Question

Compare:
Quantity A: The median of the 24 integers
Quantity B: 50

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.
• E.

Hint:

For median problems, always check if enough information about the data set is given. If the distribution of numbers is unknown, the median cannot be compared with a fixed value.

Answer 1

The Correct Option is D

Step 1: Understanding the problem.
We are given 24 integers and asked to compare their median with the fixed value 50.
Step 2: Median definition.
The median of an even number of terms is the average of the two middle terms when the data is arranged in ascending order.
Here, since there are 24 integers, the median will be: \[ \text{Median} = \frac{12\text{th term} + 13\text{th term}}{2}. \] Step 3: Limitation.
No information is given about the values of the 24 integers. They could all be less than 50, all greater than 50, or spread around 50. Thus, the median could be less than, equal to, or greater than 50 depending on the specific set.
Step 4: Conclusion.
Since no definite relationship can be determined, the correct answer is: \[ \boxed{\text{(D) The relationship cannot be determined.}} \]