OSSSC Nursing Officer-2023
Nursing Research & Statistics
Hard
The average of 20 numbers is 48. If two numbers, namely, 53 and 70 are discarded, what is the average of the remaining numbers?
Appeared in: OSSSC Nursing Officer-2023
Explanation
- The initial sum of the 20 numbers is calculated by multiplying the average by the count (48 * 20 = 960).
- The sum of the two discarded numbers (53 and 70) is 123.
- The new sum is found by subtracting the discarded sum from the initial sum (960 - 123 = 837).
- The number of remaining items is now 18 (20 - 2).
- The new average is the new sum divided by the new count (837 / 18 = 46.5).
Why Other Options Were Wrong
- Option A: This value (47.5) is incorrect and likely results from a calculation error, such as incorrectly subtracting the values or dividing by the wrong number.
- Option C: This value (45.5) is incorrect. It may arise from miscalculation, for instance, an error in the subtraction or division step.
- Option D: This value (45) is incorrect. It could be obtained by rounding down or through a significant calculation mistake.
Related Visual
Clinical Relevance
- Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the new arithmetic mean (average) of a dataset after removing specific values as background academic context rather than a clinical decision trigger.
- While this is a mathematics question, the ability to calculate and interpret averages is a fundamental skill for nurses.
- Nurses use averages to understand trends in vital signs, lab results (e.g., average blood glucose over a week), and patient outcomes data.
- Understanding how removing or adding values affects an average is crucial for data interpretation in clinical research and quality improvement projects.
How to Approach the Question
- First, identify the initial number of items and their average.
- Calculate the total sum using the formula: Sum = Average × Number of items.
- Identify the values that are being removed or added.
- Calculate the new sum by subtracting or adding the values from the total sum.
- Determine the new number of items.
- Calculate the new average by dividing the new sum by the new number of items.
Concept Tested & Keywords
- Concept Tested: Calculating the new arithmetic mean (average) of a dataset after removing specific values.
- Stem keywords: average, 20 numbers, 48, discarded, 53, 70
- Lead-in keywords: what is the average
Question ID
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