Sum of the deviation of the variable values 3, 4, 8, 7, 8, 14 from their mean is _____.

Appeared in: Haryana CHO - 2022

Explanation

This question tests a fundamental property of the arithmetic mean.
The sum of the algebraic deviations of each value in a dataset from the mean of that dataset is always zero.
This property defines the mean as the center of balance for the data, where the sum of negative deviations perfectly cancels out the sum of positive deviations.
Therefore, without any calculation, the answer can be identified as 0.

Option B: A sum of 1 is incorrect. This would imply an imbalance where positive deviations are greater than negative deviations, which contradicts the definition of the mean.
Option C: A sum of 5 is incorrect. This value is arbitrary and does not represent any property related to the sum of deviations from the mean.
Option D: A sum of 7 is incorrect. While 7 is one of the values in the dataset and close to the mean, it is not the sum of the deviations.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Property of Arithmetic Mean as background academic context rather than a clinical decision trigger.
Understanding basic statistical properties like the mean is crucial for nurses involved in research, evidence-based practice, or quality improvement projects to correctly interpret data.
For example, when analyzing patient data like blood pressure readings, blood glucose levels, or length of hospital stay, the mean provides a measure of central tendency, and this property ensures the calculation is balanced.
What if the question asked for the sum of the squared deviations? The answer would no longer be zero. This value is the basis for calculating variance and standard deviation, which are key measures of data dispersion.

How to Approach the Question

First, identify the core statistical concept being asked. The question asks for the 'sum of the deviation... from their mean'.
Recall the fundamental properties of the arithmetic mean. One of the most important properties is that the algebraic sum of the deviations of a set of values from their arithmetic mean is zero.
Based on this property, the answer must be 0, without needing to perform any calculations.
To verify, you can perform the calculation: 1. Find the mean of the data. 2. Subtract the mean from each data point to find the deviation. 3. Sum all the deviations. The result will be 0.
Select the option that matches this definitional property.

Concept Tested & Keywords

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E6 NursingResearch Sukhpal Kaur pp. 459-461, 458-460, 460-462

Practise the full Haryana CHO - 2022

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