the third number will still be 7.
Step 7: Therefore, for the median to be 7, x must be 7 or less. The only value that satisfies this is x = 7.

Median Calculation – Understanding how to find the median of a data set and the implications of adding a variable.
Inequalities – Recognizing that the value of x must be less than or equal to 7 to maintain the median.