A Data Project from Question to Report

A brief note on A Data Project from Question to Report: a whole data project, from the question to the report. Try each question at the end before you open its answer.

The six steps

1. Ask one clear question.
2. Collect the data in a table.
3. Clean it: check any value that cannot be true.
4. Show it: a frequency table or histogram for the shape, a line graph for the change over time.
5. Summarise it: the centre, the spread and the chances.
6. Report it: the question, the method, the numbers, a graph and one limit.

Summaries for a month of weather

Weather comes in spells, so the chance of two rainy days in a row is often more than the product of the two chances.

What a report may claim

• Compare groups with their means and their sizes.
• An association is not a cause: "the rainy days were cooler" is fine; "rain makes it cooler" is not proved.
• One month in one town is a limit; say so.

A worked example

Ten spring days had the highest temperatures $24, 22, 21, 25, 27$, $26, 23, 20, 22, 26\ ^\circ\text{C}$, with rain on days 2, 3, 8 and 9.

1. Typical day. Sorted: $20, 21, 22, 22, 23$, $24, 25, 26, 26, 27$. The median is $\dfrac{23 + 24}{2} = 23.5\ ^\circ\text{C}$.
2. Chance of rain. $\dfrac{4}{10} = 0.4$.
3. Two groups. The 4 rainy days had a mean of $21.25\ ^\circ\text{C}$, and the 6 dry days $25.17\ ^\circ\text{C}$.
4. The report. "On these 10 days, the rainy days were cooler on average. Ten days in one town cannot tell us about other seasons."

Practice with new numbers

A program to try

The program works out the worked example.

Mistakes to avoid

• Starting with a graph before there is a clear question.
• Giving a mean with no spread and no group sizes.
• Multiplying the chances of linked days as if they were separate.
• Writing "because" when the data only shows that two things went together.

Check yourself

1. Which graph shows how the temperature changed from day to day, and which shows how many days had each temperature?

2. It rained on 8 of 40 days. Estimate the chance of rain, and the number of rainy days to expect in 25 days.

3. A report says: "Foggy mornings make the afternoons cooler." What should it say instead?

4. Give two limits for a report on 30 days of weather at one school.