Biostatistics Practice Questions

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.

Q: The systolic blood pressure of 10 individuals was measured. The mean and median values were calculated to be 130 mmHg and 140 mmHg respectively. What is the shape of the frequency distribution curve?

Negatively skewed distribution. ### Explanation In biostatistics, the relationship between the **Mean, Median, and Mode** determines the shape and skewness of a frequency distribution curve. **1. Why Negatively Skewed is Correct:** A distribution is **negatively skewed** (also known as left-skewed) when the tail of the curve extends toward the lower values (left side). In such distributions, the values follow the mathematical relationship: **Mean < Median < Mode**. * In this question: **Mean (130 mmHg) < Median (140 mmHg)**. * Since the mean is "pulled" down by a few unusually low blood pressure readings (outliers), the distribution is negatively skewed. **2. Analysis of Incorrect Options:** * **A. Symmetrical Distribution:** In a normal (Gaussian) distribution, the Mean, Median, and Mode are all **equal** (Mean = Median = Mode). Here, 130 ≠ 140. * **B. Bimodal Distribution:** This refers to a curve with **two peaks** (two modes). The relationship between mean and median alone does not define bimodality. * **C. Positively Skewed Distribution:** Also known as right-skewed, the tail extends toward higher values. The relationship is **Mean > Median > Mode**. If the mean had been 150 and the median 140, this would be the correct choice. **3. Clinical Pearls & High-Yield Facts for NEET-PG:** * **Mnemonic:** To remember the order, follow the alphabet from the tail. In a **P**ositive skew, the **M**ean is the **G**reatest (Mean > Median). In a **N**egative skew, the **M**ean is the **L**east (Mean < Median). * **Outliers:** The **Mean** is the most affected by extreme values (outliers), while the **Median** is the most robust measure of central tendency for skewed data. * **Normal Distribution:** 68% of values fall within ±1 SD, 95% within ±2 SD, and 99.7% within ±3 SD.

Q: Which of the following is a true statement about the standard normal curve?

There is equal distribution on either side of the curve.. ### Explanation The **Standard Normal Curve** (or Z-distribution) is a specific type of normal distribution used in biostatistics to standardize data and calculate probabilities. **Why Option A is correct:** The standard normal curve is **perfectly symmetrical** around its center. In a normal distribution, the mean, median, and mode are all equal and located at the center. This symmetry ensures that exactly **50% of the distribution lies to the left** and **50% lies to the right** of the mean. Therefore, there is an equal distribution on either side. **Why the other options are incorrect:** * **Option B:** The total area under the curve represents the total probability of all possible outcomes, which is always **1 (or 100%)**, not 2. * **Option C:** By definition, a *Standard* Normal Distribution is transformed so that its **Mean ($\mu$) is 0**. * **Option D:** In a *Standard* Normal Distribution, the **Standard Deviation ($\sigma$) is 1**. A standard deviation of 0 would mean there is no variability in the data (all values are the same), which does not form a curve. **High-Yield Clinical Pearls for NEET-PG:** * **Z-score:** This indicates how many standard deviations a data point is from the mean. Formula: $Z = (X - \mu) / \sigma$. * **Empirical Rule (68-95-99.7 Rule):** * Mean ± 1 SD covers **68.2%** of the area. * Mean ± 2 SD covers **95.4%** of the area. * Mean ± 3 SD covers **99.7%** of the area. * **Point of Inflection:** The points where the curve changes from convex to concave occur at **Mean ± 1 SD**.

Q: Non-sampling errors may occur due to all the following except?

Repeated sampling. In epidemiology, errors in data collection are broadly categorized into **Sampling Errors** and **Non-sampling Errors**. ### Why "Repeated Sampling" is the Correct Answer **Sampling error** occurs because we study a subset (sample) rather than the entire population. It is the inherent variation that occurs by chance. **Repeated sampling** (increasing the sample size or taking multiple samples) actually helps in estimating and **reducing** the standard error. It is the fundamental basis of sampling theory, not a source of non-sampling error. ### Explanation of Incorrect Options (Sources of Non-sampling Errors) Non-sampling errors occur during the actual process of data collection and can happen even if a total census is taken. * **A. Inadequately calibrated instruments:** This is a type of **Systematic Error (Bias)**. If a weighing scale is off by 1kg, every measurement will be wrong regardless of sample size. * **C. Observer variation:** This includes inter-observer (between different people) or intra-observer (same person at different times) inconsistency. It leads to measurement or information bias. * **D. Conceptual errors:** These occur due to faulty study design, poorly worded questionnaires, or incorrect definitions of the variables being studied. ### High-Yield Pearls for NEET-PG * **Sampling Error:** Can be minimized by increasing the sample size ($n$). It is quantified by the **Standard Error**. * **Non-sampling Error:** Can occur at any stage (planning, data collection, or analysis). It **cannot** be minimized by increasing the sample size; in fact, it may increase with larger samples due to decreased supervision. * **Precision vs. Accuracy:** Sampling errors affect **precision** (reliability), while non-sampling errors (bias) affect **accuracy** (validity).

Q: The limits of confidence of a hypothesis are determined by?

1 - Level of significance. ### Explanation **1. Why the Correct Answer is Right:** In biostatistics, the **Level of Significance ($\alpha$)** represents the probability of committing a Type I error (rejecting a true null hypothesis). It defines the threshold for "statistical significance," commonly set at 0.05 (5%). The **Confidence Level (or Limits of Confidence)** is the probability that the true population parameter falls within the calculated interval. It is mathematically defined as **$1 - \alpha$**. For example, if the level of significance is 0.05 (5%), the confidence level is $1 - 0.05 = 0.95$ (or 95%). Therefore, the limits of confidence are directly determined by subtracting the level of significance from the total probability (1). **2. Why the Other Options are Wrong:** * **A. Power Factor ($\beta$):** This is the probability of correctly rejecting a false null hypothesis (detecting an effect when one exists). It is $1 - \text{Type II error}$. * **B. Level of Significance ($\alpha$):** This determines the "p-value" threshold, not the confidence limit itself. It represents the "error" margin, whereas confidence represents the "certainty" margin. * **C. 1 - Power Factor:** This equals $\beta$ (Type II error), which is the probability of failing to reject a false null hypothesis (a "false negative"). **3. NEET-PG High-Yield Pearls:** * **Confidence Interval (CI):** A range of values likely to contain the population mean. If a 95% CI for a Relative Risk or Odds Ratio includes **1**, the results are **not** statistically significant. * **Type I Error ($\alpha$):** "False Positive" (Finding a difference where none exists). * **Type II Error ($\beta$):** "False Negative" (Missing a difference that actually exists). * **Power ($1 - \beta$):** The ability of a study to detect a difference. It is increased by increasing the sample size. * **Standard Error:** Used to calculate the Confidence Interval ($Mean \pm 1.96 \times SE$ for 95% CI).

Q: Which of the following statements about the crude birth rate is NOT true?

It is a ratio, not a rate.. **Explanation** **1. Why the Correct Answer is Right:** In biostatistics, a **rate** measures the occurrence of an event in a population during a given period, where the numerator is a part of the denominator and a time multiplier is used. The **Crude Birth Rate (CBR)** is defined as the number of live births per 1,000 mid-year population in a given year. Since the live births (numerator) are derived from the total population (denominator), it is mathematically a **rate**, not a ratio. Therefore, the statement "It is a ratio, not a rate" is false. **2. Analysis of Other Options:** * **B. It is a measure of fertility:** This is true. While it is the simplest and most "crude" measure because it includes the entire population (including men and children) in the denominator, it remains the most widely used indicator of fertility. * **C. It is independent of the age structure:** This is true. The CBR is called "crude" specifically because it does not take into account the age or sex composition of the population. It treats all individuals in the denominator as equally capable of contributing to the numerator. * **D. The numerator does not include stillbirths:** This is true. By definition, the numerator for CBR is **live births** only. Stillbirths are excluded. **High-Yield Clinical Pearls for NEET-PG:** * **Formula:** $\frac{\text{Number of live births during the year}}{\text{Estimated mid-year population}} \times 1000$. * **Mid-year population** is calculated as of **July 1st** of that year. * **General Fertility Rate (GFR)** is a better indicator than CBR because the denominator is restricted to women in the reproductive age group (15–44 or 15–49 years). * **Total Fertility Rate (TFR)** is the best indicator of the overall fertility level and is used to project population growth.

Question 1

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 2

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 3

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 4

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 5

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.

Question 6

The systolic blood pressure of 10 individuals was measured. The mean and median values were calculated to be 130 mmHg and 140 mmHg respectively. What is the shape of the frequency distribution curve?

Accepted Answer

Negatively skewed distribution

Answer

Symmetrical distribution

Answer

Bimodal distribution

Answer

Positively skewed distribution

Question 7

Which of the following is a true statement about the standard normal curve?

Accepted Answer

There is equal distribution on either side of the curve.

Answer

The total area under the curve is 2.

Answer

Its mean is 1.

Answer

The standard deviation is 0.

Question 8

Non-sampling errors may occur due to all the following except?

Accepted Answer

Repeated sampling

Answer

Inadequately calibrated instruments

Answer

Observer variation

Answer

Conceptual errors

Question 9

The limits of confidence of a hypothesis are determined by?

Accepted Answer

1 - Level of significance

Answer

Power factor

Answer

Level of significance

Answer

1 - Power factor

Question 10

Which of the following statements about the crude birth rate is NOT true?

Accepted Answer

It is a ratio, not a rate.

Answer

It is a measure of fertility.

Answer

It is independent of the age structure of the population.

Answer

The numerator does not include stillbirths.

Biostatistics — MCQs

Biostatistics — MCQs

On this page

Practice by Chapter

Want unlimited practice?