Statistical Summary Computation Median Range

statistical-summary-computation-median-range

Summary

Compute median and range (min/max) statistics across grouped categorical dimensions (e.g., plot types and plotting backends) from execution-time or performance measurements. This skill transforms raw timing observations into ranked summary tables and comparative visualizations to identify fastest and slowest performers within each category.

When to use

When you have a table of execution times or performance metrics indexed by two or more categorical dimensions (e.g., plot_type × backend, or sample × condition), and you need to compare central tendency and spread across groups to rank or benchmark alternatives. Specifically useful when the source data is a multi-row observation table (e.g., 19 gallery scripts with timing measurements) that must be aggregated by category to isolate the effect of each dimension.

When NOT to use

• Input is already a pre-aggregated summary statistic (e.g., mean or median reported in a published table); re-computing from such compressed data introduces bias and loss of information.
• The timing observations have extreme outliers driven by system state (e.g., cache misses, GC pauses) that warrant robust trimming or removal before aggregation; median alone may still mask bimodal distributions.
• The categorical dimensions are continuous or have natural orderings that should be preserved in the analysis (e.g., parameter sweep); use regression or ANOVA-based approaches instead.

Inputs

• Raw timing observation table (e.g., pandas DataFrame or CSV with columns: plot_type, backend, execution_time_ms)
• Categorical grouping dimensions (e.g., plot_type: [chromatogram, mobilogram, peakmap, peakmap-marginals, spectrum, subplots]; backend: [matplotlib, bokeh, plotly])

Outputs

• Structured summary table (pandas DataFrame or CSV) with columns: plot_type, backend, median_time, min_time, max_time, rank_within_category
• Comparative visualization (bar chart or heatmap) showing median execution times across backends per plot type
• Ranked list of backends by median performance within each plot category

How to apply

Load the raw timing observations into a pandas DataFrame, grouping by the categorical axes (e.g., plot_type and backend). For each group, compute the median execution time as the central performance estimate, and the min/max values to characterize the range of variability. Rank backends within each plot type by median time to establish a performance hierarchy. Organize results into a structured summary table with columns: category_1, category_2, median_time, min_time, max_time, rank_within_category. Finally, produce a comparative visualization (bar chart or heatmap) to expose patterns across groups. The median is robust to outliers and single slow runs; the min/max pair shows the spread without assuming normality.

Related tools

• pandas (Group timing observations by plot_type and backend; compute median, min, and max for each group; construct and export summary DataFrame)
• matplotlib (Generate comparative bar chart or heatmap visualization of median execution times across backends per plot type)
• Python (Execute the statistical aggregation and visualization pipeline using pandas groupby, agg, and matplotlib plotting routines)
• pyOpenMS-Viz (Provides the gallery scripts and execution-time measurements that serve as the raw input data for this aggregation skill) — https://github.com/OpenMS/pyopenms_viz

Examples

import pandas as pd
df = pd.read_csv('gallery_execution_times.csv')
summary = df.groupby(['plot_type', 'backend'])['execution_time_ms'].agg(['median', 'min', 'max']).reset_index()
summary['rank'] = summary.groupby('plot_type')['median'].rank()
print(summary)
summary.to_csv('execution_summary.csv', index=False)

Evaluation signals

• Summary table rows equal the number of (plot_type, backend) pairs; all numeric columns (median_time, min_time, max_time) are positive and min_time ≤ median_time ≤ max_time for every row.
• Rank_within_category is an integer in [1, num_backends], with no ties unless median times are identical; ranking is consistent within each plot_type group.
• Visualization (bar chart or heatmap) visually renders the summary table without distortion, with axis labels matching the original categorical values and color/height encoding median times.
• The summary table can be reconstructed by grouping the original raw timing table on (plot_type, backend) and applying pandas .agg({execution_time_ms: ['median', 'min', 'max']}).
• No rows are duplicated in the summary table, and the total observation count across all groups equals the input table row count.

Limitations

• Median and range ignore the frequency and distribution shape of observations; if sample sizes per group are very small (n < 3), the median may be unstable and should be reported with confidence intervals.
• The min and max values are vulnerable to single-run anomalies (e.g., system interference); consider trimming extreme 5% of observations or reporting quantiles (e.g., 0.25, 0.5, 0.75) for more robust spread estimates.
• Ranking backends by median time within a plot type does not account for statistical significance or interaction effects; overlapping confidence intervals between backends may indicate no practically meaningful difference.
• The skill assumes the raw timing data are drawn from the same execution environment and hardware; cross-platform or cross-machine comparisons require normalization or stratified analysis.

Evidence

• [other] Extract the 19 gallery script execution times from the computation-times table in the methods section, categorizing each by plot type and backend.: "Extract the 19 gallery script execution times from the computation-times table in the methods section, categorizing each by plot type (chromatogram, mobilogram, peakmap, peakmap-marginals, spectrum,"
• [other] Compute median execution time and range for each group, then rank backends and tabulate results.: "Compute median execution time for each plot-type and backend combination. Compute min and max execution times (range) for each plot-type and backend combination. Rank backends by median execution"
• [other] Produce a comparative visualization showing median times across backends per plot type.: "Produce a comparative visualization (bar chart or heatmap) showing median times across backends per plot type."
• [other] Generate a structured summary table documenting the aggregated statistics.: "Generate a structured summary table with columns: plot_type, backend, median_time, min_time, max_time, rank_within_category."
• [readme] pyOpenMS-Viz integrates with pandas for data manipulation and multiple plotting backends.: "It integrates seamlessly with various plotting library backends (matpotlib, bokeh and plotly) and leverages the power of Pandas for data manipulation and representation."