--- title: "Comparing data sets" subtitle: "Data and chance · Data · Lesson 5" --- # Comparing data sets **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Two classes sit the same quiz. One has the top score; the other has nobody below 12. Which class did better? It depends on what you compare. :::teacher-note **In one sentence:** Students describe data sets by shape (symmetrical or skewed, clusters, gaps, outliers), centre and spread, and compare two sets on both centre and spread, with numbers and in context (AC9M7ST02, nodes 2 and 3). **Students should be able to say:** I can describe the shape of a data set (symmetrical, skewed, clusters, gaps, outliers). I can compare two data sets using a measure of centre and a measure of spread. I can write a comparison with numbers and in context. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Look at how far apart each class's lowest and highest scores are. :::keep-together **Quiz scores. Class A: $12, 14, 15, 15, 16, 17, 18$. Class B: $6, 10, 13, 16, 19, 20, 22$. Which class's scores are more consistent?** ☐ Class B ☐ Class A ☐ They are the same My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** Class A. Its scores range from 12 to 18 (a range of 6); Class B's go from 6 to 22 (a range of 16). The centres are close: medians 15 and 16. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Describe, then compare :::keep-together ### Shape, centre, spread Here is how to describe and compare. 1. $\text{Shape}$ — Symmetrical, or skewed with a tail? Clusters, gaps, outliers? 2. $\text{Centre: medians } 15 \text{ and } 16$ — Close: a typical score is about the same. 3. $\text{Spread: ranges } 6 \text{ and } 16$ — Very different: Class B's scores vary much more. 4. $\text{Compare both}$ — "Similar centres, but A is more consistent (range 6, not 16)." Now describe the shape of the books data. **Which describes the shape of this data?** ☐ Every value is equally common ☐ Skewed: most values are low, with a tail of a few high values ☐ Symmetrical about the middle ::: :::teacher-note **Answer:** Skewed: most values are low, with a tail of a few high values Most students read 1 to 3 books, a few read many: the data is skewed, with a tail to the right. ::: :::keep-together ### Find the mistake **Mia compares the two classes. Click the line where her reasoning goes wrong.** ``` 1 Class A: 12, 14, 15, 15, 16, 17, 18. Class B: 6, 10, 13, 16, 19, 20, 22. 2 The best score in Class B is 22; in Class A it is 18. 3 So Class B did better. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: one student's score does not describe a class. Compare centres (medians 15 and 16: close) and spreads (ranges 6 and 16: A is much more consistent). ::: :::keep-together ### A good comparison **Which is the best comparison of Class A and Class B?** ☐ Class B is better because it has a 22. ☐ Class A is better because 15 + 14 is more than 6 + 10. ☐ The classes have similar medians (15 and 16), but Class A's scores are much less spread (range 6 against 16), so A was more consistent. ::: :::teacher-note **Answer:** The classes have similar medians (15 and 16), but Class A's scores are much less spread (range 6 against 16), so A was more consistent. A good comparison names the centre and the spread of both, with numbers, and says what they mean. ::: :::typical ## One change at a time **Same centre, smaller spread.** Each task changes one thing. **Symmetrical.** **An outlier.** **Difference in centre.** **Same mean.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Compare in context :::keep-together ### Centre and spread **Two bakeries' delivery times (min). Bakery X: median 25, range 10. Bakery Y: median 22, range 30. Which statement is right?** ☐ Y is slower and more reliable ☐ Y is usually a bit faster, but X is more reliable ☐ X is faster and more reliable ::: :::teacher-note **Answer:** Y is usually a bit faster, but X is more reliable Lower median: Y is faster typically. Smaller range: X is more reliable. ::: :::keep-together ### A fair comparison **Which is NOT a fair comparison of two netball teams' goals?** ☐ Team 1 scored the single highest game, so Team 1 is better ☐ Team 1's median was 3 goals higher ☐ Team 2's goals varied less (smaller range) ::: :::teacher-note **Answer:** Team 1 scored the single highest game, so Team 1 is better One game does not describe a team. ::: :::keep-together ### Skewed **Data bunched at the high end with a few low values. What shape is it?** ☐ Skewed, with a tail to the right ☐ Skewed, with a tail to the left ☐ Symmetrical ::: :::teacher-note **Answer:** Skewed, with a tail to the left The tail points towards the few low values: to the left. ::: :::keep-together ### Review: stem-and-leaf **Review: a stem-and-leaf plot reads $2 \mid 1\ 4\ 6$ and $3 \mid 0\ 5$. What is the median?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 26 Values 21, 24, 26, 30, 35: the 3rd is 26. ::: ## Make: a surprising comparison Write two headlines about your sets: one where A wins, one where B wins. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Group 1 reaction times (s): median 0.32, range 0.10. Group 2: median 0.28, range 0.35. Compare the groups in one sentence.** {{lines-3}} ::: :::teacher-note **Answer:** Group 2 was faster on a typical try (median 0.28 s against 0.32 s), but much less consistent (range 0.35 s against 0.10 s). :::