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

Appeared in: PGIMER NO - 2020

Explanation

The median represents the middle value of a dataset after it has been sorted in ascending or descending order.
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 an odd number of observations, the median is the value at the ((n + 1) / 2)th position.
Calculation: (9 + 1) / 2 = 5. The median is the 5th value in the sorted list.
The 5th value in the sorted dataset is 32.

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

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of the median for a dataset with an odd number of observations as background academic context rather than a clinical decision trigger.
Understanding basic statistics like the median is essential for nurses to interpret clinical data, patient outcomes, and evidence-based practice research.
The median is often a more reliable measure of central tendency than the mean when data is skewed, such as when analyzing hospital length of stay, where a few patients with very long stays can inflate the average.
What if? - If the dataset had an even number of values (e.g., by adding the number 60), the median would be the average of the two middle numbers. The sorted list would be (12, 18, 25, 30, 32, 40, 45, 50, 55, 60), and the median would be (32 + 40) / 2 = 36.

How to Approach the Question

Step 1: Identify the core task. The question asks to find the 'median' of a given set of numbers.
Step 2: Recall the definition of a median: it is the middle value of a dataset that has been sorted.
Step 3: The first and most critical step is to arrange all the numbers in ascending (or descending) order: 12, 18, 25, 30, 32, 40, 45, 50, 55.
Step 4: Count the total number of values in the set (n). Here, n = 9.
Step 5: Determine how to find the middle. Since n is an odd number, the median is the single value in the middle position. Use the formula (n+1)/2 to find this position.
Step 6: Calculate the position: (9+1)/2 = 5. This means the median is the 5th number in the sorted list.

Concept Tested & Keywords

Concept Tested: Calculation of the median for a dataset with an odd number of observations.
Stem keywords: median, data, 45, 50, 55, 12, 18, 25
Lead-in keywords: Find

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Practise the full PGIMER NO - 2020

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