Find the median of the following data: 150, 147, 140, 120, 135, 139, 148, 148

Appeared in: SGPGI Nursing Officer-2022

Explanation

The median is the middle value of a dataset when it is sorted in ascending or descending order.
For an even number of observations (n=8 in this case), the median is the average of the two middle values.
The data is first sorted: 120, 135, 139, 140, 147, 148, 148, 150.
The two middle values are the 4th (140) and 5th (147) terms.
The median is calculated as (140 + 147) / 2 = 143.5.

Option B: 144 is not the correct median. It may result from a miscalculation, such as incorrectly identifying the middle numbers or an arithmetic error when averaging.
Option C: 150 is the maximum value (and also the last value in the sorted list), not the median. The median represents the center of the data, not its extreme.
Option D: 5 is incorrect. This value might be obtained by incorrectly averaging two other numbers in the dataset, for example, the 6th and 8th values (148 and 150), which gives 149.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Measures of Central Tendency: Median as background academic context rather than a clinical decision trigger.
In nursing research and biostatistics, the median is often preferred over the mean when reporting data that is skewed, such as length of hospital stay or patient income, because it is not influenced by unusually high or low values (outliers).
For example, when analyzing the effectiveness of a new treatment, researchers might report the median survival time. This gives a more typical picture than the mean if a few patients have exceptionally long or short survival times.
What if? If the dataset had one more value, say 160, the total count would be 9 (odd). The sorted list would be 120, 135, 139, 140, 147, 148, 148, 150, 160. The median would then be the single middle value, which is the 5th term: 147.

How to Approach the Question

First, identify the task: The question asks for the 'median' of a given set of numbers.
Recall the definition of a median: it is the middle value of a sorted dataset.
Step 1: Arrange all the numbers in the dataset in ascending (or descending) order.
Step 2: Count the total number of values (n) in the dataset.
Step 3: Determine if 'n' is odd or even. This dictates the next step.
Step 4: If 'n' is even, identify the two middle values and calculate their average. This average is the median. If 'n' is odd, the median is simply the single middle value.

Concept Tested & Keywords

Qe_eLSy8KAaoA7eMHJPDvI

E6 NursingResearch Suresh Sharma 5e Part 2 p. 133-135

E6 NursingResearch Sukhpal Kaur p. 446-448

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