Biostatistics — MCQs

Biostatistics Indian Medical PG Practice Questions and MCQs

Question 71: The median weight of 100 children was 12 kgs, and the Standard Deviation was 3. Calculate the percentage coefficient of variance.

A. 25% (Correct Answer)
B. 35%
C. 45%
D. 55%

Explanation: ### Explanation **Concept and Calculation:** The **Coefficient of Variation (CV)** is a measure of relative variability. It expresses the Standard Deviation (SD) as a percentage of the Mean. It is used to compare the precision or consistency of two different datasets, especially when they have different units or widely different means. The formula for Coefficient of Variation is: $$\text{CV} = \frac{\text{Standard Deviation (SD)}}{\text{Mean}} \times 100$$ In this question, we are given the **Median** (12 kg) and **SD** (3). In a normal distribution (which is generally assumed for large samples like $n=100$ unless stated otherwise), the **Mean is equal to the Median**. * **Calculation:** $\text{CV} = (3 / 12) \times 100 = 0.25 \times 100 = \mathbf{25\%}$. **Why Incorrect Options are Wrong:** * **Option B (35%), C (45%), and D (55%):** These values result from mathematical errors or incorrect application of the formula (e.g., dividing the mean by the SD or using the sample size in the denominator). They do not represent the ratio of 3 to 12. **Clinical Pearls & High-Yield Facts for NEET-PG:** 1. **Unitless Measure:** Unlike SD, which has the same units as the data (e.g., kg), CV is a **unitless** percentage. This makes it the best tool to compare the variability of height (cm) vs. weight (kg). 2. **Normal Distribution:** In a perfectly symmetrical distribution: **Mean = Median = Mode**. 3. **Standard Error (SE):** Do not confuse CV with SE. $SE = SD / \sqrt{n}$. SE measures the variability of sample means, while CV measures the relative dispersion of data points. 4. **Low CV** indicates higher consistency/precision; **High CV** indicates greater volatility or dispersion in the data.

Question 72: Standard deviation does not depend on which of the following?

A. Mean
B. Median (Correct Answer)
C. Range
D. Sample size

Explanation: **Explanation:** Standard Deviation (SD) is a measure of **dispersion** that quantifies the amount of variation or spread of a set of values around the **Arithmetic Mean**. **Why Median is the correct answer:** The calculation of Standard Deviation is mathematically derived from the mean ($\text{SD} = \sqrt{\frac{\sum(x - \bar{x})^2}{n-1}}$). It uses every individual value in a dataset to determine how far, on average, each point deviates from the center. The **Median**, being a positional average (the middle-most value), does not enter the formula for SD. In descriptive statistics, the Median is paired with the **Interquartile Range (IQR)**, not the Standard Deviation. **Analysis of incorrect options:** * **Mean:** SD is fundamentally the "root mean square deviation" from the mean. If the mean changes or the distance of values from the mean increases, the SD changes directly. * **Range:** Both are measures of dispersion. While they are different, the range (maximum – minimum) influences the spread; a wider range often correlates with a larger SD in a normal distribution. * **Sample Size ($n$):** The formula for SD (specifically the denominator) includes the sample size. Larger samples tend to provide a more stable and accurate estimate of the population standard deviation. **High-Yield Pearls for NEET-PG:** * **Relationship:** $\text{Standard Error} = \frac{\text{SD}}{\sqrt{n}}$. * **Normal Distribution:** Mean = Median = Mode. In this specific case, SD relates to all three, but by definition, it is calculated from the Mean. * **Skewed Data:** For skewed distributions, the Median and IQR are preferred over Mean and SD because they are "robust" (less sensitive to outliers). * **Unit:** Unlike Variance (which is squared), SD has the same units as the original data/mean.

Question 73: License to a blood bank is granted by which authority?

A. Drugs Controller General of India (Correct Answer)
B. Director General of Health Services
C. Director General, Indian Council of Medical Research
D. Director General of Blood Bank Services

Explanation: In India, blood is legally classified as a **"Drug"** under the **Drugs and Cosmetics Act, 1940**, and the Drugs and Cosmetics Rules, 1945. Consequently, the regulation, licensing, and quality control of blood banks fall under the jurisdiction of the drug regulatory authorities. ### Why the Correct Answer is Right: **A. Drugs Controller General of India (DCGI):** The DCGI heads the Central Drugs Standard Control Organization (CDSCO). Since blood is a drug, the DCGI is the central licensing approving authority. Licenses for blood banks are issued by the State Licensing Authority but must be **jointly inspected and approved** by the DCGI to ensure national standards are met. ### Why the Other Options are Wrong: * **B. Director General of Health Services (DGHS):** While the DGHS provides technical knowledge and oversees medical services in India, it does not have the statutory power to issue pharmaceutical or blood bank licenses. * **C. Director General, ICMR:** The Indian Council of Medical Research is the apex body for the formulation, coordination, and promotion of biomedical research. It does not perform regulatory or licensing functions. * **D. Director General of Blood Bank Services:** This is a distractor; no such specific statutory regulatory designation exists for licensing in the Indian administrative framework. ### High-Yield Clinical Pearls for NEET-PG: * **National Blood Policy:** Formulated by the Government of India in 2002. * **NACO (National AIDS Control Organization):** Primarily responsible for policy-making and advocacy regarding blood safety and HIV screening, but it is **not** the licensing authority. * **NBTC (National Blood Transfusion Council):** The apex policy-making body for blood transfusion services. * **Mandatory Tests:** Every unit of blood must be screened for five infections: HIV, Hepatitis B (HBsAg), Hepatitis C (HCV), Syphilis (VDRL), and Malaria.

Question 74: What describes the standard normal distribution?

A. Asymmetrical
B. Has a mean of 1.0
C. Has a variance of 0.0
D. Mean, median, and mode are equal (Correct Answer)

Explanation: The **Standard Normal Distribution** (also known as the Z-distribution) is a specific type of normal distribution characterized by its symmetrical, bell-shaped curve. ### Why the Correct Answer is Right In any normal distribution, the data is perfectly symmetrical around the center. Because the highest point of the curve represents the most frequent value (**Mode**), and exactly 50% of the data lies on either side of the center (**Median**), the central peak also represents the arithmetic average (**Mean**). Therefore, in a standard normal distribution, **Mean = Median = Mode**. ### Why the Other Options are Wrong * **A. Asymmetrical:** This is incorrect. A normal distribution is perfectly **symmetrical**. If it were asymmetrical, it would be described as "skewed" (positively or negatively). * **B. Has a mean of 1.0:** This is incorrect. By definition, a *Standard* Normal Distribution has a **mean of 0**. * **C. Has a variance of 0.0:** This is incorrect. A *Standard* Normal Distribution has a **variance of 1** (and consequently, a standard deviation of 1). A variance of 0 would mean all data points are identical, resulting in no curve at all. ### High-Yield NEET-PG Pearls * **Z-Score:** The standard normal distribution is used to calculate the Z-score, which tells you how many standard deviations a value is from the mean. * **The 68-95-99.7 Rule (Empirical Rule):** * Mean ± 1 SD covers **68.2%** of values. * Mean ± 2 SD covers **95.4%** of values. * Mean ± 3 SD covers **99.7%** of values. * **Total Area:** The total area under the curve is always equal to **1** (or 100%). * **Shape:** It is asymptotic to the x-axis, meaning the tails get closer to the horizontal axis but never actually touch it.

Question 75: What is the sensitivity of a diagnostic test?

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

Explanation: **Explanation:** **Sensitivity** is the ability of a diagnostic test to correctly identify those who truly have the disease. It represents the "True Positive Rate." 1. **Why Option A is Correct:** Sensitivity is calculated as **True Positives (TP) / (True Positives + False Negatives)**. The denominator (TP + FN) represents the total number of people who actually have the disease. Therefore, sensitivity measures the proportion of diseased individuals who are correctly identified by the test. 2. **Analysis of Incorrect Options:** * **Option B:** This formula does not represent a standard epidemiological metric. * **Option C:** This is the formula for **Specificity** [TN / (TN + FP)]. Specificity measures the test's ability to correctly identify those without the disease (True Negative Rate). * **Option D:** This is the formula for **False Negative Rate** if inverted, or simply an incorrect ratio. **Clinical Pearls for NEET-PG:** * **SNOUT:** A test with high **S**ensitivity, when **N**egative, rules **OUT** the disease. This makes sensitive tests ideal for **screening**. * **SPIN:** A test with high **S**pecificity, when **P**ositive, rules **IN** the disease. This makes specific tests ideal for **confirmation**. * Sensitivity is **independent of disease prevalence**, whereas Predictive Values (PPV/NPV) are highly dependent on it. * As sensitivity increases, the number of False Negatives decreases.

Question 76: A contraceptive is used by 100 couples for a continuous period of 2 years. During this period, 20 women become pregnant despite using the contraceptive. What is the Pearl Index of the contraceptive?

A. 0.1 per couple-years of exposure
B. 1 per couple-years of exposure
C. 10 per couple-years of exposure (Correct Answer)
D. 1000 per couple-years of exposure

Explanation: ### Explanation **Pearl Index** is the most common method used in clinical trials to report the effectiveness of a contraceptive method. It calculates the number of unintended pregnancies per 100 woman-years (or couple-years) of exposure. **The Formula:** $$\text{Pearl Index} = \frac{\text{Total Number of Pregnancies} \times 1200}{\text{Total Months of Exposure}}$$ *OR* $$\text{Pearl Index} = \frac{\text{Total Number of Pregnancies} \times 100}{\text{Total Years of Exposure}}$$ **Calculation for this question:** * **Total Pregnancies:** 20 * **Total Exposure:** 100 couples × 2 years = 200 couple-years. * **Calculation:** $\frac{20 \times 100}{200} = \mathbf{10}$ Thus, the Pearl Index is **10 per 100 couple-years of exposure**. --- ### Analysis of Options: * **Option A (0.1) & B (1):** These values significantly underestimate the failure rate. They would only be correct if the number of pregnancies were 0.2 or 2, respectively, over the same exposure period. * **Option C (10):** **Correct.** This accurately reflects 10 pregnancies occurring for every 100 years of use. * **Option D (1000):** This is mathematically incorrect and would imply a failure rate impossible for standard contraception. --- ### High-Yield Clinical Pearls for NEET-PG: 1. **Denominator:** Always ensure the denominator is in "100 woman-years." If the data is in months, use the multiplier 1200; if in years, use 100. 2. **Life Table Analysis:** While the Pearl Index is common, **Life Table Analysis** is considered superior because it calculates failure rates for specific time intervals (e.g., month-by-month), accounting for users who drop out of a study. 3. **Efficiency:** The lower the Pearl Index, the more effective the contraceptive method. * *Example:* Implants (0.05) and Vasectomy (0.1) have very low Pearl Indices, whereas the Rhythm method (~25) is high.

Question 77: In a study of 100 glaucoma patients, the intraocular pressure (IOP) has a mean of 30 mm Hg and a standard deviation of 10 mm Hg. What is the lower limit of the average IOP?

A. 28 (Correct Answer)
B. 26
C. 32
D. 25

Explanation: ### Explanation The question asks for the **lower limit of the average (mean) IOP**, which refers to the **95% Confidence Interval (CI)** for the population mean. In biostatistics, while Standard Deviation (SD) describes the spread of individual data points, the **Standard Error of Mean (SEM)** describes the precision of the sample mean compared to the true population mean. **1. Why Option A is Correct:** To find the lower limit, we use the formula: **Mean – (1.96 × SEM)**. * **Step 1: Calculate SEM.** SEM = SD / √n. * SEM = 10 / √100 = 10 / 10 = **1**. * **Step 2: Calculate the 95% Confidence Interval.** * Lower Limit = Mean – (1.96 × SEM) ≈ 30 – (2 × 1) = **28 mm Hg**. * Upper Limit = Mean + (1.96 × SEM) ≈ 30 + (2 × 1) = **32 mm Hg**. Thus, we are 95% confident that the true average IOP of the population lies between 28 and 32 mm Hg. **2. Why Other Options are Incorrect:** * **Option B (26):** This would be the lower limit if we used 4 SEM (approx. 99% CI) or if the SEM was 2. * **Option C (32):** This represents the **upper limit** of the 95% Confidence Interval, not the lower limit. * **Option D (25):** This value does not correspond to standard confidence interval calculations (1.96 or 2.58 SD/SEM). **3. Clinical Pearls & High-Yield Facts:** * **SD vs. SEM:** Use SD to describe variability in a sample; use SEM to estimate population parameters (Confidence Intervals). * **95% CI:** Mean ± 2 SEM (Exact: 1.96). * **99% CI:** Mean ± 3 SEM (Exact: 2.58). * **Sample Size Impact:** As sample size ($n$) increases, SEM decreases, resulting in a narrower (more precise) Confidence Interval.

Question 78: According to the Sample Registration System (SRS) 2017 data, which state had the lowest Infant Mortality Rate (IMR)?

A. Kerala
B. Goa (Correct Answer)
C. Assam
D. Sikkim

Explanation: **Explanation:** The **Infant Mortality Rate (IMR)** is defined as the number of deaths of children under one year of age per 1,000 live births. It is a sensitive indicator of the overall health status of a community and the effectiveness of its maternal and child health services. **Why Goa is Correct:** According to the **SRS 2017** data, **Goa** recorded the lowest IMR in India with a value of **9 per 1,000 live births**. While Kerala has historically led this metric, Goa surpassed it in the 2017 report, making it the top-performing state for this specific period. **Analysis of Incorrect Options:** * **Kerala:** Long considered the benchmark for healthcare in India, Kerala had an IMR of **10** in 2017. While exceptionally low, it was slightly higher than Goa’s. * **Sikkim:** This state also performed well with an IMR of **12**, but it did not reach the record low set by Goa. * **Assam:** In contrast, Assam represented the other end of the spectrum, recording one of the highest IMRs in the country (44) during the same period. **High-Yield Clinical Pearls for NEET-PG:** * **National Average (SRS 2017):** The IMR for India was **33**. * **Highest IMR (SRS 2017):** Madhya Pradesh (47). * **IMR Components:** It consists of Neonatal Mortality (0-28 days) and Post-Neonatal Mortality (28 days to 1 year). * **Most Common Cause of IMR in India:** Low Birth Weight (LBW) and Prematurity, followed by Pneumonia and Diarrheal diseases. * **Current Trend:** Always check the most recent SRS bulletin (e.g., 2020/2021) before the exam, as rankings can shift (e.g., Kerala and Mizoram often compete for the lowest spot).

Question 79: The blood pressure of 2000 randomly selected persons from a population was plotted in a graph. What type of distribution is it most likely to follow?

A. Normal Distribution (Correct Answer)
B. Maxwell Distribution
C. Radial Distribution
D. Poisson Distribution

Explanation: **Explanation:** The correct answer is **Normal Distribution (Gaussian Distribution)**. In biostatistics, biological variables such as blood pressure, height, weight, and serum cholesterol levels typically follow a **Normal Distribution** when measured in a large, randomly selected population. This distribution is characterized by a symmetrical, bell-shaped curve where the mean, median, and mode coincide at the center. The "Law of Large Numbers" and the Central Limit Theorem suggest that as the sample size increases (in this case, 2000 persons), the distribution of these continuous biological variables tends to become perfectly normal. **Why other options are incorrect:** * **Maxwell Distribution:** This is a concept from physics (kinetic theory of gases) describing particle speeds; it is not used to describe human biological data. * **Radial Distribution:** This is used in chemistry and physics to describe the probability of finding a particle at a specific distance from a point; it has no application in population blood pressure studies. * **Poisson Distribution:** This is a discrete probability distribution used for rare events (e.g., the number of deaths from a rare disease in a year or the number of hospital admissions per day). Blood pressure is a continuous variable, not a discrete count of rare events. **High-Yield Clinical Pearls for NEET-PG:** * **Standard Normal Curve:** The area under the curve represents the total probability (1). * **68-95-99.7 Rule:** In a normal distribution, Mean ± 1 SD covers 68.2% of values, Mean ± 2 SD covers 95.4%, and Mean ± 3 SD covers 99.7%. * **Skewness:** If the curve is not symmetrical, it is "skewed." Human body weight often shows a **positive (right) skew** because there is a limit to how low weight can go, but no upper limit.

Question 80: What is the range of the correlation coefficient?

A. Zero to -1.0
B. -1.0 to +1.0 (Correct Answer)
C. +1.0 to zero
D. +2.0 to -2.0

Explanation: **Explanation:** The **Correlation Coefficient (r)**, specifically Pearson’s product-moment correlation, is a statistical measure used to quantify the strength and direction of a linear relationship between two continuous variables. **1. Why Option B is Correct:** The value of 'r' is mathematically constrained between **-1.0 and +1.0**. * **+1.0 (Perfect Positive Correlation):** As one variable increases, the other increases in a perfectly linear fashion. * **-1.0 (Perfect Negative Correlation):** As one variable increases, the other decreases in a perfectly linear fashion. * **0 (No Correlation):** There is no linear relationship between the variables. **2. Analysis of Incorrect Options:** * **Options A & C:** These represent only one half of the possible spectrum. Correlation can be both positive (e.g., height and weight) and negative (e.g., exercise and resting heart rate). * **Option D:** A correlation coefficient cannot exceed 1.0 or be less than -1.0. If a calculation results in a value like 2.0, it indicates a mathematical error. **3. High-Yield Clinical Pearls for NEET-PG:** * **Coefficient of Determination ($r^2$):** This is the square of the correlation coefficient. It represents the proportion of variance in one variable that is predictable from the other. Its range is **0 to 1**. * **Direction vs. Strength:** The *sign* (+ or -) indicates direction, while the *numerical value* indicates strength. For example, a correlation of -0.8 is stronger than +0.5. * **Scatter Diagram:** This is the visual representation of correlation. A straight line indicates $r = 1$, while a circle or random dots indicate $r = 0$. * **Limitation:** Correlation does **not** imply causation. It only describes a mathematical association.

Practice by Chapter

Collection and Presentation of Data

Practice Questions

Measures of Central Tendency

Practice Questions

Measures of Dispersion

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Normal Distribution

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Sampling Methods

Practice Questions

Sample Size Calculation

Practice Questions

Hypothesis Testing

Practice Questions

Tests of Significance

Practice Questions

Correlation and Regression

Practice Questions

Survival Analysis

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Multivariate Analysis

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Statistical Software in Research

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