Overview
This lecture covers how to use statistical software (StatKey and StatCato) to analyze normal quantitative data, focusing on calculating and interpreting mean and standard deviation, and visualizing data distributions.
Accessing and Preparing Data
- Use the health data Excel file, which includes ages, heights, and wrist measurements for 40 women and 40 men.
- Copy the desired data column (e.g., women's wrist circumference in inches) from Excel for analysis.
- Ensure to select only the relevant quantitative data, avoiding identifiers unless required.
- Paste the data into StatKey or StatCato, making sure the header row is correctly identified.
Using StatKey for Analysis
- Go to StatKey (lock5stat.com) and select "One Quantitative Variable" under Descriptive Statistics.
- Upload or paste your data, uncheck the identifier box if not present.
- StatKey immediately calculates key statistics: sample size (n = 40), mean (5.067), and standard deviation (0.331).
- Visualize the distribution using dot plots and histograms; adjust the number of buckets (bars) as needed for clarity.
- A normal (bell-shaped) histogram justifies using the mean and standard deviation as accurate summary measures.
Using StatCato for Analysis
- Paste your data into StatCato, ensuring the correct column is selected and header row is set.
- Create histograms and dot plots via the Graph menu; adjust number of bins for optimal visualization.
- Find statistics under Statistics > Basic Statistics > Descriptive Statistics.
- Record mean, standard deviation, minimum, maximum, and sample size for a complete summary.
Interpreting Results and Theory Connections
- For normal data, use the mean as an accurate average and the standard deviation as the measure of spread.
- If mean and median are close, it's likely the data distribution is symmetric (normal).
- Typical values fall within one standard deviation from the mean (mean ± standard deviation), roughly covering 68% of the data.
- Sorting the data from smallest to largest can help visually identify typical values.
Key Terms & Definitions
- Mean — Average of the data set.
- Standard Deviation — Measure of data spread around the mean.
- Histogram — Bar graph showing frequency distribution of data.
- Dot Plot — Graph showing each data point as a dot.
- Normal Distribution — Symmetric, bell-shaped data pattern.
- Sample Size (n) — Number of observations in the data set.
- Identifier — Label attached to a data point, not always needed.
Action Items / Next Steps
- Practice uploading and analyzing a quantitative data set using StatKey and StatCato.
- Review the shapes of histograms and dot plots for normality.
- Compute and interpret the mean and standard deviation for various data sets.