The Typhoon Day and the Mean
Ms. Rivera teaches Grade 5 in a public elementary school with 42 learners. In a combined Science–Math activity, her class recorded daily rainfall for 10 days. Nine days ranged from 0 to 15 mm; Day 7, a typhoon day, recorded 320 mm. When the class computed the mean, the result was about 45 mm. A learner, Ben, objected: 'That number is a lie. It never rained like that on a normal day.' Another learner suggested deleting the typhoon day 'so the average will be correct.' Ms. Rivera has 25 minutes left in the period, a prescribed Math competency on interpreting data, and a Science competency on the two seasons and typhoon season. She knows the quarterly test includes a mean/median item and a question on why the Philippines has a wet and dry season. She must respond to Ben in a way that respects his reasoning while keeping the lesson on track.
1. Diagnose Ben's statistical reasoning and decide the next instructional move. Justify your decision with the mathematics.
Read the worked answer
Ben is not confused; he is noticing that the mean is not resistant to extreme values. The 320 mm reading is a legitimate outlier, and it pulls the mean far above the typical day. The median for these data is 8 mm, which matches his intuition about a 'normal day.' Treating his objection as an error would teach him to distrust his own correct reasoning.
The instructional move should be a short comparison, not a full statistics lesson, because only 25 minutes remain. Display the ordered data, have learners compute both the mean and the median, and ask which number better answers 'What is a typical day?' and which better answers 'How much water fell in 10 days?' The mean still has a purpose: mean × 10 estimates total volume. Name the concept outlier and connect it to why both measures are reported in real weather summaries. This keeps the prescribed competency on interpreting data while using Ben's thinking as the lesson's center.
2. How would you handle the suggestion to delete the typhoon day, including the Science connection? Give one question you would ask and anticipate two learner responses.
Read the worked answer
Deleting the observation is not acceptable: it is data tampering and it teaches a bad habit. Real datasets contain extreme but valid values; analysts document and contextualize them, and remove a value only when there is evidence of measurement error. Here, 320 mm is plausible during a typhoon.
The Science connection is direct: the extreme value is not noise, it is the phenomenon. The wet season, roughly June to November, brings typhoons and heavy rainfall, while the dry season is drier and more variable. Ask: 'If we deleted the typhoon day, what would our average say about this place, and what would it hide?' Anticipated responses: 'It would look like it never floods,' and 'The average would be lower but it would not be true.' Those answers let you distinguish the typical day (median) from the seasonal risk (the full distribution), which is the Science point. Close by having learners write one sentence: 'The mean changed because ____, but the data should be kept because ____.'
3. Describe a short formative assessment that checks whether learners can choose between mean and median for a given purpose.
Read the worked answer
Use a three-item exit ticket with unfamiliar contexts, not the rainfall data, so it tests transfer:
- A class of 30 learners has one adult visitor. Which measure better describes a typical age in the room: mean or median? Why?
- A school wants to know how much water to collect for a garden over 10 days. Which measure is more useful: mean or median? Why?
- For the data set 3, 4, 5, 6, 22, compute both and state which one you would report to describe a typical value.
Success criteria: correct computation of both measures, correct selection with reference to an outlier, and an explanation that uses the purpose of the question rather than a memorized rule. Sort responses into 'mean' and 'median' piles with justifications on the board the next day. This checks whether learners can reason about measures of center, not just recall definitions.