Track 2 · Describing Data · Lesson 11 of 11
Choosing and reporting summaries
Choose summaries that fit each variable's type and shape, present them in a clear summary table with sensible precision, and write a summary sentence a decision-maker can trust.
A retail director reads one line of your report: “Average basket value: 97.564533 SAR.” Is that typical? How variable? Based on how many baskets? Good reporting answers those questions before they are asked — with the right measures, the right precision and the context that makes a number meaningful.
Every earlier lesson in this track added a tool. Reporting is choosing among them. Two questions decide most choices:
- What type of variable is it? Categories need counts and percentages. Ordered categories (ratings, levels) can add a median. Numbers can use the full toolkit.
- What shape does it have? Look at a histogram first. Roughly symmetric, no extreme values → mean and standard deviation. Skewed or with outliers → median and IQR (or percentiles), often with the mean as well.
| Variable | Centre | Spread / detail | Example |
|---|---|---|---|
| Nominal categories | Mode | Counts and percentages of every category | Payment method |
| Ordinal categories | Median (and mode) | Counts and percentages; cumulative % | Performance rating 1–5 |
| Numeric, roughly symmetric | Mean | Standard deviation; range | Exam scores |
| Numeric, skewed or with outliers | Median (mean too, if totals matter) | IQR or –; selected percentiles | Basket value, delays, salaries |
| Numeric with many zeros | Share of zeros + median of the non-zero values | Percentiles of the non-zero part | Annual bonus, insurance claims |
Dataset
Retail transactions
1,500 rows · one row = one transaction (basket) · synthetic data
| Store | Customer type | Items (items) | Basket value (SAR) |
|---|---|---|---|
| University | returning | 6 | 129.86 |
| Harbour Mall | returning | 2 | 60.64 |
| Downtown | new | 1 | 14.65 |
| Airport Road | returning | 1 | 6.95 |
| Airport Road | returning | 2 | 63.04 |
1 500 baskets. basket_value_sar is right-skewed: mean 97.56 SAR, median 87.13 SAR.
A summary table puts groups side by side with the same measures in the same order. For basket values by customer type in the (synthetic) transactions dataset:
| Customer type | n | Median | IQR (–) | Mean (SD) |
|---|---|---|---|---|
| New | 276 | 65.0 | 37.7–104.7 | 77.0 (56.1) |
| Returning | 768 | 82.9 | 51.2–124.8 | 92.4 (56.7) |
| Loyalty | 456 | 108.8 | 70.4–153.6 | 118.7 (66.9) |
| All | 1 500 | 87.1 | 52.0–129.4 | 97.6 (61.7) |
Notice the habits: the group sizes are shown; the units (SAR) and data source are in the caption; the quartile method is stated; numbers are rounded to one decimal, which is plenty for baskets worth tens of riyals; and the median comes first because the data are skewed.
Worked example
From raw output to a report line
Software output for the 1 500 baskets: n = 1500, mean = 97.564533, SD = 61.711934, Q1 = 52.0475, median = 87.13, Q3 = 129.4375, skewness = 1.19. Write one line for a management report.
Shape first. Skewness 1.19 and mean > median: right-skewed. Lead with the median and the quartiles.
Round to what matters. Baskets are worth tens of riyals and vary by about 60 SAR, so whole riyals are enough: median 87 SAR, middle half 52–129 SAR.
Add the mean only if it serves a purpose — here it links to revenue: mean 98 SAR × 1 500 baskets ≈ 146 000 SAR.
Give the context: units, n, period and the source.
“In March 2024 the median basket was 87 SAR (middle half 52–129 SAR; mean 98 SAR; n = 1 500 baskets, synthetic transactions data).”
Precision and rounding
- Keep full precision while calculating; round only the final reported numbers.
- Round to what the reader can use. Two or three significant figures usually suffice: “a median of 87 SAR” or “87.1 SAR”, not “87.130000 SAR”.
- Means and SDs: often one more decimal than the raw data were recorded with; never more digits than the data can support.
- Percentages: whole numbers or one decimal, with the denominator stated (“23% of 1 477 baskets with a recorded payment method”).
- Be consistent within a table: the same number of decimals for the same kind of quantity.
Quick check
Of 600 employees, 171 received no bonus. Which summary of annual_bonus_sar is most informative?
Exercises
The lesson is complete when every exercise is answered correctly. Hints are free; viewing a worked solution before solving means the exercise won't count towards mastery.
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Exercise 1 · Practice, difficulty 1 of 3
Match the summary to the variable
Choose the main summary you would report for each variable.
Exercise 2 · Application, difficulty 2 of 3
A two-part summary of bonuses
annual_bonus_sar in the salaries dataset is zero for employees who received no bonus. Give a two-part summary: (a) the percentage of employees with no bonus (1 decimal place) and (b) the median bonus among employees who received one (SAR, 2 decimal places).
Data: salaries · Open in the lab to explore and calculate.
Exercise 3 · Application, difficulty 2 of 3
One row of a summary table
Complete the returning customers' row of a summary table for basket_value_sar in the transactions dataset: the number of baskets, the median, and the IQR (type 7 quartiles). Give the median and IQR in SAR to 2 decimal places.
Data: transactions · Open in the lab to explore and calculate.
Exercise 4 · Interpretation, difficulty 1 of 3
How many decimals?
Software reports for 1 500 basket values: mean = 97.564533, SD = 61.711934, median = 87.13. Which line is best for a management report?
Exercise 5 · Practice, difficulty 2 of 3
Spot the reporting flaw
Match each reported statement to its main flaw.
Exercise 6 · Practice, difficulty 1 of 3
A summarising workflow
Put the steps for summarising a numeric variable for a report in order.
Exercise 7 · Interpretation, difficulty 2 of 3
Write the summary sentence
Using the summary table in this lesson, write two or three sentences for a retail director describing basket values in the transactions data, including how loyalty-card customers compare with new customers.
Exercise 8 · Interpretation, difficulty 2 of 3
Averaging ratings
Performance ratings are coded 1 (lowest) to 5 (highest). A dashboard shows “mean rating 3.17”. A manager asks if that is the right summary. What is the most defensible answer?
What you can now do
- Choose summaries to match a variable's type and shape
- Build a summary table with n, units, method and consistent precision
- Summarise zero-inflated variables in two parts
- Spot and fix misleading summaries: false precision, hidden zeros, mean ± SD for skewed data