The average of 25 results is 18. The average of first 12 of them is 14 and that of last 12 results is 17. Find the 13th result.

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

The core principle is that the sum of a set of numbers is their average multiplied by the count of numbers.
First, calculate the total sum of all 25 results: 25 × 18 = 450.
Next, calculate the sum of the two subsets: the sum of the first 12 results (12 × 14 = 168) and the sum of the last 12 results (12 × 17 = 204).
The sum of these two subsets (168 + 204 = 372) represents the sum of 24 of the 25 results.
The 13th result is the difference between the total sum and the sum of the other 24 results: 450 - 372 = 78.

Option A: This is an incorrect value, likely resulting from a calculation error during the subtraction (e.g., 450 - 376) or addition (e.g., 168 + 208) steps.
Option C: This value is also incorrect and likely stems from an arithmetic mistake, such as miscalculating the sum of the subsets or the final subtraction.
Option D: This incorrect answer probably arises from a simple error in arithmetic, for instance, calculating the sum of the subsets as 370 instead of 372.

Visual 1: Infographic: A simple bar chart visualizing the problem. A large bar represents the total sum (450), and two smaller bars within it represent the sum of the first 12 (168) and last 12 (204) results. The gap between them is labeled as the '13th Result (78)'.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the understanding of the concept of average (arithmetic mean) and its application in finding a missing value within a dataset as background academic context rather than a clinical decision trigger.
This type of question is a staple of the General Intelligence or Quantitative Aptitude sections of nursing and other competitive examinations.
While not directly clinical, the logical and mathematical skills tested are crucial for nurses in tasks like calculating medication dosages, interpreting patient data charts, and managing fluid balances.
What if the question involved an overlapping set, such as the average of the first 13 and last 13 results? In that case, the 13th result would be counted twice, and the formula would change to: (Sum of first 13 + Sum of last 13) - Total Sum = 13th result.

How to Approach the Question

First, read the question carefully to identify the total number of items and their overall average.
Calculate the total sum using the formula: Sum = Average × Number of items.
Next, identify the given subsets (e.g., first 12, last 12) and their respective averages.
Calculate the sum for each of these subsets.
Determine how the subsets relate to the total set. In this case, they are two distinct groups with one item missing in between.
Subtract the sum of the subsets from the total sum to isolate the value of the missing item.

Concept Tested & Keywords

Concept Tested: This question tests the understanding of the concept of average (arithmetic mean) and its application in finding a missing value within a dataset.
Stem keywords: average, 25 results, first 12, last 12
Lead-in keywords: Find

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