If the sum of a few numbers is 450 and their mean is 50 and if another number 100 is included, the mean would become

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

The first step is to determine the original quantity of numbers by dividing the total sum (450) by the mean (50), which gives 9 numbers.
Next, calculate the new sum by adding the new number (100) to the original sum (450), resulting in a new sum of 550.
The total count of numbers increases by one, from 9 to 10.
Finally, the new mean is found by dividing the new sum (550) by the new count (10), which equals 55.

Option B: A new mean of 60 would imply a new total sum of 600 (60 x 10). The actual new sum is 550.
Option C: A new mean of 75 would imply a new total sum of 750 (75 x 10). The actual new sum is 550.
Option D: This is a result of a common calculation error where the new number (100) is added directly to the old mean (50). The mean calculation involves the total sum and count, not just adding values to the previous mean.

Visual 1: Infographic: A visual breakdown of the formula for the arithmetic mean (Mean = Sum of Values / Number of Values) and a step-by-step illustration of how to recalculate it when a new value is added.

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 after adding a value to a dataset as background academic context rather than a clinical decision trigger.
While this is a general aptitude question, strong numeracy skills are essential in nursing for tasks like calculating drug dosages, titrating IV drips, and interpreting lab results, where precision is critical for patient safety.
What if? If the included number was 10 instead of 100, the new mean would decrease. The new sum would be 450 + 10 = 460, and the new mean would be 460 / 10 = 46. This demonstrates that adding a value below the mean reduces the average.

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).
Recall the formula for the mean: Mean = Sum / Count. Use this to find the original number of items in the set.
Calculate the new sum by adding the new number to the original sum.
Determine the new count of items by adding one to the original count.
Use the new sum and new count to calculate the new mean.
Compare your calculated new mean with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Calculating the new arithmetic mean after adding a value to a dataset.
Stem keywords: sum, mean, included
Lead-in keywords: mean would become
Negative lead-in flag: false

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