Question

A study examining the health risks of smoking measured the cholesterol levels of people who had smoked for at least 25 years and people of similar ages who had smoked for no more than 5 years and then stopped. Create appropriate graphical displays for both groups, and write a brief report comparing their cholesterol levels. Here are the data: $$ \begin{array}{llll|lll} {\text { Smokers }} &&&& {\text { Ex-Smokers }} \\ \hline 225 & 211 & 209 & 284 & 250 & 134 & 300 \\ 258 & 216 & 196 & 288 & 249 & 213 & 310 \\ 250 & 200 & 209 & 280 & 175 & 174 & 328 \\ 225 & 256 & 243 & 200 & 160 & 188 & 321 \\ 213 & 246 & 225 & 237 & 213 & 257 & 292 \\ 232 & 267 & 232 & 216 & 200 & 271 & 227 \\ 216 & 243 & 200 & 155 & 238 & 163 & 263 \\ 216 & 271 & 230 & 309 & 192 & 242 & 249 \\ 183 & 280 & 217 & 305 & 242 & 267 & 243 \\ 287 & 217 & 246 & 351 & 217 & 267 & 218 \\ 200 & 280 & 209 & & 217 & 183 & 228 \end{array} $$

Short answer

Box plots reveal significant differences in median cholesterol levels between smokers and ex-smokers, with smokers generally having higher levels.

Step-by-step solution

Organize the Data

First, separate and organize the data given for 'Smokers' and 'Ex-Smokers'. These two sets of data should be listed independently to avoid confusion. Check the list to ensure all data points are included and nothing is missing.

Create Graphical Displays

Choose an appropriate type of graph to represent the data. A box plot is efficient for summarizing the distribution of each group's cholesterol levels and highlighting differences. Another option is to use histograms for a detailed frequency distribution.

Draw Box Plot for Smokers

Construct a box plot for the smokers. Identify the minimum, first quartile (Q1), median, third quartile (Q3), and maximum of the smoker's cholesterol levels. Draw a box from Q1 to Q3 with a line at the median and lines (whiskers) extending to the minimum and maximum.

Draw Box Plot for Ex-Smokers

Repeat the process for ex-smokers. Create a box plot identifying the minimum, Q1, median, Q3, and maximum cholesterol levels for this group. Ensure the plots for both sets are on the same scale for easy comparison.

Interpret Box Plots

Compare the box plots of smokers and ex-smokers. Note the median values—any significant differences indicate the central tendency differences between the groups. Also, compare the spread (range and interquartile range) and any potential outliers that appear in the plots.

Write a Brief Report

Summarize the findings in a brief report. Comment on the differences in median cholesterol levels, the spread of data, and any outliers observed. Highlight any noticeable trends or observations that arise from the data comparison.

Key concepts

Cholesterol Levels

Cholesterol levels are crucial indicators of heart health, representing the amount of cholesterol present in the blood. Cholesterol is a fatty substance found in your blood. It's essential for building cells, but too much of it can lead to heart disease.

• Normal cholesterol levels should be under 200 mg/dL.
• Levels between 200-239 mg/dL are considered borderline high.
• Anything 240 mg/dL or above is high and a cause for concern.

In our study, we deal with two groups: long-term smokers and those who quit smoking early. Analyzing these numbers helps us understand the impact of smoking on cholesterol levels. It shows the risk factors associated with sustained smoking.

Data Interpretation

Data interpretation involves making sense of numerical data sets. In the context of our study, we assess cholesterol levels in two groups: smokers and ex-smokers. Understanding these numbers and their distributions reveal important insights.
Site at the data for both groups, you can see trends or patterns. For instance, if the smoker group tends to have higher cholesterol values on average than the ex-smoker group, this indicates how smoking might impact cholesterol adversely.
Data interpretation also hazards spotting outliers or anomalies, which are numbers that deviate significantly from the rest of the data. These can skew overall interpretations if not considered properly.

Graphical Displays

Graphical displays are visual tools to summarize and analyze data. They make complex data more accessible and easier to interpret. In our exercise, we utilize box plots.
Box plots are highly effective for displaying the distribution of cholesterol levels in each group. They allow us to visualize key statistics such as:

• Minimum and maximum values
• Quartiles (Q1, Q2, Q3)
• Median
• Any outliers

Box plots provide a quick way to discern differences between the cholesterol levels of smokers versus ex-smokers visually. By placing both box plots on the same scale, comparisons become straightforward.

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a data set. They provide a useful overview of data without diving into detailed analysis. Key descriptors include:

• Mean - the average cholesterol level in each group.
• Median - the midpoint value separating the higher half from the lower half of the data.
• Mode - the most frequently occurring cholesterol level.
• Range - the difference between the highest and lowest values.
• Interquartile range (IQR) - the range of the middle 50% of the data.

In the context of the box plot analysis, descriptive statistics enable us to make meaningful comparisons between the smokers and ex-smokers. Recognizing variations in median, spread, and outliers helps in concluding the potential health risks associated with prolonged smoking.