Given the ordered data set $3$, $5$, $7$, $x$, $12$, $14$, if the median is $9$, what is the value of $x$?

• A. $11$
• B. $8$
• C. $9$
• D. $10$

Answer: (C)

Verified step by step guidance

1. Identify the number of data points in the ordered data set. Here, the data set is 3, 5, 7, x, 12, 14, which contains 6 values.
2. Recall that for an even number of data points, the median is the average of the two middle values. Since there are 6 values, the median is the average of the 3rd and 4th values.
3. Express the median in terms of the data points: Median = \(\frac{7 + x}{2}\), because 7 is the 3rd value and x is the 4th value in the ordered set.
4. Set up the equation using the given median value: \(\frac{7 + x}{2} = 9\).
5. Solve the equation for x by multiplying both sides by 2 and then subtracting 7: \$7 + x = 18\( so \)x = 18 - 7$.