Answers, the misreading that survives into Year 13, and what to do with the class width buttons.
Start at width 20 and ask them to describe the distribution. They will say it is a single lump, roughly in the middle. Write that on the board.
Then switch to width 5. There are two groups with a gap: the students who walk and the students who take a bus. Nothing about the data changed. Their description was a description of a choice somebody made, and they could not tell. That is the lesson, and it is worth more to an IA than anything else on the page.
| Question | Answer |
|---|---|
| 1. Modal class | B, 20 ≤ t < 30. Highest frequency is 16, and the answer must be the class. |
| 2. Estimated mean | 34.2. 1710 divided by 50. |
| 3. Long upper section | B. More spread, same number of values. |
The worked example on the student page gives an estimated mean of 19.5 minutes from Σfx = 780 and Σf = 40.
| They choose | What it means |
|---|---|
| 25 (Q1) | They gave the midpoint. They have found the right class and then answered with a number because a number feels like an answer. One sentence fixes it: with grouped data you no longer have individual values, so you cannot name one. |
| 16 (Q1) | They gave the frequency. A different error from the midpoint: this student has not separated "how many" from "which group". |
| 427.5 (Q2) | Divided by the number of classes rather than the total frequency. The page says so explicitly, because it is a method error rather than arithmetic. |
| 342 (Q2) | Decimal point. The page tells them their digits are right, which is worth doing: this student does not need re-teaching. |
| "More values" (Q3) | The one that matters. Every quarter of a box plot holds a quarter of the data. This misreading survives into Year 13 and into IAs. If anyone picks it, stop and draw a box plot of a set with an obvious gap. |
| "Must contain an outlier" (Q3) | Reasonable instinct, wrong certainty. Worth praising and then testing: a long upper whisker is evidence worth checking, not proof. Good link back to 4.1. |
Estimated mean is marked on method. Insist they show Σfx and Σf separately. A student who does keeps most of the marks through an arithmetic slip; one who writes a single line of calculator work loses the lot.
The word estimate is a mark. Writing "the mean is 19.5" when only grouped data was given throws away something that costs nothing to keep. Ask them to say it out loud a few times this lesson.
Modal class means the class. This is the most frequent single error on this sub-topic and it is a whole mark every time.
| What is happening | |
|---|---|
| 1 | The width buttons. Describe at 20, then switch to 5, then the conversation about what a histogram actually shows. |
| 2 | Grouped frequency, modal class, the estimated mean worked example, question 1. |
| 3 | Question 2 and the method marks. Make them write the two sums down even though the calculator will do it. |
| 4 | Cumulative frequency to box plot. Draw one from the other on the board; the page states the link but seeing it built is better. |
| 5 | Question 3 and the spread versus count discussion. |
Do not say "the mean is 19.5" yourself when working the example. Say the estimated mean, every time, including when it is tedious. They copy what you say, not what the page writes.
Do not describe a box plot section as "where most of the data is". It is the exact phrasing that produces the question 3 error, and it is easy to say without noticing.
Three tiers, ramping the way practice should: the method on its own, then the method inside something real, then a challenge. Set the tier the class in front of you needs rather than one undifferentiated sheet. Answers are given so these can go straight onto a board.
The method on its own, with friendly numbers. Set these first and move on quickly once they are secure.
The same skill inside a real situation, where the first job is working out what is being asked.
Reasoning, working backwards, or spotting an error. These are where the top grades are decided.
Works on a phone, though the histogram is worth seeing on something larger if you have the choice. Nothing a student types is saved or sent anywhere.