Question 1

Which of the following best describes the shape of the cholesterol level distributions for both rural and urban Guatemalan groups, as observed in the histograms?

Accepted Answer

Both distributions are mound-shaped with some skewness to the right.

Question 2

An outlier was identified in the urban group’s cholesterol data. What is the value of this outlier, and why is it considered an outlier?

Accepted Answer

The value is 330, because it is much larger than the next largest value and separated by a large gap.

Question 3

Given the five-number summary for the rural group (min = 95, $Q_1 = 136$, median = 152, $Q_3 = 174$, max = 231), calculate the interquartile range (IQR) and interpret its meaning in this context.

Accepted Answer

$IQR = Q_3 - Q_1 = 174 - 136 = 38$; it measures the spread of the middle 50% of cholesterol levels in the rural group.

Question 4

Which statistical measure increased the most in the urban group compared to the rural group, and what does this suggest about the urban group’s cholesterol levels?

Accepted Answer

The mean increased the most, suggesting the urban group has generally higher cholesterol levels.

Question 5

If the standard deviation of the urban group is $39.92$ and for the rural group is $31.75$, what is the ratio of the standard deviations, and what does this indicate?

Accepted Answer

$\frac{39.92}{31.75} \approx 1.3$; the urban group has about 30% more variability in cholesterol levels.

Question 6

Suppose you want to compare the skewness of the two distributions using the ratio $(	ext{max} - 	ext{med})/(	ext{med} - 	ext{min})$. For the urban group, max = 330, med = 206, min = 134. Calculate this ratio and interpret the result.

Accepted Answer

$\frac{330 - 206}{206 - 134} = \frac{124}{72} \approx 1.7$; the urban group distribution is strongly right-skewed.

Question 7

Why is it important to consider the effect of the outlier (330 mg/dL) in the urban group when analyzing variability?

Accepted Answer

Because outliers can inflate measures of spread like the range and standard deviation, potentially exaggerating variability.

Question 8

Given the following percentiles for the urban group: 20th percentile = 188.5, 80th percentile = 242, what does this tell you about the distribution of cholesterol levels in the urban group?

Accepted Answer

60% of urban individuals have cholesterol levels between 188.5 and 242 mg/dL.

Question 9

If the mean cholesterol level for the rural group is $157.02$ mg/dL and for the urban group is $216.87$ mg/dL, what is the difference in means, and what does this suggest?

Accepted Answer

$216.87 - 157.02 = 59.85$ mg/dL; urban individuals have, on average, much higher cholesterol levels.

Question 10

Which of the following is a plausible explanation for the observed differences in cholesterol distributions between rural and urban Guatemalans?

Accepted Answer

Urban Guatemalans likely have less physical activity and higher-fat diets, leading to higher cholesterol and more variability.

Question 11

If the interquartile range (IQR) for the urban group is 42 and for the rural group is 38, what is the ratio of the IQRs, and what does this suggest about the central spread of the two groups?

Accepted Answer

$\frac{42}{38} \approx 1.1$; the central spread is only slightly greater in the urban group.

Question 12

Which summary statistic is LEAST affected by the presence of an outlier in the data?

Accepted Answer

Median

Question 13

Suppose you want to visually compare the cholesterol distributions of the two groups. Which graphical method would be most effective for comparing both the center and spread of the distributions?

Accepted Answer

Side-by-side boxplots

Question 14

If the range for the rural group is $231 - 95 = 136$ and for the urban group is $330 - 134 = 196$, what does this suggest about the variability in the two groups?

Accepted Answer

The urban group has a much larger range, indicating greater overall variability.

Question 15

Which of the following statements about skewness in the cholesterol distributions is supported by the data?

Accepted Answer

Both distributions are right-skewed, with longer right tails.

Question 16

If you remove the outlier (330 mg/dL) from the urban group, what is the likely effect on the standard deviation and the shape of the distribution?

Accepted Answer

The standard deviation will decrease, and the distribution will appear more symmetric.

Question 17

Which of the following best explains why the urban group has more variability in cholesterol levels than the rural group?

Accepted Answer

Urban individuals have more diverse lifestyles and diets, leading to greater variability.

Question 18

If the median cholesterol level for the rural group is 152 mg/dL and for the urban group is 206 mg/dL, what is the difference in medians, and what does this indicate?

Accepted Answer

$206 - 152 = 54$ mg/dL; the urban group has a much higher typical cholesterol level.

Statistical Analysis of Guatemalan Cholesterol Levels: Distributions, Summary Statistics, and Comparative Measures

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