--- title: "Mean, median, mode and range" subtitle: "Data and chance · Data · Lesson 2" --- # Mean, median, mode and range **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A team scored 3, 5, 5, 6 and 11 goals. What is a typical game? There are at least three good answers, and they are all useful. :::teacher-note **In one sentence:** Students calculate the mean, median, mode and range of small data sets (odd and even counts, two modes, no mode, negative values), watching each measure move on a dot plot as values are added (AC9M7ST01, node 2). **Students should be able to say:** I can calculate the mean, median, mode and range of a data set. I can find the median of an even number of values. I can handle data with two modes or no mode. **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 The mean shares the total equally. What is the total? :::keep-together **A team scored $3, 5, 5, 6$ and $11$ goals in five games. What is the mean?** ☐ $8$ ☐ $6$ ☐ $5$ ☐ $5.5$ My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 6. The total is 3 + 5 + 5 + 6 + 11 = 30, shared equally between 5 games is 6. (5 is the median and the mode; 8 is the range.) ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## The four measures :::keep-together ### Mean, median, mode, range Here is each measure for the goals data. 1. $3, 5, 5, 6, 11$ — The data, sorted (the median and range need it sorted). 2. $\text{mean} = \tfrac{3 + 5 + 5 + 6 + 11}{5} = \tfrac{30}{5} = 6$ — Add, then divide by how many. 3. $\text{median} = 5$ — The middle (3rd of 5) value of the sorted list. 4. $\text{mode} = 5$ — The most common value (it appears twice). 5. $\text{range} = 11 - 3 = 8$ — Highest minus lowest. 6. $8, 3, 9, 4, 6, 7 \to 3, 4, 6, 7, 8, 9$ — An even count: sort, then the median is halfway between the two middle values, $\tfrac{6 + 7}{2} = 6.5$. Now find the median of $8, 3, 9, 4, 6, 7$. **Find the median of $8, 3, 9, 4, 6, 7$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6.5 Sorted: 3, 4, 6, 7, 8, 9. The two middle values are 6 and 7, so the median is 6.5. ::: :::keep-together ### Find the mistake **Leo finds a median. Click the line where his working goes wrong.** ``` 1 Find the median of 9, 2, 7, 4, 5. 2 There are 5 values, so the median is the 3rd one. 3 The 3rd value in the list is 7. 4 So the median is 7. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: sort first. 2, 4, 5, 7, 9: the 3rd value is 5, so the median is 5. ::: :::keep-together ### The mean **Find the mean of $4, 8, 9, 3$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6 4 + 8 + 9 + 3 = 24, and 24 ÷ 4 = 6. ::: :::typical ## One change at a time **Two modes.** Each task changes one thing. **No mode.** **Range with negatives.** **Keep the median.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## The four measures :::keep-together ### Mean **Find the mean of $12, 15, 9, 14$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 12.5 50 ÷ 4 = 12.5. ::: :::keep-together ### Median **Find the median of $21, 17, 30, 25, 19$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 21 Sorted: 17, 19, 21, 25, 30. The middle value is 21. ::: :::keep-together ### Range **Find the range of $4.5, 7.2, 3.9, 6.1$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3.3 7.2 − 3.9 = 3.3. ::: :::keep-together ### Review: kinds of data **Review: the number of pets in each house. Discrete or continuous?** ☐ Continuous ☐ Discrete ::: :::teacher-note **Answer:** Discrete Counted: discrete. ::: ## Make: build a data set Then make a different set with the same mean and median. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Find the mean, median, mode and range of 6, 2, 9, 6, 7, 12.** {{lines-3}} ::: :::teacher-note **Answer:** Mean 42 ÷ 6 = 7; median (6 + 7) ÷ 2 = 6.5; mode 6; range 10. :::