Construct three views of one dataset

Try

Eight synthetic waiting times are 1,1,2,3,3,5,6,15 minutes. A mean alone cannot reveal the repeated short waits or the unusually long one. Constructing a display forces decisions: what counts as one observation, how boundaries are handled, and which details a summary hides.

A dotplot preserves every observed value. A histogram groups values into intervals. A boxplot summarizes ordered positions. These are complementary views, not competing decorations. We will make all three and retain the raw observations so every mark can be checked.

Predict

Predict how many waits lie in each interval [0,4), [4,8), [8,12), [12,16). The left square bracket includes its endpoint; the right parenthesis excludes it. Predict whether a wider bin will change the observations or only their grouping. Then consider whether the long wait must be a recording error merely because it is far from the others.

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.

Enter the eight worked values in A; leave B as a comparison or enter the same values there. Predict the dot stacks and boxplot before revealing the output. The live histogram offers selected widths rather than every possible width; choose a supported width, record its actual displayed edges, and independently draw the width-4 histogram requested above. Changing a bin setting is not changing the data.

The live boxplot uses minimum and maximum whiskers. It uses medians of the lower and upper halves for quartiles, excluding the overall median when the sample size is odd. Some practice tasks request a different, modified-boxplot convention: whiskers reach the most extreme observed values within 1.5 IQR fences, and values outside are marked individually. Construct that version on paper or with a precise coordinate description; do not mislabel the workbench’s min-max output as modified.

Worked representation	Required marks	Independent check
Dotplot	Heights 2,1,2,1,1,1 at 1,2,3,5,6,15	Eight dots total
Width-4 histogram	Counts 5,2,0,1	Counts sum to eight
Box summary	Minimum 1,Q1=1.5,median 3,Q3=5.5,maximum 15	Quartiles from two four-value halves

Understand

For the worked boxplot, IQR=Q3−Q1=4 minutes. The usual 1.5 IQR fences are 1.5−6=−4.5 and 5.5+6=11.5. A modified boxplot therefore has whiskers at 1 and 6, with 15 displayed separately. Fences are thresholds, not necessarily observed values and not automatic whisker endpoints. A min-max boxplot instead extends to 15. Both can be valid if their conventions are declared.

A histogram’s count belongs to an interval, not its midpoint as an observed value. Adjacent intervals must not overlap or omit observations; the live display closes its final upper endpoint so a maximum lying there is retained. Always check that counts sum to sample size. For equal-width bins, count heights provide an honest comparison. For unequal widths, use frequency density: divide count by width so rectangle area represents count. Otherwise a wide interval can look prominent simply because it covers more measurement space.

Axes need names and units. The horizontal axis here is minutes; the vertical dot/histogram axis is count. Probability is a different quantity and would require dividing counts by the total. When comparing groups, use the same numerical horizontal scale and compatible bin edges. If group sizes differ, raw counts mix sample size with distribution shape; relative frequencies may answer the comparison better.

The workbench supports bounded editable data and supplies all count tables. It also includes a licensed Iris example, separate from these invented waits. Its source and selected row ranges are stated in the widget. Do not treat that convenience subset as a random survey or relabel its centimeter measurements as minutes.

Apply

For a fresh dataset, produce three labeled artifacts and write the data, bins, endpoint conventions, quartile rule and whisker rule beside them. Exact coordinate descriptions are acceptable when a graph cannot be attached. Explain one pattern and one limitation of each view.

Investigate the 15-minute wait by checking source, units and context. A valid long delay belongs in the data. An outlier flag is a prompt to investigate, not permission to delete inconvenient evidence or a proof of a measurement mistake.

Continue

Next compare two distributions using shared displays. Their means can agree while their typical outcomes and upper-tail risks differ substantially. Keep the raw values and conventions available for that comparison.