Biostatistics — MCQs

Biostatistics Indian Medical PG Practice Questions and MCQs

Question 741: The table below shows the results of ELISA test for HIV infection : Consider the following statements : 1. The sensitivity is 98%. 2. The specificity is 99%. Which of the statements given above is/are correct?

A. Both 1 and 2
B. 2 only (Correct Answer)
C. Neither 1 nor 2
D. 1 only

Explanation: ***2 only*** - From the ELISA test table, we need to calculate sensitivity and specificity using standard formulas. - **True Positives (TP)** = Infected individuals who tested positive = **4900** - **False Negatives (FN)** = Infected individuals who tested negative = 5800 - 4900 = **900** - **True Negatives (TN)** = Non-infected individuals who tested negative = 95000 - 950 = **94050** - **False Positives (FP)** = Non-infected individuals who tested positive = **950** - **Sensitivity = TP / (TP + FN)** = 4900 / 5800 = **84.48%** (NOT 98%) - **Specificity = TN / (TN + FP)** = 94050 / 95000 = **99.0%** ✓ - **Statement 1 is INCORRECT** (sensitivity is 84.48%, not 98%) - **Statement 2 is CORRECT** (specificity is indeed 99%) *1 only* - This option is incorrect because statement 1 claims sensitivity is 98%, but the calculated sensitivity is only 84.48%. - The test correctly identifies only about 84.5% of infected individuals, missing approximately 15.5% (false negatives). *Both 1 and 2* - This option is incorrect because statement 1 is false. - While statement 2 regarding specificity (99%) is correct, statement 1 regarding sensitivity (98%) is incorrect. *Neither 1 nor 2* - This option is incorrect because statement 2 is correct. - The specificity calculation clearly shows 99%, so at least one statement is correct.

Question 742: As per the United Nations definition of a vital events registration system, ‘vital events’ include which of the following? 1. Foetal deaths 2. School admissions 3. Legal separations 4. College graduations Select the correct answer using the code given below.

A. 2 and 3
B. 2 and 4
C. 1 and 3 (Correct Answer)
D. 1 and 2

Explanation: ***Correct: 1 and 3*** According to the **United Nations Principles and Recommendations for a Vital Statistics System (Rev. 3)**, vital events are demographic events that have significant impact on an individual's legal status and population statistics. **Foetal deaths (1)** are explicitly included as vital events because they impact **reproductive health statistics** and **population data**. They represent crucial demographic outcomes related to pregnancy and birth outcomes. **Legal separations (3)** are recognized vital events as they fundamentally **alter the civil/marital status** of individuals and must be recorded in vital statistics systems. They fall within the category of marriage-related vital events (marriages, divorces, annulments, legal separations). ### Core vital events per UN definition: - Live births - Deaths (including foetal deaths) - Marriages - Divorces - Legal separations - Adoptions - Legitimations - Recognitions - Annulments *Incorrect: 2 and 3* While **legal separations (3)** are vital events, **school admissions (2)** are NOT considered vital events. School admissions are **administrative processes** related to education, not fundamental demographic or legal changes that affect civil status or population dynamics. *Incorrect: 2 and 4* Neither **school admissions (2)** nor **college graduations (4)** are vital events per UN definition. These are **educational milestones and administrative records** for educational purposes. They do not represent changes in vital status or core demographic events like births, deaths, marriages, or divorces. *Incorrect: 1 and 2* While **foetal deaths (1)** are vital events, **school admissions (2)** are not. School admissions are administrative educational records that do not represent demographic events or changes in an individual's legal/civil status that would be captured in a vital statistics system.

Question 743: While calculating the ‘total dependency ratio’, which one of the following is used in the denominator?

A. Midyear population
B. Population 15 to 64 years (Correct Answer)
C. Population 14 to 70 years
D. Population 0 to 65 years

Explanation: ***Population 15 to 64 years*** - The **total dependency ratio** is calculated by dividing the sum of the **dependent population** (ages 0-14 and 65+) by the **working-age population** (ages 15-64). - Therefore, the **denominator** represents the segment of the population that is generally considered to be in their most productive working years. *Midyear population* - The **midyear population** refers to the population at the midpoint of a given year and is often used as a general denominator for various rates (e.g., birth rates, death rates). - However, in the context of the dependency ratio, a specific age group—the **working-age population**—is required in the denominator to reflect economic burden. *Population 14 to 70 years* - This age range does not accurately represent the standard definition of the **working-age population** or the traditional age groups used for calculating dependency ratios. - The internationally accepted age range for the working population is typically **15-64 years**. *Population 0 to 65 years* - This range includes both **dependent children** (0-14) and potentially some of the **elderly dependent population** (65 and over), thus it does not represent the **working-age population** for the denominator. - The denominator for the dependency ratio specifically excludes these dependent age groups.

Question 744: A researcher has obtained the country-level data on the average Body Mass Index (BMI) and the average sugar intake for 100 countries. Which among the following will be best suited to present the relationship between BMI and sugar intake in the 100 countries?

A. Frequency polygon
B. Bar chart
C. Scatter diagram (Correct Answer)
D. Pie diagram

Explanation: ***Scatter diagram*** - A **scatter diagram** is ideally suited for visualizing the relationship or **correlation** between two continuous variables, in this case, average BMI and average sugar intake per country. - Each point on the diagram represents a single country, with its coordinates determined by its corresponding BMI and sugar intake values, allowing for easy identification of patterns or trends. *Frequency polygon* - A **frequency polygon** is used to display the **frequency distribution** of a single continuous variable, showing the shape of the data. - It is not designed to show the relationship between two different variables. *Bar chart* - A **bar chart** is typically used to compare **categorical data** or show changes in a **single variable over time**. - It does not effectively display the relationship or correlation between two continuous variables like BMI and sugar intake. *Pie diagram* - A **pie diagram** is used to represent **proportions** or percentages of a whole for a single categorical variable. - It is not suitable for visualizing the relationship between two continuous quantitative variables.

Question 745: The following table shows the 'Total Fertility Rate (TFR)' by the Wealth Index, as per the National Family Health Survey, (NFHS–4) findings. Which among the following is/are correct about the information?

A. 2. The information given in the table can be presented as a pie chart.
B. 4. Each of the higher divisions of the Wealth Index had lower TFR than the previous (or lower) division. (Correct Answer)
C. 1. The divisions of Wealth Index in the NFHS–4 can be called 'quartiles'.
D. 3. The Wealth Index was calculated in NFHS–4 by asking about the per capita income.

Explanation: ***Each of the higher divisions of the Wealth Index had lower TFR than the previous (or lower) division.*** - Examining the table data: Lowest (3.17), Second (2.45), Middle (2.07), Fourth (1.84), Highest (1.54) - The **Total Fertility Rate consistently decreases** as the wealth index category increases from lowest to highest - This demonstrates an **inverse relationship between wealth and fertility**, a well-established demographic pattern - Each successive higher wealth category shows a lower TFR than the previous category without exception *The divisions of Wealth Index in the NFHS–4 can be called 'quartiles'.* - The table divides the population into **five wealth index categories**: Lowest, Second, Middle, Fourth, and Highest - When a population is divided into five equal groups, these are called **quintiles**, not quartiles - **Quartiles** would divide the population into four groups (25th, 50th, 75th, 100th percentiles) - **Quintiles** divide the population into five groups (20th, 40th, 60th, 80th, 100th percentiles) *The information given in the table can be presented as a pie chart.* - A **pie chart** is used to show parts of a whole, representing proportions or percentages that sum to 100% - The data shows **Total Fertility Rate (TFR)** values for different wealth categories, which are rates (average births per woman), not proportions - TFR values don't sum to a meaningful total and don't represent parts of a whole - This data is better presented as a **bar chart or line graph** to show the trend across wealth categories *The Wealth Index was calculated in NFHS–4 by asking about the per capita income.* - The **Wealth Index** in NFHS surveys is calculated using **principal component analysis** of household assets and characteristics - It includes: consumer durables (TV, refrigerator, vehicles), housing characteristics (flooring type, wall material, roof type), water source, sanitation facilities, cooking fuel, and livestock ownership - **Per capita income is NOT used** because it's difficult to measure accurately in informal economies, has seasonal variations, and suffers from recall bias and underreporting - Asset-based wealth indices are considered more reliable proxies for socioeconomic status in developing countries

Question 746: Forty patients with diarrhoeal diseases were studied. Their age distribution is given in the table below : What is the mean age of the patients in this study?

A. 5 years (Correct Answer)
B. 4 years
C. 6 years
D. 2 years

Explanation: ***5 years*** - To calculate the **mean age** from grouped data, first find the midpoint of each age range. - The midpoints are: **2** for 0-4 years (22 patients), **7** for 5-9 years (12 patients), and **12** for 10-14 years (6 patients). - Multiply each midpoint by the number of patients in that range: (2 × 22) + (7 × 12) + (12 × 6) = 44 + 84 + 72 = **200**. - Divide the sum of these products by the total number of patients (**40**) to get the mean age: **200 / 40 = 5 years**. *2 years* - This is the **midpoint** of the first age group (0-4 years), not the mean of the entire dataset. - While 22 patients (the majority) fall in this age group, the mean must account for the **weighted distribution** across all age groups. - This would only be correct if all 40 patients were in the 0-4 years age group. *4 years* - This answer suggests an **incorrect calculation** of the weighted mean or an error in summing the products. - It does not match the correct weighted mean formula: Σ(midpoint × frequency) / total frequency. - May result from miscalculating the sum (200) or the total number of patients. *6 years* - This value is higher than the calculated mean and likely results from a **mathematical error**. - The correct calculation yields 5 years, not 6 years. - This might arise from rounding errors or incorrect midpoint selection.

Question 747: In a normal curve, the area of one standard deviation around the mean includes which of the following per cent of values in a distribution ?

A. 95.4%
B. 48.6%
C. 68.3% (Correct Answer)
D. 99.7%

Explanation: ***68.3%*** - In a **normal distribution**, approximately 68.3% of the data falls within **one standard deviation** (±1σ) of the mean. - This is a fundamental property of the **empirical rule** (68-95-99.7 rule) applied to normally distributed data. *95.4%* - This percentage represents the data within **two standard deviations** (±2σ) of the mean in a normal distribution. - It is often rounded to 95% for confidence intervals, but the precise value is 95.4%. *48.6%* - This value does not correspond to a standard interval around the mean in a **normal distribution**. - It might be a distracter derived from incorrectly calculating or misremembering the percentages of the empirical rule. *99.7%* - This percentage represents the data within **three standard deviations** (±3σ) of the mean in a normal distribution. - It indicates that almost all data points in a normal curve lie within this range.

Question 748: To understand the relationship between weight and height of a group of school children, the data can graphically be best depicted through

A. Histogram
B. Scatter diagram (Correct Answer)
C. Bar diagram
D. Pictogram

Explanation: ***Scatter diagram*** - A **scatter diagram** (also called a scatter plot) is ideal for showing the relationship between **two continuous variables**, such as weight and height. - Each point on the graph represents an individual's paired values for weight and height, allowing visual identification of **patterns or correlations**. *Histogram* - A **histogram** is used to display the distribution of **a single continuous variable**, showing the frequency of data points within specific intervals or bins. - It would not effectively demonstrate the **relationship or correlation** between two variables simultaneously. *Bar diagram* - A **bar diagram** (or bar chart) is typically used for comparing **categorical data** or discrete values, showing frequencies or proportions for different categories. - It is not suitable for visualizing the relationship between **two continuous numerical variables** like weight and height. *Pictogram* - A **pictogram** uses images or symbols to represent data, often used for presenting simple statistics to a general audience. - It is generally used for **categorical data** or simple comparisons and lacks the precision needed to display the continuous relationship between weight and height.

Question 749: For a screening test, 90% specificity means that 90% of non-diseased persons will give a

A. False negative result
B. True positive result
C. True negative result (Correct Answer)
D. False positive result

Explanation: ***True negative result*** - **Specificity** is defined as the proportion of **true negatives** among individuals **without the disease**. - A 90% specificity means that 90% of healthy individuals will correctly test negative for the disease. *False negative result* - A **false negative** occurs when a diseased person tests negative, which is related to the concept of **sensitivity**, not specificity. - This would imply missing actual cases of the disease. *True positive result* - A **true positive** occurs when a diseased person tests positive, which is also related to **sensitivity**. - This indicates accurate detection of the disease in affected individuals. *False positive result* - A **false positive** occurs when a non-diseased person inappropriately tests positive. - If 90% of non-diseased persons give a negative result (true negative), then 10% would give a **false positive result**.

Question 750: What is the method of sampling in which the units are picked up at regular intervals from the universe ?

A. Stratified random sampling
B. Snow-ball sampling
C. Simple random sampling
D. Systematic random sampling (Correct Answer)

Explanation: ***Systematic random sampling*** - This method involves selecting samples at a **fixed and regular interval** from a larger population after a random starting point is chosen. - It ensures representation across the entire population list by picking every nth unit, making it **efficient for large datasets**. *Stratified random sampling* - This method involves dividing the population into **homogeneous subgroups** (strata) and then drawing a random sample from each stratum. - It is used when there is a need to ensure **representation of specific subgroups**, which is not the primary characteristic described. *Snow-ball sampling* - This is a **non-probability sampling technique** where initial subjects recruit future subjects from among their acquaintances, typically used for hard-to-reach populations. - It relies on existing social networks and is not characterized by picking units at regular intervals. *Simple random sampling* - In this method, every member of the population has an **equal chance of being selected**, and selections are made fully at random. - While random, it does not involve the specific process of picking units at **regular, predetermined intervals**.

Practice by Chapter

Collection and Presentation of Data

Practice Questions

Measures of Central Tendency

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Measures of Dispersion

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Normal Distribution

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Sampling Methods

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Sample Size Calculation

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Hypothesis Testing

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Tests of Significance

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Correlation and Regression

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Survival Analysis

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Multivariate Analysis

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Statistical Software in Research

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