30 out of 50 smokers & 10 out of 50 non-smokers are positive cases. Calculate the ratio?

Appeared in: AIIMS CRE SNO - 2023

Explanation

The proportion of positive cases in the smoker group is calculated as 30 divided by 50, which equals 0.6.
The proportion of positive cases in the non-smoker group is calculated as 10 divided by 50, which equals 0.2.
The ratio is found by dividing the proportion of the smoker group by the proportion of the non-smoker group.
The final calculation is 0.6 divided by 0.2, which results in 3.

Option B: The number 5 is incorrect. It does not result from the correct calculation of the ratio between the two proportions.
Option C: The number 7 is incorrect. There is no mathematical operation using the given numbers (30, 10, 50) that logically results in 7.
Option D: The number 2 is incorrect. This might be obtained by incorrectly subtracting the number of positive cases (30 - 10 = 20) and then dividing by the non-smoker positive cases (20 / 10 = 2). This is not the correct method for calculating a ratio of proportions.

Visual 1: Bar Chart - A simple bar chart comparing the two proportions (0.6 for smokers vs. 0.2 for non-smokers) would visually demonstrate that the smoker group's proportion is three times higher.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of a ratio from given population data as background academic context rather than a clinical decision trigger.
Understanding ratios is fundamental in epidemiology and public health nursing. It helps quantify the strength of association between an exposure (like smoking) and an outcome (like a disease).
This calculation is a simplified form of 'Relative Risk' or 'Risk Ratio', a key metric used in cohort studies to compare the risk of an outcome in an exposed group to the risk in an unexposed group.
Nurses use this evidence to educate patients about risk factors and to advocate for public health policies, such as smoking cessation programs.

How to Approach the Question

First, identify the two distinct groups for comparison mentioned in the question (here, smokers and non-smokers).
Next, for each group, calculate the proportion or rate of the event of interest (positive cases). A proportion is calculated as (number of events) / (total number in the group).
For smokers, calculate 30 / 50 = 0.6.
For non-smokers, calculate 10 / 50 = 0.2.
To find the ratio, divide the proportion of the first group by the proportion of the second group: 0.6 / 0.2.
Simplify the result to get the final answer and match it with the given options.

Concept Tested & Keywords

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