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:

Always double-check if the dataset is sorted before finding the median. If it's not, sorting it is the crucial first step. For an odd number of values, you can find the middle by simply crossing out one value from each end until only one remains.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The median is the middle value in a dataset that has been arranged in numerical order. It separates the higher half of the data from the lower half.
Step 2: Key Formula or Approach
1. Arrange the data points in ascending (or descending) order.
2. Determine the number of data points, \(n\).
3. If \(n\) is odd, the median is the middle value, which is 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 already in ascending order: \[ 12, 18, 22, 26, 30, 30, 32 \] 2. Count the number of data points:
There are \(n = 7\) scores. Since 7 is an odd number, the median will be the single middle value.
3. Find the position of the median:
The position is \(\left(\frac{n+1}{2}\right) = \left(\frac{7+1}{2}\right) = \frac{8}{2} = 4\). So, the median is the 4th value in the ordered list.
4. Identify the median value:
Counting from the beginning of the list: 1st: 12
2nd: 18
3rd: 22
4th: 26
The 4th value is 26.
Step 4: Final Answer
The median of the scores is 26. This corresponds to option (B).