Biostatistics Practice Questions

Q: Calculate the range from the following frequency distribution: | Class Interval | Frequency | |----------------|-----------| | 10 – 15 | 3 | | 15 – 20 | 7 | | 20 – 25 | 5 | Total n = 15

15. ***15*** - **Range** is calculated as the difference between the **maximum value** and the **minimum value** in the dataset. - From the frequency distribution, the **lowest class boundary is 10** and the **highest class boundary is 25**, so Range = 25 - 10 = **15**. *10* - This represents the **lower boundary** of the first class interval, not the range of the distribution. - Range requires calculating the **difference between extremes**, not just identifying the minimum value. *20* - This is the **upper boundary** of the second class interval, which is neither the maximum nor the range. - It does not represent the **spread** or **variability** of the entire dataset. *25* - This is the **upper boundary** of the highest class interval, representing the maximum value but not the range. - Range is the **difference between maximum and minimum**, not just the maximum value alone.

Q: An investigator finds that 5 independent factors influence the occurrence of a disease. Comparison of multiple factors that are responsible for the disease can be assessed by:

Multiple logistic regression. ### Explanation The core of this question lies in identifying the relationship between multiple independent variables (risk factors) and a single dependent variable (disease occurrence). **1. Why Multiple Logistic Regression is Correct:** In medical research, the "occurrence of a disease" is typically a **dichotomous (binary) outcome**—meaning the patient either has the disease or does not (Yes/No). When you need to assess the influence of multiple independent factors (which can be continuous or categorical) on a single binary outcome, **Multiple Logistic Regression** is the statistical tool of choice. It calculates the **Odds Ratio (OR)** for each factor while controlling for confounders. **2. Why the Other Options are Incorrect:** * **ANOVA (Analysis of Variance):** Used to compare the **means** of a continuous variable across three or more categorical groups (e.g., comparing mean blood pressure across three different diet groups). * **Multiple Linear Regression:** Used when the dependent variable is **continuous** (e.g., predicting exact blood sugar levels based on age, weight, and exercise). It is not used for binary "yes/no" outcomes. * **Chi-square Test:** Used to find an association between two **categorical** variables (e.g., smoking and lung cancer). It cannot handle multiple independent factors simultaneously in its basic form. **3. High-Yield Clinical Pearls for NEET-PG:** * **Logistic Regression = Dichotomous Outcome** (Disease vs. No Disease). It yields **Odds Ratio**. * **Linear Regression = Continuous Outcome** (Height, Weight, BP). It yields a **Correlation Coefficient (r)**. * **ANOVA** = Comparison of **Means** (3+ groups). * **Paired t-test** = Comparison of means in the **same group** (Before vs. After treatment). * **Unpaired t-test** = Comparison of means between **two different groups**.

Q: A 95% confidence interval for the prevalence of cancer in smokers aged over 65 years is 56% to 76%. What is the chance that the true prevalence is less than 56%?

2.50%. ### Explanation **1. Understanding the Correct Answer (C: 2.50%)** A **95% Confidence Interval (CI)** represents the range within which we are 95% certain the true population parameter (prevalence) lies. This means there is a **5% total probability** that the true value falls *outside* this range. In a normal distribution (bell curve), this 5% error is distributed equally into two "tails": * **Lower Tail:** 2.5% chance the true value is *less than* the lower limit (56%). * **Upper Tail:** 2.5% chance the true value is *greater than* the upper limit (76%). Therefore, the probability that the true prevalence is less than 56% is exactly **2.5%**. **2. Why Other Options are Incorrect** * **A (Nil):** Incorrect. A confidence interval does not provide absolute certainty; there is always a calculated risk of error (alpha). * **B (44%):** Incorrect. This is simply the complement of the lower limit (100% - 56%), which has no statistical relevance to the probability of the true mean. * **D (5%):** Incorrect. This represents the *total* probability of the true value being outside the interval (both tails combined). The question specifically asks for the probability of being *less than* the lower limit (one tail). **3. High-Yield Clinical Pearls for NEET-PG** * **Confidence Interval (CI) Formula:** $Mean \pm (1.96 \times SE)$ for 95% CI; $Mean \pm (2.58 \times SE)$ for 99% CI. * **Precision vs. Sample Size:** A larger sample size results in a narrower (more precise) confidence interval. * **P-value vs. CI:** If a 95% CI for a difference between two groups includes **zero**, the results are not statistically significant ($p > 0.05$). If a 95% CI for an Odds Ratio or Relative Risk includes **one**, it is not significant. * **Interpretation:** A 95% CI means if the study were repeated 100 times, the true value would fall within the calculated interval in 95 of those instances.

Q: Due to an effective prevention program, the prevalence of an infectious disease in a community has been reduced by 90%. A physician continues to use the same diagnostic test for the disease that she has always used. How have the test’s characteristics changed?

Its negative predictive value has increased. ### Explanation The core concept tested here is the relationship between **disease prevalence** and **predictive values**. **1. Why Option D is Correct:** Negative Predictive Value (NPV) is the probability that a person who tests negative truly does not have the disease. NPV is **inversely proportional** to prevalence. When the prevalence of a disease decreases (in this case, by 90%), the number of "True Negatives" in the population increases significantly relative to "False Negatives." Therefore, a negative test result becomes even more reliable, leading to an **increase in NPV**. **2. Why the Other Options are Incorrect:** * **Option A & C:** Sensitivity and Specificity are **intrinsic properties** of a diagnostic test. They depend on the test’s design (e.g., the cutoff point) and are independent of the prevalence of the disease in the population. Thus, they remain unchanged. * **Option B:** Positive Predictive Value (PPV) is **directly proportional** to prevalence. As prevalence falls, the likelihood that a positive result is a "False Positive" increases. Therefore, the PPV would **decrease**, not increase. **3. High-Yield Clinical Pearls for NEET-PG:** * **Prevalence $\uparrow$:** PPV increases, NPV decreases. * **Prevalence $\downarrow$:** PPV decreases, NPV increases. * **Sensitivity/Specificity:** These are fixed characteristics of the test and do not change with prevalence. * **Screening in Low-Prevalence Areas:** When screening for rare diseases, the PPV is usually low, meaning many positive results will be false positives. This is why confirmatory tests are essential. * **Formula Recall:** * $PPV = \text{True Positives} / (\text{True Positives} + \text{False Positives})$ * $NPV = \text{True Negatives} / (\text{True Negatives} + \text{False Negatives})$

Q: In a community of 6000 people, there are 150 cases of TB and 30 deaths due to TB. What is the TB-specific death rate per 1000 population?

0-5. ### Explanation **1. Understanding the Correct Answer (D)** The **Specific Death Rate** measures the number of deaths due to a specific cause per 1,000 population in a given year. The formula is: $$\text{Specific Death Rate} = \frac{\text{Number of deaths from a specific disease}}{\text{Total mid-year population}} \times 1000$$ **Calculation:** * Total Population = 6,000 * Deaths due to TB = 30 * Calculation: $(30 / 6,000) \times 1,000 = 5$ per 1,000 population. Since the result is exactly 5, it falls within the range of **Option D (0-5)**. **2. Why Other Options are Incorrect** * **Option A (20):** This value is obtained if you calculate the **Case Fatality Rate (CFR)**. CFR is the percentage of people diagnosed with a disease who die from it: $(30 / 150) \times 100 = 20\%$. While 20 is a relevant number, it represents lethality, not the population death rate. * **Option B (10):** This is a distractor resulting from calculation errors (e.g., using 3,000 as the denominator). * **Option C (5):** While the numerical value is 5, in many competitive exams, if a range is provided that includes the exact value (0-5), it is selected as the most appropriate category. **3. NEET-PG High-Yield Pearls** * **Case Fatality Rate (CFR):** Reflects the **virulence** or killing power of a disease. It is a ratio, not a true rate (expressed as a percentage). * **Cause-Specific Death Rate:** Reflects the **burden** of a disease on the total community. * **Proportional Mortality Rate:** (Deaths from TB / Total deaths from all causes) × 100. It indicates the relative importance of a specific cause of death. * **Prevalence of TB in this scenario:** $(150 / 6,000) \times 100 = 2.5\%$.

Q: If the mean is less than the median, the data is said to be?

Negatively skewed. ### Explanation In biostatistics, the relationship between the **Mean, Median, and Mode** determines the shape of the data distribution (skewness). **1. Why the correct answer is right:** In a **Negatively Skewed distribution** (also known as Left-skewed), the tail of the distribution extends toward the lower values (left side). Because the **Mean** is highly sensitive to extreme values (outliers), it is "pulled" down toward the tail more than the Median or Mode. Therefore, the mathematical relationship is: **Mean Median > Mode**. * **Option C (Equitable distribution):** This is not a standard statistical term for describing the shape or symmetry of a frequency distribution. * **Option D (Normal distribution):** This is a perfectly symmetrical, bell-shaped curve where there is no skew. In this case: **Mean = Median = Mode**. **3. High-Yield Clinical Pearls for NEET-PG:** * **The "Rule of Alphabetical Order":** In a **P**ositively skewed curve, the Mean is the **G**reater than the Median. In a **N**egatively skewed curve, the Mean is **L**ess than the Median. * **Best Measure of Central Tendency:** * For **Skewed data**: The **Median** is the most robust measure because it is not affected by outliers. * For **Normal distribution**: The **Mean** is the preferred measure. * **Visual Aid:** Remember that the "Tail tells the Tale." If the tail is on the left (negative side of the X-axis), it is negatively skewed.

Q: The postoperative quality of life (QOL) scores of 200 prostate cancer patients have a mean of 60 and a standard deviation of 10. How many patients are expected to have a QOL score between 40 and 80?

190. ### Explanation This question tests your understanding of the **Normal Distribution (Gaussian Distribution)** curve, a fundamental concept in biostatistics. In a normal distribution, data is symmetrically distributed around the mean, and the spread is defined by the Standard Deviation (SD). **1. Why Option A is Correct:** The Empirical Rule (68-95-99.7 rule) states: * **Mean ± 1 SD** covers ~68% of the population. * **Mean ± 2 SD** covers ~95% of the population. * **Mean ± 3 SD** covers ~99.7% of the population. In this scenario: * Mean = 60; SD = 10. * The range provided is 40 to 80. * Calculation: $60 - (2 \times 10) = 40$ and $60 + (2 \times 10) = 80$. * Since the range is **Mean ± 2 SD**, it encompasses **95%** of the patients. * Total patients = 200. Therefore, $95\% \text{ of } 200 = 0.95 \times 200 = \mathbf{190}$. **2. Why Other Options are Incorrect:** * **Option B (136):** This represents 68% of 200 ($0.68 \times 200$). This would be the answer if the range was Mean ± 1 SD (50 to 70). * **Options C & D (120, 140):** These are arbitrary numbers that do not correspond to standard confidence intervals or SD boundaries in a normal distribution. **3. Clinical Pearls & High-Yield Facts:** * **Normal Distribution Properties:** Mean = Median = Mode. The curve is bell-shaped and asymptotic (never touches the x-axis). * **Z-score:** This indicates how many SDs a value is from the mean. A score of 80 has a Z-score of +2. * **Standard Error (SE):** Remember that $SE = SD / \sqrt{n}$. SE is used for calculating confidence intervals for the population mean, whereas SD describes the variability within the sample. * **Skewness:** If Mean > Median, it is **Positively Skewed** (tail to the right); if Mean < Median, it is **Negatively Skewed** (tail to the left).

Q: Which of the following statements is NOT true about a normal curve?

The value of the mean is 1.. ### Explanation The **Normal Distribution** (also known as the Gaussian Distribution) is a fundamental concept in biostatistics used to describe how continuous biological variables (like height, blood pressure, or Hb levels) are distributed in a population. **Why Option D is the Correct Answer (The False Statement):** In a general normal curve, the mean can be **any value** (positive, negative, or zero) depending on the data being measured. The statement "The value of the mean is 1" is only true for a specific case called the **Standard Normal Distribution**, where the mean is 0 and the standard deviation is 1. Therefore, it is not a universal property of all normal curves. **Analysis of Incorrect Options (True Statements):** * **Option A (Bell-shaped):** The normal curve is characteristically bell-shaped, with the highest frequency of observations at the center and tapering tails at both ends. * **Option B (Symmetrical):** It is perfectly symmetrical. If folded at the mean, the two halves would overlap exactly. This implies there is no "skewness." * **Option C (Mean, Median, and Mode coincide):** In a perfectly normal distribution, the average (mean), the middle value (median), and the most frequent value (mode) are all equal and located at the center of the curve. **High-Yield Clinical Pearls for NEET-PG:** * **Area under the curve:** * Mean ± 1 SD covers **68.3%** of values. * Mean ± 2 SD covers **95.4%** of values. * Mean ± 3 SD covers **99.7%** of values. * **Standard Normal Curve (Z-score):** A normal distribution transformed to have a **Mean = 0** and **SD = 1**. * **Limits:** The tails of the curve are asymptotic, meaning they approach the horizontal axis but never actually touch it.

Question 1

Calculate the range from the following frequency distribution:

| Class Interval | Frequency |
|----------------|-----------|
| 10 – 15        | 3         |
| 15 – 20        | 7         |
| 20 – 25        | 5         |

Total n = 15

Accepted Answer

15

Answer

10

Answer

20

Answer

25

Question 2

An investigator finds that 5 independent factors influence the occurrence of a disease. Comparison of multiple factors that are responsible for the disease can be assessed by:

Accepted Answer

Multiple logistic regression

Answer

ANOVA

Answer

Multiple linear regression

Answer

Chi-square test

Question 3

A 95% confidence interval for the prevalence of cancer in smokers aged over 65 years is 56% to 76%. What is the chance that the true prevalence is less than 56%?

Accepted Answer

2.50%

Answer

Nil

Answer

44%

Answer

5%

Question 4

Due to an effective prevention program, the prevalence of an infectious disease in a community has been reduced by 90%. A physician continues to use the same diagnostic test for the disease that she has always used. How have the test’s characteristics changed?

Accepted Answer

Its negative predictive value has increased

Answer

Its sensitivity has increased

Answer

Its positive predictive value has increased

Answer

The test’s characteristics have not changed

Question 5

In a community of 6000 people, there are 150 cases of TB and 30 deaths due to TB. What is the TB-specific death rate per 1000 population?

Accepted Answer

0-5

Answer

20

Answer

10

Answer

5

Question 6

Which of the following statements regarding the normal distribution curve is FALSE?

Accepted Answer

Approximately 95% of values lie within one standard deviation of the mean.

Answer

The mean, median, and mode are all equal.

Answer

The median represents the midpoint of the data.

Answer

The total area under the curve represents 100% or 1.

Question 7

If the mean is less than the median, the data is said to be?

Accepted Answer

Negatively skewed

Answer

Positively skewed

Answer

Equitable distribution

Answer

Normal distribution

Question 8

The postoperative quality of life (QOL) scores of 200 prostate cancer patients have a mean of 60 and a standard deviation of 10. How many patients are expected to have a QOL score between 40 and 80?

Accepted Answer

190

Answer

136

Answer

120

Answer

140

Question 9

An ECG was performed on 700 subjects with complaints of acute chest pain. Of these, 520 patients had myocardial infarction. What is the positive predictive value of the ECG?

Accepted Answer

98%

Answer

40%

Answer

55%

Answer

95%

Question 10

Which of the following statements is NOT true about a normal curve?

Accepted Answer

The value of the mean is 1.

Answer

It is bell-shaped.

Answer

It is symmetrical about the mean.

Answer

The mean, mode, and median coincide.

Biostatistics — MCQs

Biostatistics — MCQs

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