If the sum of a few numbers is 450 and their mean is 50, and if another number 100 is added to the sum, what will be the new mean?

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The initial number of values is determined by dividing the total sum (450) by the mean (50), which results in 9 values.
When a new number (100) is included, the sum increases to 450 + 100 = 550, and the total count of values increases to 9 + 1 = 10.
The new mean is calculated by dividing the new sum (550) by the new count of values (10), which equals 55.

Option B: This is an incorrect calculation. It might result from rounding or miscalculating the division, for instance, incorrectly dividing the new sum (550) by the old number of values (9), which is approximately 61.1, and then rounding down.
Option C: This value is likely the result of a conceptual error in calculation, such as incorrectly combining the numbers. It does not follow the correct formula for recalculating a mean.
Option D: This incorrect answer might be obtained by erroneously adding the new number (100) to the old mean (50). The mean is an average, not a simple sum.

Visual 1: Infographic: A flowchart demonstrating the 3-step process: 1. Find original count (Sum / Mean). 2. Calculate new sum and new count. 3. Calculate new mean (New Sum / New Count).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of Arithmetic Mean as background academic context rather than a clinical decision trigger.
Nurses frequently calculate averages to monitor patient health trends, such as mean arterial pressure (MAP), average blood glucose levels over a week, or average fluid intake/output per shift.
Understanding how a new, single value (like a sudden high blood pressure reading) affects the average is crucial for clinical interpretation. It helps distinguish between a stable trend and a potential acute event that requires intervention.
What if the number added was 20 instead of 100? The new sum would be 450 + 20 = 470. The new mean would be 470 / 10 = 47. This demonstrates that adding a value lower than the original mean (50) will pull the new mean down.

How to Approach the Question

First, identify the given information: the initial sum (450), the initial mean (50), and the new number being added (100).
Use the fundamental formula for the mean (Mean = Sum / Count) to find the original number of values. Rearrange it to Count = Sum / Mean.
Calculate the new sum by adding the new number to the original sum.
Determine the new count of values by adding 1 to the original count.
Finally, calculate the new mean by dividing the new sum by the new count of values.
Check your final answer against the given options.

Concept Tested & Keywords

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