Presenting Data in Graphs
Three slides carry the week's whole treatment of charts. Both of the images they refer to are unrecoverable from the file, so the deck's own illustration of its one worked chart type cannot be shown — and the rule attached to it is the only formula in the week.
The three principles the source states for any graph
The graphs material opens with a general claim and three instructions. The claim is that a well-drawn graph conveys the key patterns and relationships within a data set; the instructions are about labelling, about restraint, and about the relationship between the amount of ink on the page and the effectiveness of the display.
- Label the graph clearly — name any axis involved, and give the graph a title.
- Make the data the feature. Elaboration and pattern fills distract the reader from the meaning of the data.
- Watch the data-to-ink ratio: the more ink you use to represent a data set, the less effective the representation is.
All three are usable as stated, and the third is the one worth internalising, because it gives you a test you can apply to any draft chart: ask what each mark on the page is doing, and delete the marks that are not carrying data. The paired instruction on tables — keep the grid plain — is the same idea applied to a different display, and is covered at Presenting Data in Tables.
The histogram class rule — the only formula in the week
Stated as the source states it, the rule is: number of classes ≈ square root of the number of observations. It is offered explicitly as a rule of thumb, not as a requirement, and it is the only mathematical rule anywhere in the week — no other statistic in the material is given a formula, a symbol or a notation.
Both figures are the source's own and neither is attributed. The 25-to-5 case is a worked example, not a standard; the 20-observation figure is a threshold, and it is hedged in both directions at once — "not so effective" for "less than about 20". It is also, remarkably, the only numeric sample-size guidance anywhere in the four weeks of material this batch covers. The subject states no minimum number of participants for a study and one minimum number of observations for a chart. The wider record of these absences is consolidated at What This Material Does Not Teach.
Histogram, scatter diagram and line graph: what is supplied for each
The week names three chart types and assigns each a purpose. None of the three is defined in the sense a reader needs — that is, in a way that would let someone who had not seen one before produce one. The degrees differ, and it is worth being precise about which is which. A fourth display, the bell-shaped curve, belongs to the week's normal-distribution slides and is treated at The Normal Model and the 68-95-99.7 Rule.
THE THREE CHART TYPES AGAINST WHAT THE SOURCE SUPPLIES
| Display | Purpose the source assigns | Definition | Construction guidance | What you must get elsewhere |
|---|---|---|---|---|
| Histogram | "Representing the overall pattern" | None | The class-count rule; about 20 observations minimum | What a histogram is — what the bars represent, that they show frequencies over classes of a continuous variable, that they sit adjacent, and how it differs from a bar chart |
| Scatter diagram | "Small sample sizes" | Partial: "essentially individual data presented as points" | None | That the points plot one variable against another; axes; what pattern in the points means; correlation and association, which appear nowhere in the week |
| Line graph | "To show data across time"; preserving time order; identifying trends | None | None | How to construct one; what a trend is and how to establish that you have found one; anything at all about smoothing or seasonality |
Two further displays appear in the week and are treated on their own pages: the table typology by number of variables, and the bell-shaped curve used to sketch a normal distribution.
What a reader can and cannot do with this
You can do this from the material
- Apply three general principles to any chart you draw
- Choose a class count for a histogram, from the square-root rule
- Know that a histogram needs roughly 20 observations to be worth drawing
- State the purpose the source assigns to each of the three chart types
- Recognise that heavy decoration weakens a display
You cannot do this from the material
- Build any of the three charts from a definition given here
- Choose between them on any stated criterion
- Match a display to the level at which your variable was measured
- Show variation or spread on a chart — no measure of it exists in the week
- See a single worked example of any chart, because both images are unrecoverable
Using the graph material in a project research report
The source does not prescribe the following. It is a way of getting a defensible chart out of guidance that stops short of construction, and of being honest in your method about where the rest came from. Once the chart exists, the week does supply a procedure for reading it — see Reading a Graphical Display.
A working sequence for a chart you intend to publish
Count your observations first
The count decides whether a histogram is worth drawing at all. Below about 20 the source says histograms are "not so effective" and points, without quantifying it, at the scatter diagram instead.
Set the class count from the rule, then look at the result
Take approximately the square root of the number of observations. The source gives one worked case — 25 observations suggesting approximately 5 classes — and no rounding convention, so record the count you chose and why.
Draw it, then strip it
Remove every mark not carrying data: fills, shadows, gridline clutter, decorative borders. This is the data-to-ink principle applied, and it is the one instruction in the week that survives contact with any charting tool.
Label past what the source asks
The slide asks for axis names and a title. It never mentions units, scale, the number of observations, or the source of the data. Add them anyway — a reader cannot judge a chart without them.
Say where your construction rules came from
If your histogram bars, your fitted line or your time axis follow a convention this material never states — and they will — attribute that convention to the text you actually took it from, not to this week.
Before a chart goes into your report
- The number of observations behind the chart is stated somewhere on or beside it
- The class count, if a histogram, is consistent with the square-root rule of thumb, or the departure is explained
- Every axis is named and every unit is stated
- Nothing on the chart is ink that is not data
- The caption says what the reader should notice, in the same way the tables guidance asks for a brief summary
- Any construction convention not stated in this material is attributed elsewhere
- You have not implied that the material supplies a definition of the chart type you used, because it supplies none
What to carry forward
- Three principles — label it, make the data the feature, keep the ink down — are the transferable content, and the third is the most useful test you can apply to a draft chart.
- The class rule is the week's only formula: classes approximately equal to the square root of the number of observations, illustrated once with 25 observations suggesting about 5 classes.
- About 20 observations is the stated minimum for a histogram, hedged twice, and it is the only numeric sample-size figure anywhere in this material.
- All three chart types are named without being defined, to differing degrees: the histogram not at all, the scatter diagram without its second variable, the line graph with a purpose and nothing else.
- Both chart images in the week are missing from the file, so nothing here shows you what a correctly built display looks like.
Frequently asked questions
How many classes should my histogram have?
The source gives a rule of thumb: use a number of classes approximately equal to the square root of the number of observations. Its single worked example is 25 observations suggesting approximately 5 classes. It states no rounding convention, so record the count you chose and the reasoning behind it.
Is there a minimum sample size for a histogram?
The source says histograms are "not so effective for less than about 20 observations". That is a threshold, hedged twice, and it is the only numeric sample-size guidance in the four weeks of material this batch covers. It governs observations on a chart, not participants in a study.
What is the data-to-ink ratio?
The source names it and states its direction — the more ink you use to represent a data set, the less effective the representation is — without ever saying what is divided by what. Use the principle as a test for stripping decoration from a chart, and cite the published treatment the concept comes from rather than this material.
Does the material tell me when to use a scatter diagram rather than a histogram?
Not directly. It says a scatter diagram suits "small sample sizes" without quantifying small, and separately that histograms need about 20 observations. The implication that one takes over below the other's threshold is never stated, and no decision rule for choosing among displays appears anywhere in the week.
Why is there no example chart on this page?
Because there is none in the source. One slide carries the placeholder text "Images for histogram" with no recoverable image, and the other image slide has no extractable content at all. Inventing a chart and presenting it as the week's would misrepresent what was supplied.
Can I use a bar chart or a pie chart instead?
Nothing in the week names either, so it offers no view. The bar chart, the pie chart, the box plot and the Pareto chart are absent from the material entirely, which means any guidance you follow on them has to come from, and be attributed to, a second source.
References and source attribution
- Veal, A. J. 2005, Business Research Methods: A Managerial Approach, 2nd ed., Longman. — the single entry on the week's reference slide; it accounts for the normal-distribution slide and none of the graphs material.
- The prescribed text, Chapter 16, pp. 353–374 — the week's only set reading, on statistical software. No author, year, title or publisher is given for it anywhere in the week's slides.
- The supplied teaching source: the week 11 slide deck on analysing data and the presentation of quantitative data, whose three graph slides are reproduced in full on this page. No study notes for this week were supplied, and neither chart image is recoverable from the file.
Suggested questions for Ask KEVOS
- How many classes should I use for a histogram of my response data?
- Review my chart against the three graph principles in this material.
- What does this teaching material fail to tell me about building a scatter diagram?
- Help me write a caption that states units, sample size and data source.
- Which display types are missing from this week, and where should I read about them?