Q: Which formula is used to calculate excess kurtosis for a sample?

$$\text{Excess Kurtosis} = \text{Kurtosis} - 3$$

Q: In grouped data, which formula is used to estimate the median?

$$\text{Median} = L + \frac{\frac{n}{2} - F}{f} \times w$$

Question 1

A hospital administrator wants to summarize the average length of stay for patients. The data is highly skewed due to a few patients with extremely long stays. Which measure of central tendency is most appropriate to report?

Accepted Answer

Median

Question 2

Given the dataset: 120, 130, 135, 140, 500, which measure of central tendency is most affected by the outlier (500)?

Accepted Answer

Mean

Question 3

A nutritionist collects the following daily calorie intakes from 5 patients: 1800, 2000, 2200, 2100, 1900. What is the arithmetic mean?

Accepted Answer

$$\frac{1800+2000+2200+2100+1900}{5}=2000$$

Question 4

Which formula correctly calculates the sample variance for a dataset $$x_1$$, $$x_2$$, ..., x_n$$ with sample mean $$\bar{x}$$?

Accepted Answer

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

Question 5

A researcher wants to compare the variability of blood pressure readings between two clinics. Clinic A has a mean of 120 mmHg and standard deviation of 12 mmHg. Clinic B has a mean of 140 mmHg and standard deviation of 14 mmHg. Which clinic has greater relative variability?

Accepted Answer

Both clinics have the same relative variability, $$CV = 10\%$$

Question 6

Which of the following best describes a distribution with skewness $$\u003e 0$$?

Accepted Answer

Positively skewed (right-skewed)

Question 7

A dataset of cholesterol levels in patients shows high kurtosis. What does this indicate?

Accepted Answer

There are more extreme values (outliers) than expected in a normal distribution

Question 8

Which formula is used to calculate the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 9

In a box-and-whisker plot, which feature indicates the presence of outliers?

Accepted Answer

Points marked outside the fences (L and R)

Question 10

A dataset is summarized as follows: Mean = 50, Median = 45, Mode = 40. What is the likely skewness of the distribution?

Accepted Answer

Positively skewed

Question 11

Which measure of dispersion is most robust to outliers?

Accepted Answer

Interquartile range (IQR)

Question 12

A health researcher wants to report the most common BMI category among patients. Which measure should be used?

Accepted Answer

Mode

Question 13

Which formula is used to calculate the weighted mean for values $$x_1$$, $$x_2$$, ..., x_n$$ with weights w_1$, w_2$, ..., w_n$$?

Accepted Answer

$$\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}$$

Question 14

A boxplot of patient recovery times shows the median line closer to the bottom of the box and a longer upper whisker. What does this suggest about the distribution?

Accepted Answer

Positively skewed

Question 15

Which of the following is NOT a limitation of using the mean as a summary statistic in health data?

Accepted Answer

Always exists for numerical data

Question 16

A sample of systolic blood pressure readings: 110, 115, 120, 125, 130. What is the range?

Accepted Answer

$$130 - 110 = 20$$

Question 17

Which formula is used to calculate excess kurtosis for a sample?

Accepted Answer

$$	ext{Excess Kurtosis} = 	ext{Kurtosis} - 3$$

Question 18

In grouped data, which formula is used to estimate the median?

Accepted Answer

$$	ext{Median} = L + \frac{\frac{n}{2} - F}{f} 	imes w$$

Question 19

A dataset of patient ages is summarized as: Q1 = 25, Q2 = 35, Q3 = 45. What is the interquartile range (IQR)?

Accepted Answer

$$45 - 25 = 20$$

Question 20

Which summary statistic is most appropriate for reporting the typical survival time in a clinical trial with highly skewed data?

Accepted Answer

Median

Module 5

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드