Presentation on theme: "Teach GCSE Maths x x x x x x x x x x Weekly Household Income (£) f (millions) weekly household income (£) Data Handling."— Presentation transcript:
Teach GCSE Maths x x x x x x x x x x Weekly Household Income (£) f (millions) weekly household income (£) Data Handling
The pages that follow are sample slides from the 30 presentations that cover the work for Data Handling. The animations pause after each piece of text. To continue, either click the left mouse button, press the space bar or press the forward arrow key on the keyboard. A Microsoft WORD file, giving more information, is included in the folder. Animations will not work correctly unless Powerpoint 2002 or later is used.
F1: The 3 Ms and Range The following extract comes from the 1 st foundation presentation. Here the students are shown the importance of ordering the data when finding the median.
144 Can you find the medians of these data sets? 4 6101416 ANS: The numbers in the 2 sets are the same so the medians are both 10. The median is only in the centre of the list if the data are in order. Set A 10 6 16 61441016 Set B median = 10
F9: Reading Stem and Leaf Diagrams The work on stem and leaf diagrams gives an opportunity to revise the method of finding the median. This is shown on the next slide.
Key: 6 2 means 62 mm Rainfall data 10 9 8 7 31 7 7 6 56 0 2 50 7 Remind your partner how to find the median of a data set. Can you find the median here? e.gThe diagram shows the average rainfall (mm) for Newton Rigg ( UK ) from 1971 – 2000 for Jan. to Nov. 3 Ans: Median rainfall is 73 mm The numbers are in order and there are 11 of them, so the median is the 6 th. 123 4 56 Tip: Check there are the same number of numbers before and after the median. (Here there are 5 before and 5 after) Adapted from Crown copyright data supplied by the Met Office
F12: Histograms – Equal Class Widths A short summary is provided in each presentation in a form suitable for note-taking. The next slide shows the summary for the introductory work on histograms.
frequency density SUMMARY Frequencies on a histogram are shown by area. E.g. We plot frequency density on the y -axis. Frequency density is found by dividing each frequency by the class width. frequency = 10 8 = 80 10 8
F14: Two-Way Tables In addition to the questions asked of students as the theory is being developed, there are short exercises to check that the main points have been understood. The icon in the top right hand corner indicates that in this exercise a calculator is not required.
Number of Computers Number of People Exercise 1.The two-way table shows how the number of computers in a sample of 100 households is related to the number of people in the household. 01234 144110 23311 313350 411302 503211 (a) What does the 6 in the table tell us? (c) Find the mean number of computers per household. (b) How many households had more computers than the number of people? 6
Exercise (a) There are 6 households with 2 people and 1 computer. Number of Computers Number of People 3 1 3 6 4 1 1 0 5 1 1 3 0313 1332 2314 1205 0141 420 (b) There are 4 households with more computers than people. Solution:
Exercise Solution: total number of computers total number of households The mean number of computers per household = = 1·62 Number of Computers Number of People 7112305 4 2 0 1 0 4 17 1 3 6 4 1 8 0 5 1 1 3 12313 14332 7314 50129 Total 10141 Total 20 4 4= 16 81 50 = Total number of computers = 81 0 9= 0 1 17= 17 2 12= 24 3 8= 24
H3: Box Plots As well as showing students how to draw box plots, the presentation on box plots uses real data to illustrate the usefulness of the diagrams when comparing data.
Rainfall in UK Rainfall in France Box and whisker diagrams are very useful for comparing data sets. The median rainfall was higher in France. e.g. The following diagrams represent the rainfall in the first 16 days of March 2004 in 20 regions of the UK and of France:
Rainfall in UK Rainfall in France The range of rainfall amounts is greater in the U.K.... Box and whisker diagrams are very useful for comparing data sets. e.g. The following diagrams represent the rainfall in the first 16 days of March 2004 in 20 regions of the UK and of France:
Rainfall in UK Rainfall in France but the interquartile range ( giving the middle 50% of amounts ) is greater in France. The range of rainfall amounts is greater in the U.K.... Box and whisker diagrams are very useful for comparing data sets. e.g. The following diagrams represent the rainfall in the first 16 days of March 2004 in 20 regions of the UK and of France:
H6: Probability and Independent Events It is important for students to recognise the difference between independent events and those that are not independent. The presentation gives examples of situations involving both types.
, so multiplying the probabilities does not give the correct answer. Its starting to look as though we can always multiply probabilities of separate events to get the probability of both. However, this isnt true. e.g. If I pick one of the following cards at random, what is the probability that it is pink and has a square on it? Can you see the answer directly ? Ans: p = 1 4 However, the probability of pink = 1 4 and the probability of a square = 2 4
The next 2 slides contain a list of the 30 files that make up Data Handling. The files have been labelled as follows: F:Topics for the Foundation level. H:Topics which appear only in the Higher level content. Also for ease of access, colours have been used to group topics. For example, blue is used at both levels for work on probability. The 2 underlined titles contain links to the complete files that are included in this sample.
F13 Ms and Range F3Frequencies and the Mean F4Grouped Data and the Mean F7Reading Pie Charts F8Drawing Pie Charts F19Collecting Data F12Histograms – Equal Class Intervals F13Scatter Graphs F16Calculating Probabilities F5Discrete and Continuous Data F6Pictograms, Bar Charts and Line Graphs F21Index Numbers F2More About the Three Ms Teach GCSE Maths – Data Handling F17Probability - Theory and Experiment F14Two Way Tables F18 Sample Spaces F20Questionnaires F9Reading Stem and Leaf Diagrams F11Frequency Diagrams F10Drawing Stem and Leaf Diagrams Foundation F15Introduction to Probability continued Page 1
H1Cumulative Frequency Diagrams H3Box Plots H4Histograms – Unequal Class Widths H7Tree Diagrams H8Two-Way Tables and Probability H5Time Series and Moving Averages H6Probability and Independent Events H2Using Cumulative Frequency Diagrams H9Sampling Methods Page 2 Higher Teach GCSE Maths – Data Handling