Question

What is the median for the following scores: 2, 5, 4, 1, 8

• A. 5
• B. 0
• C. 5
• D. 0

Hint:

Always arrange the raw data in order before identifying the middle value.
Selecting the middle value from the unordered raw list is a common mistake.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The median is a measure of central tendency that represents the middle value of a dataset when the observations are arranged in order of magnitude.
It divides the ordered dataset into two equal halves.
Key Formula or Approach:
To find the median of a dataset:
Arrange the data scores in ascending or descending order.
If the number of observations (\(n\)) is odd, the median is the value at the following position:
\[ \text{Position} = \frac{n + 1}{2} \]
If the number of observations (\(n\)) is even, the median is the average of the two middle values.

Step 2: Detailed Explanation:
Let us apply these steps to the given dataset:
The raw scores are:
\[ 2, 5, 4, 1, 8 \]
First, we arrange these five scores in ascending order:
\[ 1, 2, 4, 5, 8 \]
The number of observations is:
\[ n = 5 \]
Since \(n\) is an odd number, the median is the value at the middle position:
\[ \text{Position} = \frac{5 + 1}{2} = 3\text{rd position} \]
The value at the 3rd position in our ordered list is
This value divides the dataset such that two observations (1 and 2) are smaller than 4, and two observations (5 and 8) are larger than
Therefore, the median score is 0.

Step 3: Final Answer:
The median for the given scores is 0.