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Revision Tips

Revision Tips. G. Check the side of the slide to see what level you are working at!. F. E. D. C. B. A. A*. WEBSITES. Website: www.mymaths.co.uk School and personal logins and passwords have been given out. Website: http://www.samlearning.com/ Centre Mk14SC2

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Revision Tips

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  1. Revision Tips

  2. G Check the side of the slide to see what level you are working at! F E D C B A A*

  3. WEBSITES Website: www.mymaths.co.uk School and personal logins and passwords have been given out. Website: http://www.samlearning.com/ Centre Mk14SC2 User ID: ddmmyyfs Password ddmmyyfs

  4. Areas to cover • Charts: • Bar charts / Pictograms / Tally Charts • Pie charts • Stem&leaf / Scatter graphs / Correlation / Lines of best fit • Histograms • Averages: • Simple mode, median and mean. • Modal class • Estimated grouped mean, • Cumulative frequency median. • Moving averages • Measures of spread. • Range • IQR, Box Plots

  5. Areas to cover • Probability • Simple theoretical / Experimental / Historical methods • Addition (OR rule) / Combined (AND rule) • Tree Diagrams/Dependent(conditional) Events • Sampling • Random • Stratified

  6. G Pictograms It shows the results when a group friends were asked what they liked most about going to parties

  7. G

  8. G BAR CHART SHOWING AVERAGE MONTHLY RAINFALL FOR ENGLAND. 70 65 60 55 50 45 40 35 30 26 20 15 10 5 Rainfall in mm Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months

  9. G BAR CHART SHOWING AVERAGE MONTHLY RAINFALL FOR ENGLAND. 70 65 60 55 50 45 40 35 30 26 20 15 10 5 Rainfall in mm Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months

  10. G LINE GRAPH SHOWING AVERAGE MONTHLY RAINFALL FOR ENGLAND. 70 65 60 55 50 45 40 35 30 26 20 15 10 5 Rainfall in mm Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months

  11. Averages (The Mode) The mode is the data value that occurs most frequently Example 1. The number of matches in a random sample of 14 boxes were counted and the results are recorded below. Find the mode of the data. 48, 49, 52, 50, 51, 49, 49, 55, 47, 48, 50, 51, 50, 50, G Mode = 50 (as it occurs more often than the other numbers).

  12. Averages (The Mode) The mode is the data value that occurs most frequently Example 2. Twenty people sat a maths test. Their marks out of 10 are recorded below. Find the modal mark for the test. 2, 5, 9, 3, 7, 6, 8, 6, 10, 4, 3, 2, 0, 9, 5, 1, 8, 6, 1, 5 G Mode = 5 and 6

  13. Averages (The Median) The median is the middle value of a set of data once the data has been ordered. Example 1.Robert hit 11 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives. 85, 125, 130, 65, 100, 70, 75, 50, 140, 95, 70 50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 140 Ordered data Single middle value G Median drive = 85 yards

  14. Averages (The Median) The median is the middle value of a set of data once the data has been ordered. Example 1.Robert hit 12 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives. 85, 125, 130, 65, 100, 70, 75, 50, 140, 135, 95, 70 50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 135, 140 Two middle values so take the mean. Ordered data F Median drive = 90 yards

  15. Averages (The Mean) The mean is also known as the common average. To find the mean value of a set of data you add up all the data values then divide by how many there are. The range is a measure of spread and is the largest data value – the smallest data value. Example1. Two dice were thrown 10 times and their scores were added together and recorded. Find the mean and range for this data. 7, 5, 2, 7, 6, 12, 10, 4, 8, 9 Mean = 7 + 5 + 2 + 7 + 6 + 12 + 10 + 4 + 8 + 9 10 = 70 10 = 7 E Range = 12 – 2 = 10

  16. Mean = 3.6+5.8+57.5+14.3+2.5+125.6+5.8+10.5+16.8+33.1+4.6+5.2 12 = 285.3 12 Averages (The Mean) Example2. This data shows the populations in millions of a random sample of 12 countries. Find the mean population and range. 3.6, 5.8, 57.5, 14.3, 2.5, 125.6, 5.8, 10.5, 16.8, 33.1, 4.6, 5.2 E = 23.78 million people. Range = 125.6 – 2.5 = 123.1 million people

  17. Pie Charts • YOU MUST HAVE A PROTRACTOR IN THE EXAM TO WORK WITH PIE CHARTS. • All pie charts are based on the 360º of a circle. • Each piece of pie will be so many degrees, and all the pieces must add up to 360º. • Take 360 and divide it by the total of whatever is to be put into the pie chart, this will tell you how many degrees there are in each unit share of pie. Multiply the unit share in degrees by the number of shares there are in each piece of pie. E

  18. How to Draw a Pie Chart We asked 120 people where they do their weekly shopping. This is what they said: Take 360º ÷ 120 = 3º for each person. x3º E Morrison’s Asda Sainsbury’s In a pie chart, everything must add up to 360° (because there are 360° in a circle) Co-op Tesco

  19. A two-way table D Write down three facts given from the information in the table

  20. Please copy out the following blank table into your books: D

  21. Display the following facts in a table: D There are 30 students in each class. In class 1, 25 did not pick red. In class 1, no one picked yellow. In class 2, three times as many picked red as in class 1. In class 1, 10 more picked blue than red. In class 2, only three picked ‘other’. In class 2, twice as many picked blue as yellow. Question: How many picked yellow in class 2?

  22. Solution D Solution: 4 pupils picked yellow as their favourite colour in class 2.

  23. Stem and Leaf • Remember the key. • Draw stem. • Add leaves – disordered. • Draw second stem for ordered leaves. • Use ordered stem and leaf to find median and range. D

  24. Completion times 3 4 5 6 7 Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median and range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: D stem leaf

  25. Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median and range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: D Completion times 3 4 5 6 7 7

  26. Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median and range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: D Completion times 3 4 5 6 7 7 1

  27. Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median and range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: D Completion times 3 4 5 6 7 7 3 1

  28. Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median and range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: D Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2

  29. Example - drawing a stem and leaf Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median and range Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: D Completion times 3 4 5 6 7 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 (3) re draw diagram with leafs in numerical order:

  30. Example - drawing a stem and leaf Answer (a):- (3) re draw diagram with leafs in numerical order: Completion times 3 4 5 6 7 8 7366881 9254356437 374812 1835 2 Don’t forget the key D Completion times 4|7 means47 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2

  31. 15th Example - drawing a stem and leaf Answer (b):- 4|7 means47 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 4 7 8 1 3 5 8 2 D The median is the middle value: There are 29 values i.e. 15th value Median = 47

  32. Lowest Highest Example - drawing a stem and leaf Answer (b):- Range = Highest - Lowest 4|7 means47 Completion times 3 4 5 6 7 8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9 1 2 3 47 8 1 3 5 8 2 D Range = 72 – 38 = 34

  33. Scatter Graphs A good correlation means the points form a line called a LINE OF BEST FIT. £10,000 As the line slopes down, this is called a negative correlation. If the line slopped up then it would be a positive correlation £8,000 £6,000 Value of Car £4,000 D £2,000 A scatter graph is a graph with lots of points, rather than a line or curve. £0 New 1 Yr 2 Yrs 3 Yrs 4 Yrs 5 Yrs 6Yrs 7 Yrs Age of Car Estimated value of a 6 yr old car? Use the line of best fit – to find the value £2200

  34. Scatter Graphs - Correlation This is called a zero correlation as there is little or no correlation 2.5 100% This is called a positive correlation 2 80% 1.5 60% Test Score Height (metres) 1 40% D 0.5 20% 0 Born 2 Yrs 4 Yrs 6 Yrs 8 Yrs 10 Yrs 12Yrs 0kg 15kg 30kg 45kg 60kg Age of Person Weight

  35. 22 12 17 27.5 7 A frequency polygon can be drawn directly from the frequency table by finding the mid-point of each class interval. Test Scores 20 D 15 Frequency 10 5 0 25-30 20-24 5-9 10-14 15-19 Marks

  36. Frequency Polygons A frequency distribution can be shown using a frequency polygon. 2. Draw in straight lines connecting points. 1. Mark the mid - points of each bar at the top with a point. A Frequency Polygon can be drawn onto an existing histogram. Extend lines if necessary ½ a class interval beyond first and last bars Test Scores 20 15 D Frequency 10 5 0 25-30 20-24 5-9 10-14 15-19 Marks

  37. Test 1 Test 2 The same 55 students sat two separate maths tests. The scores for each are shown by the frequency polygons below. Comment on the differences. It is often useful to show frequency polygons, side by side, in order to compare distributions. Test Scores 20 15 Frequency 10 C 5 0 25-30 20-24 5-9 10-14 15-19 Marks

  38. AVERAGES • Mode / Modal group – The most common or most frequently occurring value. • Median – Put values in order and find the middle value. If equal number of values then add two middle values together and divide by two. • Mean – add all values together and divide by the number of values.

  39. Modal Group • Mode – with grouped data this is called the modal group or class. D Modal group 60 < t ≤ 70

  40. Estimated Mean • Draw frequency table if necessary. • Find mid-point of each group and add these in a separate column. • Multiply each mid-point by its frequency, and add these calculations in another separate column. • Total the frequency column. • Total the mid-point multiplied by frequency column. • Divide the Mid-point x Frequency Total by the Frequency Total. Check that it looks sensible. This answer is the Estimated Mean C

  41. Time Taken by 200 Dansteed and Portway students to run 600 mFind estimated mean for this data. C Total20025484 Estimated mean = sum of mid-point x freq = total frequencies 25484 = 127.4 seconds 200

  42. What are Tree Diagrams • A way of showing the possibilities of two or more events • Simple diagram we use to calculate the probabilities of two or more events

  43. Possible Outcomes For example – a fair coin is spun twice 1st 2nd H HH H T HT H TH T B T TT

  44. Attach probabilities 1st 2nd H HH P(H,H)=½x½=¼ ½ H ½ ½ T HT P(H,T)=½x½=¼ H TH ½ P(T,H)=½x½=¼ ½ T B ½ T TT P(T,T)=½x½=¼ INDEPENDENT EVENTS – 1st spin has no effect on the 2nd spin

  45. Calculate probabilities 1st 2nd * H HH P(H,H)=½x½=¼ ½ H ½ ½ * T HT P(H,T)=½x½=¼ * H TH ½ P(T,H)=½x½=¼ ½ T B ½ T TT P(T,T)=½x½=¼ Probability of at least one Head?

  46. Why do we sample? • Census First started by William the Conqueror – The Domesday Book. Every 10 years there is a full census in the UK. • Disadvantges Cost and time. D

  47. Sample • Key features - a sample must be … • Random / Systemic • Stratified – representative of the population – not skewed by gender, age, etc. • Random / systemic and stratified help to minimise bias. • Advantage • Quicker • More manageable • Disadvantage • Conclusions can be unreliable due to size of sample • Conclusions can be unreliable due to the impact of outliers C

  48. Simple Sample • Find average height of a group of students. • 50 Year 7 girls; 950 Year 11 boys. • Sample size 50 (5%) • Stratified sample: 5%girls = 3; 5%boys = 47 • Random – draw out of a hat • Systemic – take every 10th person on a list. C

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