Reading the Bars as Counts
In Constructing a Bar Chart by Hand, you learned how category counts determine bar heights. Now use the same relationship in reverse: read each bar’s height to find its count, then use those counts to identify the most common category and compare categories.
A bar chart displays categories along the horizontal axis and counts along the vertical axis. To read a count, first find the category label, then trace its bar up to its top and read that height against the vertical scale. The count tells how many individuals or items in the displayed group belong to that category.
Read the axis labels and scale before interpreting any bar. A bar that is twice as tall as another represents twice the count only when both heights are read from the same zero-based scale. Check the tick-mark intervals: if the labeled marks increase by 5, for example, each step between successive marks represents 5 counts. If a bar top falls between labeled marks, use smaller grid divisions if provided; otherwise, describe the count as an estimate.
The horizontal positions identify categories, not measured numerical values. The gap between two bars does not represent a count, and category order alone does not tell you which count is greater. Compare the bar heights, not the positions or widths.
The Mode and Count Comparisons
For a categorical variable, the mode is the category with the greatest count. To find it on a bar chart, locate the tallest bar and read its category label. If two or more bars share the greatest height, the data have more than one modal category. A category with a small count is still a category; it is not omitted just because its bar is short.
A direct comparison often asks how many more individuals belong to one category than another. Subtract the smaller count from the larger count, then state the difference in context. For example, if a chart shows 21 people in one category and 16 in another, the difference is \(21-16=5\) people. Do not describe the difference as a percentage or proportion unless the question asks for one; those are different summaries.
- Read the title and axis labels to identify the group, variable, and period being shown.
- Locate the category on the horizontal axis and follow its bar to the vertical scale.
- Read the bar’s height using the labeled tick marks and any smaller grid divisions.
- Find the tallest bar or tied tallest bars to identify the mode.
- For a count difference, subtract the two counts and name the categories and units in your comparison.
Worked Example: Most Borrowed Library Items
Worked Example: Most Borrowed Library Items
A fictional library displays a bar chart of 58 items borrowed during a weekend. The horizontal axis lists Mystery, Science, Biography, and Poetry. The vertical axis is labeled “Number of items borrowed,” with marks every 5 from 0 to 25 and smaller grid divisions for individual counts. The bar tops are at 16 for Mystery, 11 for Science, 23 for Biography, and 8 for Poetry. Read the counts, identify the mode, and compare Mystery with Poetry.
Read each category at its bar top: Mystery has 16 items, Science has 11, Biography has 23, and Poetry has 8. Check that the four counts account for the stated total:
Biography has the tallest bar, so Biography is the mode: it is the most common item category in this weekend’s display. Its count is 23 borrowed items.
For the comparison, subtract the Poetry count from the Mystery count:
Eight more items were borrowed in the Mystery category than in the Poetry category during the weekend shown. This is a difference in counts, measured in items; it does not say that Mystery was eight times as common as Poetry.
Worked Example: A Tie for the Mode
Worked Example: A Tie for the Mode
A fictional student poll displays ratings of a quiet study room. The categories on the horizontal axis are Poor, Fair, Good, and Excellent. The vertical axis runs from 0 to 20, with labeled marks every 5 and smaller grid divisions for individual responses. The bar tops are at 12, 18, 18, and 7, respectively. Find the mode or modes and compare Good with Poor.
The counts are Poor: 12, Fair: 18, Good: 18, and Excellent: 7. The total number of responses represented is:
Fair and Good are tied for the greatest count, with 18 responses each. Therefore, there are two modal categories: Fair and Good. Saying only “Good is the mode” would leave out the tie.
Good has 18 responses and Poor has 12. Subtracting gives:
Six more students selected Good than Poor in this poll. Because these are ordered rating categories, their order on the horizontal axis has meaning, as discussed in Ordinal Categories and Rating Scales. However, the difference between the Good and Poor counts is still read from the vertical scale, not from the distance between the category labels.
Worked Example: Comparing Several Activity Counts
Worked Example: Comparing Several Activity Counts
A fictional recreation center makes a bar chart of 70 visits recorded on one afternoon, grouped by the activity visitors chose. The categories are Basketball, Swimming, Climbing, and Dance. The vertical axis runs from 0 to 30 in increments of 5, with smaller grid divisions for individual visits. The bar tops are at 25, 20, 15, and 10, respectively. Identify the mode and make two comparisons.
Read the count for each activity from its bar: Basketball has 25 visits, Swimming has 20, Climbing has 15, and Dance has 10. The counts check against the chart’s total:
Basketball has the greatest count, 25 visits, so it is the mode. To compare Basketball with Swimming:
The chart shows 5 more Basketball visits than Swimming visits. To compare Basketball with Dance:
The chart shows 15 more Basketball visits than Dance visits. The two comparisons answer different questions, so include both category names and the difference when writing each statement. Notice also that the scale’s increments are 5: a bar reaching the mark at 25 represents 25 visits, not 5 visits merely because it is five increments above zero.
Reading Carefully When a Bar Falls Between Marks
Some bar tops line up with labeled tick marks; others fall between them. Suppose the vertical axis has labeled marks at 0, 10, and 20, with no smaller grid divisions. A bar that appears about halfway between 10 and 20 has an estimated count of about 15. If it is only a little above 10, it may be reasonable to estimate a value closer to 10 than to 20. The graph’s scale and drawing limit how precisely you can read.
Do not report more precision than the graph provides. If the bar top is difficult to distinguish, say “about” or “approximately,” rather than claiming an exact count. When the chart includes finer grid divisions, use them to read more precisely. Also make sure you are aligning your reading with the top of the bar, not its center or the top of the chart.
A quick total can help you check your readings. If the chart represents all responses in a group, the category counts should add to the total number represented. A mismatch may signal a reading or addition error, though a chart may not provide a total or may display only selected categories. Do not assume the total is known unless the chart or context supports it.
Common Mistakes and What a Strong Answer Includes
- Reading the bar’s position instead of its height. The category label identifies which bar to read; its height gives the count. The horizontal distance between categories does not encode a quantity.
- Ignoring the scale interval. If each labeled step is 5, the bar height increases by 5 counts per step, not by 1. Start at the zero line and count the tick intervals carefully.
- Comparing widths or gaps. Bar widths and gaps are design features, not counts. Compare the tops of the bars on the vertical axis.
- Calling only one category the mode when there is a tie. Name every category sharing the greatest count. If all categories have the same count, they are all tied for greatest frequency.
- Reporting an estimate as exact. If the chart does not allow an exact reading, use “about” or “approximately” and do not imply more precision than the scale supports.
- Giving a difference without context. A full comparison says which categories were compared, which had the greater count, and by how many individuals or items.
A strong answer might say: “Biography is the mode, with 23 items borrowed. The chart shows 8 more Mystery items than Poetry items.” This identifies the category with the greatest count and gives the comparison in context. For a tie, a full-credit response names both categories and their shared count, such as: “Fair and Good are tied for the mode, with 18 responses each.”
Check Your Understanding
Use each chart description to answer the questions. Unless stated otherwise, assume the bar tops can be read to the nearest individual.
- A chart shows counts of 14 for Apples, 9 for Pears, 17 for Plums, and 10 for Peaches. What is the mode, and what is its count?
- A chart shows 13 responses in one category and 8 in another. How many more responses are in the first category? Write a sentence that names both categories using your own labels.
- Three categories have counts of 7, 12, and 12. How many modal categories are there, and which counts identify them?
- The vertical axis has labeled marks at 0, 5, 10, 15, and 20. A bar reaches the mark at 15. What count does that bar represent?
- A bar top appears between 10 and 20 on an axis with no smaller grid divisions. Why might “about 15” be more appropriate than reporting an exact count?