Step 11: Describing and Visualising Data
MatchesDescriptive statistics in a results chapter · see also the Statistics guide, steps 3 and 4
In 30 seconds
- Before any test, clean the data: check for impossible values, duplicates and missing answers, and record every change.
- Describe the centre (mean, median, mode) and the spread (standard deviation, range, interquartile range) of each variable.
- Use the median and IQR for skewed data or data with outliers; the mean and SD for roughly symmetric data.
- Choose the chart from the variable type: bar charts for categories, histograms and box plots for one numeric variable, scatter plots for two.
- Every table and chart needs a number, a clear title, labelled axes with units, and the sample size.
Video lesson coming soonA short animated lesson for this step will appear here.
Clean before you analyse
Raw survey data always contain problems. Someone reports working 140 hours a week; someone else answers every Likert item with “3” in 40 seconds; three people submit twice. Cleaning means finding and handling these problems using rules you decide before looking at the results, and reporting them.
| Problem | Typical rule |
|---|---|
| Impossible values | Hours above 80 a week set to missing |
| Duplicates | Keep the first complete response |
| Speeders | Exclude responses completed in under a third of the median time |
| Missing items | Report how many; do not silently fill them in |
| Reverse-worded items | Recode (5 → 1, 4 → 2…) before building a scale |
Chapter 11 of Research Methods Made Simple covers this in full, with cleaning and charting code in Python and R on the companion survey.Get the textbook · $15
Centre and spread
Worked example
Ten students report weekly hours of paid work: 0, 0, 5, 8, 10, 12, 12, 15, 20, 28. Describe the data.
Mean\( \bar x = 110/10 = 11.0 \) hours.
MedianThe middle two values are 10 and 12, so the median is 11.0 hours.
Mode0 and 12 each appear twice, so the data have two modes.
SpreadRange \( = 28 – 0 = 28 \). Standard deviation \( s = 8.67 \) hours. Quartiles (by the common linear-interpolation method) \( Q_1 = 5.75 \), \( Q_3 = 14.25 \), so IQR \( = 8.5 \).
OutliersUpper fence \( = Q_3 + 1.5 \times \text{IQR} = 14.25 + 12.75 = 27.0 \). The value 28 lies just above it, a mild outlier worth checking but plausible.
Write-up: “Students worked a median of 11 hours a week (IQR 5.75–14.25, n = 10); two did not work and one worked 28 hours.”
Key termsThe standard deviation is roughly the typical distance of values from the mean. The interquartile range is the spread of the middle 50%. Data are skewed right when a long tail of high values pulls the mean above the median.
Choosing the right chart
| What you show | Chart |
|---|---|
| One categorical variable | Bar chart (pie charts only for 2–4 categories) |
| One numeric variable | Histogram or box plot |
| Numeric by groups | Side-by-side box plots, or bar chart of means with error bars |
| Two numeric variables | Scatter plot |
| Change over time | Line chart |
| Two categorical variables | Clustered or stacked bar chart |
Weekly hours of paid work 10 students
Presenting tables and charts
- Number every table and figure, and refer to it in the text (“Table 3 shows…”).
- Give a title that says what, who and when; label axes with units; state \( n \).
- Round sensibly: one decimal place for means of marks or hours is usually enough.
- Start bar-chart axes at zero; avoid 3D effects and needless colours.
- Do not repeat every number from a table in the text: point out the pattern.
In your dissertationOpen your results chapter with a “sample characteristics” table: n, gender, year of study, share in work, mean (or median) hours and marks. It shows the reader who your findings are about before any tests.
Common mistakeReporting the mean income or hours for strongly skewed data without the median. A few very high values pull the mean up, so it misrepresents the typical student. Report the median and IQR, or both.
Practise until it sticks: Research Methods Made Simple Practice Questions has 1,004 questions, each with a worked answer.Get the practice book · $9
Practise: 6 questions
Try each one on paper first, then check the worked answer.
EasyQ1. Find the mean and median of 4, 6, 6, 9, 15. Show worked answer
Mean \( = 40/5 = 8 \). Median \( = 6 \) (the middle value). The mean is above the median because of the high value 15.
EasyQ2. Which chart would you use for (a) favourite study location; (b) hours worked vs marks? Show worked answer
(a) Bar chart (categorical). (b) Scatter plot (two numeric variables).
MediumQ3. Monthly earnings have mean £640 and median £480. What does this suggest, and which average should you report? Show worked answer
The mean is well above the median, so the data are skewed right by a few high earners. Report the median (with IQR) as the typical value, and mention the mean if useful.
MediumQ4. \( Q_1 = 8 \), \( Q_3 = 16 \). Is a value of 30 an outlier by the 1.5 × IQR rule? Show worked answer
IQR \( = 8 \). Upper fence \( = 16 + 1.5 \times 8 = 28 \). Since 30 > 28, yes, it is flagged as an outlier. Check it is a genuine value before deciding what to do.
MediumQ5. A respondent reports working 140 hours a week. What should you do? Show worked answer
It is impossible alongside full-time study (there are 168 hours in a week). Apply a pre-set cleaning rule, such as setting values above 80 to missing, and report the number of values changed. Do not quietly delete or guess a new value.
ExamQ6. Describe how you would present the descriptive results of a 300-person student survey. [5] Show worked answer
Report cleaning steps and the final n [1]. A sample characteristics table (gender, year, share working) [1]. Medians and IQRs for skewed variables such as hours and earnings, means and SDs for symmetric ones such as scale scores [1]. Suitable charts: histogram of hours, bar chart of job types, scatter plot of hours vs marks [1]. Numbered, titled, labelled tables and figures referred to in the text [1].
Check yourself
1. For skewed data, the best measure of centre is usually
The median is not pulled by extreme values.
2. To show the relationship between two numeric variables, use a
A scatter plot shows each pair of values as a point.
3. The IQR measures
IQR \( = Q_3 – Q_1 \).
Your score: 0 out of 3
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The short version
- Clean first, with rules set in advance, and report what you changed.
- Describe centre and spread for every key variable; median and IQR when skewed.
- Pick the chart from the variable type; label everything and state n.
- Start the results with a sample characteristics table.
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