Find the median of the following data. 45, 50, 55, 12, 18, 25, 30, 32, 40

Appeared in: RRB Nsg. Superintendent-2026 (Shift -1st)

Explanation

The median is the middle-most value of a dataset when the data are arranged in ascending or descending order of magnitude.
First, arrange the given data in ascending order: 12, 18, 25, 30, 32, 40, 45, 50, 55.
The total number of observations (n) is 9, which is an odd number.
For a dataset with an odd number of observations, the median is the value at the ((n + 1) / 2)th position.
Calculation: ((9 + 1) / 2) = 10 / 2 = 5th position.
The value at the 5th position in the ordered dataset is 32.

Option A: 25 is the 3rd value in the ordered dataset, not the middle (5th) value.
Option B: 30 is the 4th value in the ordered dataset, not the middle (5th) value.
Option D: 40 is the 6th value in the ordered dataset, not the middle (5th) value.

Visual 1: Flowchart - A step-by-step flowchart illustrating how to find the median for a dataset with an odd number of values. The steps include: 1. Arrange data in ascending order. 2. Count the number of values (n). 3. Use the formula (n+1)/2 to find the position. 4. Identify the value at that position.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of median for ungrouped data as background academic context rather than a clinical decision trigger.
While this is a basic statistics question, understanding measures of central tendency like the median is crucial for nurses when interpreting research data, patient statistics, or quality improvement metrics.
The median is often preferred over the mean (average) when data is skewed by outliers, such as in studies on hospital length of stay or patient income levels, as it provides a more accurate representation of the 'typical' value.
What if the dataset had an even number of observations (e.g., if we added the number 60)? The median would then be the average of the two middle numbers. The new ordered set would be {12, 18, 25, 30, 32, 40, 45, 50, 55, 60}. The two middle numbers are 32 and 40, so the median would be (32 + 40) / 2 = 36.

How to Approach the Question

Step 1: Identify the core task, which is to find the 'median' of the given set of numbers.
Step 2: The first and most crucial step in finding the median is to arrange the data in numerical order, either ascending (smallest to largest) or descending.
Step 3: Count the total number of data points (n) in the set.
Step 4: Determine if 'n' is odd or even, as this dictates the formula to use.
Step 5: If 'n' is odd, the median is the single middle number located at the (n+1)/2 position. If 'n' is even, the median is the average of the two middle numbers.
Step 6: Apply the correct formula to the ordered data to find the median and match it with the given options.

Concept Tested & Keywords

QtFAQLGUUFt9H8N8Zt9wbb

Practise the full RRB Nsg. Superintendent-2026 (Shift -1st)

Attempt every question from this paper in a timed mock, then review the full solution for each one.