Histogram worksheets.
Count every boundary once.

Sort observations into nonoverlapping intervals, then build four frequency histograms. Repeated values exactly on a boundary make the bin rule matter.

Use the student pack for an attempt, then compare the separate reference or worked answer. Every case is original. All PDF and editable SVG resources are free without signup; each collection pack repeats its individual sheets in the same order.

The examples and datasets are made for these worksheets. They are not measured classroom results, published textbook questions or evidence about real people. Axis values and the supplied data determine the answers; paper measurements do not replace those numbers.

HG01: Equal five-unit bins

The table gives one worked case so you can check the method. The separate answer files contain the completed plots and results for every case. Keep all bin intervals, including an interval whose frequency is zero.

1. Applying the Boundary Rule When sorting data into bins, apply the lower-inclusive upper-exclusive rule strictly. A value exactly matching an internal boundary belongs to the next bin, not the current one. For instance, in HG01, the value five falls into the second bin because the first bin covers zero to five, excluding five. This prevents double counting and ensures every observation is placed correctly. The final upper edge must exceed all observations to capture the maximum value. This specific rule guarantees consistent frequency counts across all four histogram cases provided in the resource pack.
2. Verifying Frequency Counts Calculate frequencies by counting observations within each defined interval. Since these exercises use equal bin widths, the y axis represents frequency count rather than density. Ensure no observations are omitted or counted twice. For HG04, repeated boundary values like four and eight must be assigned to the subsequent bin. Verify that the sum of all bin frequencies equals the total number of data points. This check confirms that the specified graph scale aligns with the raw dataset without requiring physical measurement tools or manual ruler checks.
3. Draw adjacent bins, including empty ones Keep the numerical bin edges in their printed positions and draw each frequency above its own interval. The bins are equal in width, so these exercises use frequency counts as bar heights. Adjacent bars touch at a shared boundary. HG02 contains an empty [6,8) bin: leave its span visible with height zero instead of closing the gap by moving the next bar left. Add the frequencies and compare the sum with the raw observation count before using the completed answer as a visual check.

Choose the Letter or A4 file that matches your paper. Actual size / 100% preserves the designed layout; a different uniform print scale changes physical lengths but does not change the listed numbers or the arithmetic. Keep the whole chart and all labels inside the printable area. A ruler can help draw straight segments, but calculate from the stated numerical scale.

These files have digital geometry, arithmetic and page-boundary checks. Physical printer and classroom trials have not been completed. The resources are practice material, with no claim of curriculum certification or precision-instrument accuracy. The original files use CC BY 4.0: credit Zumola, link the license and indicate changes.

Further reading: OpenStax: histogram bins and frequency. The data tables, illustrations and exercise cases here are original Zumola work.