The average of 13 numbers is 14. If each number is multiplied by 4, then what will the new average be:

Appeared in: DSSSB 14 August 2024

Explanation

This question tests a fundamental property of the arithmetic mean (average).
When every number in a dataset is multiplied by a constant value, the new average is simply the original average multiplied by that same constant.
The original average is 14, and the constant multiplier is 4.
Therefore, the new average is calculated as: 14 × 4 = 56.

Option A: This is the original average. The average would not change only if the multiplier was 1.
Option C: This value represents the total count of numbers (N) in the dataset, not their average.
Option D: This is the constant value used to multiply each number. It is the multiplier, not the final calculated average.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Properties of Arithmetic Mean as background academic context rather than a clinical decision trigger.
While this is a general mathematics question from a non-nursing subject, strong numeracy skills are foundational for safe and effective nursing practice.
Nurses constantly use mathematical principles for critical tasks like calculating drug dosages, titrating IV infusions, and interpreting patient data, where a simple miscalculation can have serious patient safety consequences.
What if? - If each number were increased by 4 instead of multiplied, the new average would be the old average plus 4. The new average would be 14 + 4 = 18. Understanding the correct operation is key.

How to Approach the Question

First, carefully read the question and identify the key given values: the original average (14), the number of items (13), and the operation performed on each number (multiplied by 4).
Recognize that this is a question about a property of the arithmetic mean. You do not need to know the individual 13 numbers to solve it.
Recall the specific rule for multiplication: If every observation in a dataset is multiplied by a constant 'k', the new mean is the original mean also multiplied by 'k'.
Apply this rule directly to the given values: New Average = Original Average × Constant.
Substitute the numbers: New Average = 14 × 4.
Calculate the result, which is 56, and select the matching option.

Concept Tested & Keywords

Q2ChidAfcvbbCoOBXI1fOW

E6 NursingResearch Sukhpal Kaur p. 441-443

Practise the full DSSSB 14 August 2024

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