Histograms and distribution diagnosis

Learning objectives

• Build a well-scaled histogram in a free spreadsheet.
• Read centre, spread, skew, multimodality, gaps and heaping.
• Link visual patterns back to garment-process sources.

Core idea

Histograms show the distribution of a single continuous variable. Shape often points to stratification, measurement rounding or process changes rather than to random variation alone.

Spreadsheet lab

• Choose bin width consciously (e.g. Freedman-Diaconis: 2·IQR/n^(1/3)).
• Bins column and =FREQUENCY(data, bins) entered as array.
• Compare histogram against a boxplot and a time-order plot.
• Overlay specification limits only as reference lines, not as class boundaries.
• Stratify by line/size/shift if the histogram is bimodal or unusually wide.

Garment-factory example

Chest width on style S123 looks bimodal. Stratifying by cutting table reveals two distinct means: Table 1 sits 0.4 cm higher than Table 2. A single overall histogram would have hidden a real cutting bias.

Method

1. Pick bin width from data, not defaults.
2. Compare histogram with time and box plots.
3. Investigate multimodality by stratification before modelling.

Common mistakes

• Using default bins that hide bimodality.
• Concluding stability from a bell-shape.
• Removing bars visually rather than investigating cause.