Functional Question (and lesson) Higher (Statistics 2)

1. Functional Question (and lesson) Higher (Statistics 2) For the week beginning ….

2. Lesson Plan – Interpreting different types of chart

3. Assessment Objective - AO3 Developing AO3 skills is a process that depends on giving learners confidence to: · Try different approaches · Make mistakes and rectify them in a constructive environment · Justify decisions and explain consequences · Express ideas and communicate conclusions in a variety of ways and to different audiences. AO3 seeks to assess a learner’s ability to: · Process information · Pose problems and pursue them · Conjecture and investigate within mathematics · Reason concisely · Evaluate and check methods and results · Present solution(s) effectively There is a link to the three strands in Functional Mathematics: · Represent (strategy) · Analyse · Interpret However, not all AO3 questions will be “functional”.

4. Starter Activity This bar chart represents the scores that were obtained when a number of people entered a penalty-taking competition. Each person was allowed six penalty kicks. How many people entered the competition? How can you tell? How can you calculate the mean, median and modal number of penalties scored? What proportion of the people scored one penalty? What is that as a percentage? What proportion scored three penalties? Six penalties? Can you think of another type of statistical diagram that can be used to show proportions?

5. The same information can be shown in a pie chart..... Does the pie chart tell you how many people entered the competition? What does it tell you? How can you find the mode and median from the pie chart? Can you estimate the percentage that scored six goals? If only four people had scored six goals, what would the pie chart have looked like? If I halve/double the heights of all the bars in the bar chart, what will happen to the pie chart?

6. Forty people are asked to taste two types of wine. Each is asked to rate the wine on a scale from 1 to 6. 1 = awful, 6 =fantastic. The graphs show the results of the wine tasting. What can you say about the wines? If you had someone coming to dinner, which wine would you choose? Why?

7. Both wines have the same mean score, 3.5. People share a similar view about wine A, but they have a wide spread of views about wine B. There is a statistical diagram that is helpful when making comparisons of spread: the ‘box and whisker’ plot.

8. Five data points are used to construct a box and whisker plot: • the least and greatest values (the whiskers); • the median (the middle line); • the quartiles (the ends of the boxes). • Box and whisker plots can be drawn vertically or horizontally.

9. What is the range for wine A? What is the median for wine A? What are the quartiles for wine A? What is the range for wine B? What is the median for wine B? What are the quartiles for wine B?

10. Today’s Task • Work together to match the cards from each set. • Try to do this without doing calculations. • Take turns at explaining how you know particular cards match. • Things to think about... • Can you sort the cards into those that have a large range and • those that have a small range? • Can you sort the cards into those that have a large median • and a small median? • Does the distribution look spread out (the ‘box’ is large), or is • it concentrated in a few scores (the ‘box’ is small)? • Does the distribution look symmetrical, or is it skewed?

13. AO3 question (Higher) Two Year 11 classes both took the same test. These tables summarise results for the two classes. The class with the better marks will receive a prize. Which class should be given the prize? [6] Marks

14. Using The Mark Scheme