Question

The following data represent the scores of 7 students in a test: 12, 18, 22, 26, 30, 30, 32. What is the median of the scores?

• A. 22
• B. 26
• C. 28
• D. 30
• E.

Hint:

The most critical step in finding the median is to sort the data first. The GRE might present an unsorted list to trap you. Also, don't confuse the median with the mean (average) or the mode (most frequent value). In this set, the mean is approximately 24.3 and the mode is 30.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The median is a measure of central tendency in statistics. It represents the middle value of a dataset when the data points are arranged in ascending or descending order.
Step 2: Key Formula or Approach:
1. Arrange the data in numerical order.
2. Count the number of data points, \(n\).
3. If \(n\) is odd, the median is the middle value, found at the \(\left(\frac{n+1}{2}\right)\)th position.
4. If \(n\) is even, the median is the average of the two middle values.
Step 3: Detailed Explanation:
1. Arrange the data:
The given scores are: 12, 18, 22, 26, 30, 30, 32.
The data is already arranged in ascending order.
2. Count the number of data points:
There are 7 scores, so \(n = 7\).
3. Find the median:
Since \(n=7\) is an odd number, the median is the middle value. We find its position using the formula:
\[ \text{Position} = \frac{n+1}{2} = \frac{7+1}{2} = \frac{8}{2} = 4 \] The median is the 4th value in the ordered list.
4. Identify the median value:
Let's count to the 4th position in the list:
1st: 12
2nd: 18
3rd: 22
4th: 26
The 4th score is 26.
Step 4: Final Answer:
The median of the scores is 26.