Write the report

Compare two groups

Are the rainy days different from the dry days? Split the temperatures into the two groups and find the mean of each.

What the data shows, and what it does not

The data shows that on the days of this month, the rainy days were cooler on average. It does not show that rain made the days cooler, or that cooler days bring rain. Clouds may cause both. The data has an association, and an association is not a cause.

A careful report says what it saw, and keeps "because" for when there is more evidence.

A trend over the month?

Is the month getting warmer or cooler? The mean of the first $15$ days is $31.8\ ^\circ\text{C}$, and of the last $15$ days $29.7\ ^\circ\text{C}$. The second half was about $2\ ^\circ\text{C}$ cooler. But the line graph shows waves, not a steady fall.

You should find that splitting after day 10 or after day 20 gives different gaps from splitting after day 15. With only one month of waves, a "trend" depends on where you cut it, so we cannot say what comes next.

The five parts of the report

1. The question. What was the weather like in our town last month?
2. The method. We recorded the highest temperature and rain or no rain on $30$ days in a row.
3. The numbers. A typical day was $31\ ^\circ\text{C}$, the middle half of the days was between $29\ ^\circ\text{C}$ and $32\ ^\circ\text{C}$, and $10$ days out of $30$ were rainy.
4. A graph. The line graph with the rainy days marked.
5. A limit. One month in one town does not tell us about other months or other places.

The report is the numbers of the program, put into words.

Practise with new numbers

Common mistakes

• Writing "because" from an association. The data shows what went together, not why.
• Leaving out the group sizes. Say that there were 10 rainy days and 20 dry days.
• Reading a trend into a few waves. A month is too short to say what comes next.
• A report with no limit. Say what the data cannot tell us.

Remember these

• A report has a question, a method, numbers, a graph and a limit.
• An association is not a cause.
• Say how many days are in each group, and what the data cannot tell us.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A student writes: "Rain makes the temperature fall." Does the weather record prove it?

2. Give one limit for a report on one month of weather.

3. The 20 dry days add up to 637 °C. What is their mean?

4. Why should a report say that there were 10 rainy days and 20 dry days, and not just give the two means?