Compare shapes before choosing summaries

Try

Two synthetic checkout services each have a mean observed wait of 6 minutes. Does that make their performance equivalent? The workbench’s starting group A is 4,5,5,6,6,7,7,8; group B is 2,3,3,4,4,5,7,20. Both sums are 48 across eight observations, but their shapes differ. A customer interested in a typical wait and a customer trying to avoid a long delay may reasonably ask different questions.

Comparison should include context, shape, center, spread and unusual values. Choosing a summary before looking at the distribution can conceal the very feature that matters for the decision.

Predict

Predict the median of each group and which has the longer right tail. Decide whether moving B’s 20 to 30 would change the median, the mean, or both. Then predict how the histogram impression may change with bin width even though the underlying wait records remain identical.

Experiment

Build and question data displays

Predict which group has the larger median and which has greater spread. Choose bins and record your expected counts before showing the displays. Automatic drawing helps inspect a representation; your practice response must explain and reproduce its choices.

Synthetic checkout times in minutes. The initial groups are fictional, not evidence about a real checkout service. Editing a field replaces the source label so edited values are not presented as unaltered measurements.

Group A observations4,5,5,6,6,7,7,8Group B observations2,3,3,4,4,5,7,20

Use 2–40 decimal values per group between −100 and 100. Commas, spaces and new lines separate observations. Empty or invalid input is never silently replaced with zero.

Common histogram bin width0.512510Reset synthetic dataLoad attributed Iris subsetTry constant dataShow data calculations

Dataset provenance and limits

The Iris preset copies sepal lengths without alteration from the locally supplied bezdekIris variant: Fisher (1936), UCI Machine Learning Repository, DOI 10.24432/C56C76, CC BY 4.0. A uses row IDs iris-001–020 and B iris-051–070. These are the first twenty records of each species in file order, not fresh random samples or matched specimens. They do not establish a population model or a causal species effect. Inspect the source CSV, read attribution and source details, and read the license. Only the two sepal-length subsets are displayed here; synthetic alterations described for other site labs are not applied.

Change one value or bin width, predict the effect, and explain it from the resulting display. Record the data, units, bins, quartile convention and interpretation in your written task. This temporary workbench does not save an artifact or award mastery.

Use the synthetic checkout preset and reveal the two groups on shared axes. Compare dotplots first, then histograms at two supported widths and the min-max boxplots. Record the raw values and settings so another learner can reproduce your report. Change only the largest B value to 30, predict, then reveal again; reset afterward.

Starting summary	A	B
Mean	6 minutes	6 minutes
Median	6 minutes	4 minutes
Q1,Q3	5,7	3,6
IQR	2 minutes	3 minutes
Observed waits above 10 minutes	0 of 8	1 of 8

These are min-max boxplot inputs; a modified boxplot would separately flag B’s 20 because its upper fence is 6+1.5·3=10.5. The live min-max whisker still reaches 20. Either way the dotplot preserves that individual observation.

Understand

A is roughly symmetric and compact. B is right-skewed: most waits are shorter, but the long delay pulls its mean upward. Median and IQR describe the middle of B more robustly than mean and SD, while the upper-tail observation remains important for a deadline-sensitive customer. Robust does not mean “ignore all extremes”; it means a summary is less sensitive to their magnitude.

Replacing 20 with 30 adds 10 to the total, so B’s mean becomes 58/8=7.25. Its median and quartiles remain unchanged because the ordered middle positions do not change. This calculation explains why different summaries react differently. It does not prove that median is always preferable: total expected waiting cost may depend on the mean, while a long-delay constraint depends on the tail.

The empirical fraction above 10 minutes is 1/8 for B, not an established future probability. Eight invented observations cannot guarantee A never produces long waits. In real data, sampling time, customer mix, workload, measurement conventions and missing records determine what population a comparison describes. Morning records from one service and peak-evening records from another do not isolate the effect of service design.

For a real-data follow-up, select the Iris preset. It uses sepal lengths in centimeters from rows 1–20 of setosa and rows 51–70 of versicolor in the locally archived UCI dataset. The attribution identifies Fisher’s Iris dataset, the bezdekIris variant and CC BY 4.0 licensing; the local CSV retains measurements and row IDs. This widget subset uses those unaltered sepal values, not the separate AI cleaning exercise’s artificial duplicate/unit defects. Compare the selected specimens descriptively; these convenience rows are not a new random population sample, and species differences do not establish a causal intervention.

Apply

Write a comparison using common-scale graphs and at least one justified center/spread pair. Address an unusual value, describe the units and sample sizes, and say which decision your summaries support. Report valid extreme observations rather than deleting them to make groups look similar.

If all measurements are converted from minutes to seconds, mean, median, IQR and SD multiply by 60; variance multiplies by 3600. A unit change does not change standardized shape. Adding a fixed delay instead shifts center but leaves spread unchanged. Use these transformations as consistency checks.

Continue

Next investigate when a normal model is a reasonable approximation. Symmetry in a small display is evidence to inspect, not a certificate that a population follows a particular distribution.