Bar graph worksheets.
Make category counts visible.

More ways to practice

From tally to bar: one verifiable chain

A bar chart compares counts in named categories. Each category gets one bar, bars have equal width, and gaps separate the bars because the categories are distinct labels rather than points on a continuous scale. The vertical axis starts at zero and uses one consistent unit per grid step. Before drawing, write the counts in a table and add them; that total is your independent check on the finished graph.

A histogram is different. It groups a continuous measurement into bins, and the bars touch because neighbouring bins share boundaries. State the bin edges explicitly, for example 0 to under 10, 10 to under 20, and so on, and decide in advance which bin receives a value exactly on an edge. The sum of the bin frequencies must equal the number of measurements. A line graph is different again: it joins values across an ordered sequence such as time, so it suits trends, not category comparison.

1. List each category once and record its count beside it.
2. Add the counts and write the total at the top of the table.
3. Choose a scale where the largest count fits inside the plotting area with whole grid steps.
4. Draw equal-width bars from zero, leaving a visible gap between categories.
5. Label the axis with the category names and the unit of the counts.
6. Re-add the bar heights from the finished graph and compare with your table total.

A tie-aware comparison routine

Comparing bars is easy when one value is clearly largest. Ties need a deliberate rule so answers stay consistent. First find the largest count and list every category that reaches it. Then find the smallest count the same way. Report the difference between largest and smallest, and state how many categories sit at each extreme. If two categories tie for largest, say so rather than picking one.

A second check catches scale errors. Pick one bar, read its height from the axis, and confirm it matches the table count. Then confirm the gap between two adjacent bars equals the difference of their counts in grid steps. If the scale is two per step, a difference of six counts must appear as three steps. This check exposes uneven spacing or a mislabelled axis faster than re-reading the whole graph.

1. Identify the maximum count and name every category that reaches it.
2. Identify the minimum count and name every category that reaches it.
3. Subtract minimum from maximum to get the range.
4. Count how many categories tie at the maximum and at the minimum.
5. Verify one bar height and one adjacent gap against the stated scale.

Separating student and teacher versions

A student version should contain the category names and counts but no drawn bars, so the learner builds the scale and the bars. A teacher version should contain the same data with bars drawn and the total stated, so comparison is quick. Keep the data identical between the two; only the drawn work differs. If the student sheet asks for a total, the teacher sheet must show the same total, otherwise the pair cannot be checked against each other.

When the data includes a tie, both versions should carry the same tie rule in a short note, such as listing all categories at the maximum. That prevents a correct student answer being marked wrong because the teacher sheet silently chose one category.

1. Copy the category list and counts exactly into both versions.
2. Leave the plotting area empty on the student version.
3. Draw bars and state the total on the teacher version.
4. Add the same tie rule note to both versions.
5. Check that both totals match the sum of the counts.

Try this example

Four book genres are counted on one shelf: mystery 7, history 4, poetry 4, science 9. Build a bar chart with a scale of two counts per grid step and compare the categories.

Common mistakes

• Bars are drawn with unequal widths or no gaps between categories. Use one width for every bar and leave a consistent gap, since categories are separate labels.
• The vertical axis starts above zero, exaggerating small differences. Start the count axis at zero and keep one unit per grid step throughout.
• A histogram bin edge is ambiguous, so one measurement could fit two bins. Write bin edges as lower bound to under upper bound and state which bin takes an exact edge value.

Check your work

• Every category appears once with a count that matches the source table.
• Bar widths are equal and gaps separate all categories.
• The count axis starts at zero with one consistent unit per step.
• Bar heights read from the axis match the recorded counts.
• The stated total equals the sum of the counts and of the bar heights.
• Ties at the maximum or minimum are named rather than broken arbitrarily.
• Any histogram states bin edges and the rule for values on an edge.

Questions before you start