Q: In a clinical trial, a patient's time until death is identified as an outlier on a boxplot. According to the 1.5*IQR rule, which of the following is TRUE?

The value is either less than $$Q_1 - 1.5$$ \times IQR$$ or greater than Q_3$ + 1.5 \times IQR.$$

Question 1

A researcher is analyzing the ages of patients in a cancer study. The ages are: 30, 32, 33, 34, and 80. Which measure of central tendency is most affected by the age of 80?

Accepted Answer

The mean

Question 2

Which of the following statements about the median is TRUE?

Accepted Answer

The median is robust to extreme values (outliers).

Question 3

Given the dataset: 2, 4, 4, 5, what is the mode?

Accepted Answer

4

Question 4

A hospital administrator wants to summarize the number of cigarettes smoked per day by patients. The data are highly right-skewed. Which measure of central tendency should be reported?

Accepted Answer

The median

Question 5

Which formula correctly represents the calculation of the sample mean for $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\frac{1}{n} \sum_{i=1}^{n} x_i$$

Question 6

A dataset contains the following values: 1, 2, 3, 4, 100. What is the range?

Accepted Answer

$$100 - 1 = 99$$

Question 7

Which of the following best describes the standard deviation?

Accepted Answer

It is the square root of the variance.

Question 8

If a dataset is left-skewed, which of the following is most likely TRUE?

Accepted Answer

Mean $$\u003c$$ Median

Question 9

A boxplot is constructed for the variable 'time until death' in a clinical trial. Which summary statistics are directly visible from the boxplot?

Accepted Answer

Minimum, first quartile ($$Q_1$$), median, third quartile ($$Q_3$$), and maximum

Question 10

Which of the following is the correct formula for the interquartile range (IQR)?

Accepted Answer

$$Q_3$$ - $$Q_1$$

Question 11

A dataset has a mean of 10 and a standard deviation of 0. What does this indicate about the data?

Accepted Answer

All observations are equal to 10.

Question 12

Which of the following is NOT a robust statistic?

Accepted Answer

The mean

Question 13

A researcher finds that the mean BMI in a large sample is greater than the median BMI. What does this suggest about the distribution of BMI?

Accepted Answer

The distribution is right-skewed.

Question 14

Which of the following is the correct formula for the sample variance $$s^2$$ for $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ with sample mean $$\bar{x}$$?

Accepted Answer

$$s^2$$ = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x}$$)^2$$

Question 15

In a clinical trial, a patient's time until death is identified as an outlier on a boxplot. According to the 1.5*IQR rule, which of the following is TRUE?

Accepted Answer

The value is either less than $$Q_1 - 1.5$$ 	imes IQR$$ or greater than Q_3$ + 1.5 	imes IQR.$$

Question 16

A dataset of systolic blood pressure (SBP) for two patients is as follows: Patient A: 120, 120, 120; Patient B: 120, 120, 150. Both have a mean SBP of 120. Which patient has greater variability?

Accepted Answer

Patient B

Question 17

Which of the following best describes the mode?

Accepted Answer

The value that occurs most frequently in a dataset.

Question 18

A dataset contains the following values: 2, 2, 3, 4, 5, 6, 7, 8, 9, 10. What is the median?

Accepted Answer

5.5

Question 19

Which of the following is a correct interpretation of a boxplot with several outliers marked as open circles?

Accepted Answer

There are data points that are unusually far from the rest of the data.

Question 20

If a dataset has a mean of 20, a median of 15, and a mode of 10, what can you infer about the shape of the distribution?

Accepted Answer

It is right-skewed.

Measures of Central Tendency and Variability in Biostatistics

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