Graphical Presentation of Data

Graphical Presentation of Data

• Data visualization using charts and graphs effectively communicates insights and trends in data.
• Categorical variables (such as gender, smoking status, or age group) are best displayed using bar charts and pie charts.
• Quantitative variables (such as height, weight, or blood pressure) are suitable for histograms and box plots.

Displaying the Data

• Categorical variables' summaries involve percentages within each category.
• Nominal categories are presented in simple bar charts or pie charts.
• Ordinal categories are shown in bar charts ordered by the categories.
• Quantitative data summaries include measures of central tendency (mean, median) and spread (range, quartiles, standard deviation).

Graphical Summaries of Categorical Variables

• Tables summarizing frequency (n) and percentages (%) for different categories of variables like age and smoking habits are provided.
• Examples include age ranges (e.g., 40-49 years, 50-59 years) and smoking status (never smoked, ex-smoker, smoker).

Bar Charts

• Bar charts display frequencies or percentages of observations in each category.
• Frequency and percentage bar charts visually represent data for age groups.

Pie Charts

• Pie charts are used to represent percentages of different categories in a circle.
• Age group data is illustrated in a pie chart to show the proportion of each age group.

Graphical Summary of Numerical Data

• Summarizing birth weights of 65 babies is illustrated.
• Numerical data requires numerical summaries, which involves calculations of mean, median, and standard deviation.
• Birth weights are represented through histograms and boxplots to display their distribution.

Frequency Distribution

• Frequency distributions show how many observations fall into specific ranges.
• For discrete variables, frequencies are associated with individual values.
• Continuous numeric variables require determining grouping and interval sizes.
• All intervals in the frequency distribution should be mutually exclusive and exhaustive (covering all values).

Histograms

• Histograms graphically show the frequency distribution of continuous data.
• Birth weight data is an example of continuous numerical data visually represented in a histogram.
• The x-axis represents birth weight categories (ranges of values).
• The y-axis shows the frequency (count) or percentage of observations in each interval.

Box and Whiskers Plots (Boxplots)

• Boxplots represent important distribution features like median, quartiles, and outliers.
• Data summaries using boxplots show minimum, first quartile, median, third quartile, and maximum values.
• They are used to visually display central tendency and spread of the data (and potential outliers).

Summarize and Display Two Variables

• Analyzing associations between two variables is a common statistical task.
• Categorical-categorical: data is summarized using cross-tabulation (contingency table).
• Continuous-continuous: data is often visualized using scatter plots to view relationships.
• Categorical-continuous: data comparisons involve box plots or scatter plots.

Continuous-Continuous Data

• Scatter plot is a common visualization for continuous-continuous correlation analysis .
• Relationship between weight and waist circumference is examined through a scatter plot.

Categorical-Continuous Data

• Exploring relationships between categorical and continuous variables using box plots.
• Data visualization of weight against gender.

Shapes of Distributions

• Key shapes:
  • Symmetrical (bell-shaped): -Mean ≈ median ≈ mode
  • Positively skewed: -mean > median > mode
  • Negatively skewed: -mean < median < mode
  • Bimodal: -multiple peaks
  • Uniform: -flat distribution

The Normal Distribution

• A theoretical probability distribution important in statistics.
• Perfectly symmetric around the mean, median, and mode(central tendency).
• Perfectly bell-shaped distribution.
• Determined by its mean and standard deviation (SD).
• Informs how values will be distributed around a mean.

Distribution of Variables in Different Populations

• Data examples include height, birth weight, and hemoglobin of different populations.
• Shows variability in measured quantities across groups.

Other Distributions

• Show patterns of non-normal distributions.
• Often skewed (not symmetrical)
• Mean and median values may differ significantly due to skewness.

Properties of the Normal Distribution

• Bell-shaped, symmetric curve.
• Mean, median, and mode coincide.
• Total area under the curve is 1 (or 100%).
• Shape defined by mean and standard deviation (SD) that defines its spread.
• Sampling distributions of the mean are also normally distributed.

Changing the Mean/SD

• Changing the mean shifts the normal distribution curve horizontally (left or right).
• Changing the standard deviation changes the width and spread of the curve.

Limits according to SDs

• Useful for determining the percentage of data within certain intervals around the mean. (e.g., 68% of the data fall within one standard deviation of the mean)

Explore the essential techniques for data visualization through this quiz focusing on charts and graphs. Learn how to effectively display categorical and quantitative variables and understand the concepts of graphical summaries and data summarization. Test your knowledge of the best practices in presenting data insights.