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Tables & Charts

Tables & Charts. Frequency Tables / Relative Frequency. Cumulative Frequency Table. Stem-leaf Diagrams. Back to Back Stem Leafs. Five Figure Summaries. Box Plots. Scatter Diagrams. Starter Questions. Q1. Does 5x 2 – 16x + 3 factorise to (5x - 1)(x – 3).

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Tables & Charts

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  1. Tables & Charts Frequency Tables / Relative Frequency Cumulative Frequency Table Stem-leaf Diagrams Back to Back Stem Leafs Five Figure Summaries Box Plots Scatter Diagrams Created by Mr. Lafferty@mathsrevision.com

  2. Starter Questions Q1. Does 5x2 – 16x + 3 factorise to (5x - 1)(x – 3) Q2. Change into £’s €75 exchange rate £1  € 1.5 Q3. Convert to scientific notation 0.0675 Created by Mr. Lafferty@mathsrevision.com

  3. Aims of the Lesson • Understand the term • Frequency Table and Relative Frequency . • 2. Construct a Frequency/Relative Frequency Table. • 3. Interpret information from Tables. Created by Mr. Lafferty

  4. represents a tally of 5 llll Frequency tables Raw data can often appear untidy and difficult to understand. Organising such data into frequency tablescan make it much easier to make sense of (interpret) the data. Sum of Tally is the Frequency

  5. 58 56 59 57 60 56 62 62 58 56 58 59 56 59 56 59 57 58 60 62 61 58 59 62 60 58 60 59 56 59 60 61 56 60 62 59 61 58 60 61 62 58 57 62 59 61 58 60 Frequency tables Example1. A tomato grower ideally wants his tomatoes to have diameters of 60mm, but a diameter ranging from 58mm to 62mm will be acceptable. Organise the diameters given below into a frequency table. Lowest number 56 Highest number 62 Created by Mr. Lafferty

  6. 58 56 59 57 60 56 62 60 58 60 58 59 57 59 56 59 57 58 60 59 61 58 59 62 60 58 60 59 59 60 59 61 59 60 62 59 61 58 60 61 59 58 57 62 59 61 58 60 Frequency tables X X X X X X l l l l l l Created by Mr. Lafferty

  7. Relative Frequency used with Pie charts Relative Frequency always adds up to 1 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X lll llll llll 58 56 59 57 60 56 62 60 58 60 58 59 lll 57 59 56 59 57 58 60 59 61 58 59 62 60 58 60 59 59 60 59 61 59 60 62 59 61 58 60 61 59 58 57 62 59 61 58 60 llll llll llll llll llll llll llll Frequency Tables Relative Frequency 3 ÷ 48 = 0.0625 3 4 4 ÷ 48 = 0.0833 9 9 ÷ 48 = 0.1875 13 13 ÷ 48 = 0.2708 10 10 ÷ 48 = 0.2083 5 5 ÷ 48 = 0.1042 4 4 ÷ 48 = 0.0833 R48 Created by Mr. Lafferty

  8. Charts & Tables Now try Ex 3.1 Q2 Ch6 MIA (page 108) Created by Mr. Lafferty@mathsrevision.com

  9. Starter Questions Q2. Find the area for the shapes (w - 2) (x – 5) (x – 3) 7 Q3. Write in standard form 0.008654 Created by Mr. Lafferty Maths Dept.

  10. Cumulative Frequency Tables Learning Intention Success Criteria • Add a third column to a frequency table to create a Cumulative Frequency Table. • 1. To explain how to construct a Cumulative Frequency Table. Created by Mr. Lafferty Maths Dept.

  11. Cumulative Frequency Tables Example : This table shows the number of eggs laid by a clutch of chickens each day over a seven day period. Cum. Freq. Total so far 1 2 2 A third column is added to keep a running total (Cumulative Frequency Table). This makes it easier to get the total number of items. 2 3 5 3 1 6 4 6 12 You have 1 minute to come up with a question you can easily answer from the table. 5 5 17 6 8 25 7 4 29 Created by Mr. Lafferty Maths Dept.

  12. Cumulative Frequency Tables Now try Ex 3.2 Ch6 (page 109) Created by Mr. Lafferty Maths Dept.

  13. Starter Questions Q1. Factorise 4x2 + 9x - 9 Q2. Multiply out (a) a(ab – a) (b) -2a( b2 – a) Q3. Created by Mr. Lafferty@mathsrevision.com

  14. Stem Leaf Graphs Construction of Stem-Leaf Learning Intention Success Criteria 1. Construct and understand the Key-Points of a Stem-Leaf Graph / Dot Graphs. • To construct a Stem-Leaf Graph / Dot Graph and answer questions based on it. 2. Answer questions based on the graph. Created by Mr. Lafferty Maths Dept.

  15. 2 3 4 5 9 6 6 6 4 0 0 4 1 6 3 7 4 1 4 4 5 5 3 8 9 n = 20 Key : 2 4 means 24 Stem Leaf Graphs Construction of Stem and Leaf A Stem – Leaf graph is another way of displaying information : Ages This stem and leaf graph shows the ages of people waiting in a queue at a post office How many people in the queue? 20 How many people in their forties? 6 leaves stem Created by Mr. Lafferty Maths Dept.

  16. 3 5 5 1 3 9 3 2 2 4 0 0 1 1 5 1 4 5 5 5 7 n = 20 Key : 2 3 means 23 Stem Leaf Graphs We can now answer various questions about the data. Construction of Stem and Leaf Example : Construct a stem and leaf graph for the following weights in (kgs) : Weight (kgs) 1 2 2 2 leaves stem Created by Mr. Lafferty Maths Dept.

  17. 3 5 5 1 3 9 3 2 2 4 0 0 1 1 5 1 4 5 5 5 7 Dot Plot Weight (kgs) 1 2 2 We can convert stem leaf into a simple Dot diagram by taking each level and adding a dot for each leaf 2 leaves stem 1 2 3 4 5

  18. Charts & Tables Stem Leaf & Dot Diagram Now try Ex 4.1 Ch6 (page 112) Created by Mr. Lafferty Maths Dept.

  19. Starter Questions Explain why the statement below are true or false. Factorising x2 – 9 we get (x - 3)(x - 3) Multiply out 4x – 2( 8 – x) = 2x -16 Created by Mr. Lafferty@mathsrevision.com

  20. Stem Leaf Graphs Construction of Back to Back Stem-Leaf Learning Intention Success Criteria 1. Construct and understand the Key-Points of a Back to Back Stem-Leaf Graph. • To construct a Back to Back Stem-Leaf Graph and answer questions based on it. 2. Answer questions based on the graph. Created by Mr. Lafferty Maths Dept.

  21. 14 15 16 17 18 1 0 3 0 1 1 4 2 6 4 4 6 6 Stem Leaf Graphs Back to Back Stem – Leaf Graphs Rugby Team 1 Heights Rugby Team 2 Heights A back to back stem-leaf helps us to compare two sets of data. 4 2 1 7 8 7 6 8 5 0 Write down a question that can be answered easily from the graph. 6 4 3 3 1 7 0 n = 15 n = 15 14 | 1 represents 141cm Created by Mr. Lafferty Maths Dept.

  22. Charts & Tables Back to Back Stem Leaf Graphs Now try Ex 4.2 Ch6 (page 113) Created by Mr. Lafferty Maths Dept.

  23. Starter Questions Created by Mr. Lafferty Maths Dept.

  24. Five Figure Summary Learning Intention Success Criteria • Understand the terms • L , H, Q1, Q2 and Q3. • 1. To explain the meaning and show how to workout the five figure summary information for a set of data. • Be able to work • L , H, Q1, Q2 and Q3 • For a set of data Created by Mr. Lafferty Maths Dept.

  25. When a set of numbers are put in ORDER, it can be summarised by quoting five figures. Five Figure Summary 1. The highest number (H) 2. The lowest number (L) 3. The median, the number that halves the list (Q2) 4. The upper quartile, the median of the upper half (Q3) 5. The lower quartile, the median of the lower half (Q1)

  26. Five Figure Summary Q2 = Median (middle value) Q1 = lower middle value Q3 = upper middle value Example Find the five figure summary for the data. 2, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10 The 11 numbers are already in order ! 5 7 8 Q1 = Q2 = Q3 = 5 8 7 L = 2 H = 10 2 4 5 6 7 7 9 10 Created by Mr. Lafferty Maths Dept.

  27. Five Figure Summary Q2 = Median (middle value) Q1 = lower middle value Q3 = upper middle value Example Find the five figure summary for the data. 2, 4, 5, 5, 6, 7, 7, 8, 9, 10 The 10 numbers are already in order ! 8 Q1 = Q2 = Q3 = 5 6.5 5 7 7 8 L = H = 10 2 2 4 5 6 9 10 Created by Mr. Lafferty Maths Dept.

  28. Five Figure Summary Q2 = Median (middle value) Q1 = lower middle value Q3 = upper middle value Example Find the five figure summary for the data. 2, 4, 5, 5, 6, 7, 8, 9, 10 The 9 numbers are already in order ! 6 8.5 Q1 = Q2 = Q3 = 4.5 5 5 7 8 6 L = H = 10 2 2 4 9 10 Created by Mr. Lafferty Maths Dept.

  29. Five Figure Summary Now try Ex 5.1 Ch6 (page 115) Created by Mr. Lafferty Maths Dept.

  30. Starter Questions Q2. Find the area of the first shape and the perimeter of the second shape. (p - 2) (y – 5) 3 9 Created by Mr. Lafferty Maths Dept.

  31. Box Plot Learning Intention Success Criteria • Be able to construct a box plot using the five figure summary data. • 1. To show how to construct a box plot using the five figure summary. Created by Mr. Lafferty Maths Dept.

  32. Q2 Q1 Q3 Upper Quartile = 9 Lower Quartile = 5½ Median = 8 Finding the median, quartiles and inter-quartile range. Example 1: Find the median and quartiles for the data below. 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10 Order the data 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Inter- Quartile Range = 9 - 5½ = 3½

  33. Q2 Q3 Q1 Upper Quartile = 10 Lower Quartile = 4 Median = 8 Finding the median, quartiles and inter-quartile range. Example 2: Find the median and quartiles for the data below. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Order the data 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Inter- Quartile Range = 10 - 4 = 6

  34. Box and Whisker Diagrams. Box plots are useful for comparing two or more sets of data like that shown below for heights of boys and girls in a class. Anatomy of a Box and Whisker Diagram. Median Whisker Whisker Box Boys cm Girls 130 140 150 160 170 180 190 4 5 6 7 8 9 10 11 12 Lower Quartile Upper Quartile Lowest Value Highest Value

  35. Drawing a Box Plot. Example 1: Draw a Box plot for the data below 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Q2 Q1 Q3 Upper Quartile = 9 Lower Quartile = 5½ Median = 8 4 5 6 7 8 9 10 11 12

  36. Drawing a Box Plot. Example 2: Draw a Box plot for the data below 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Q2 Q3 Q1 Upper Quartile = 10 Lower Quartile = 4 Median = 8 12 13 3 4 5 6 7 8 9 10 11 14 15

  37. Drawing a Box Plot. Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data. Q2 Q3 Q1 137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186 Upper Quartile = 180 Lower Quartile = 158 Median = 171 130 140 150 160 170 180 cm 190

  38. Drawing a Box Plot. Question: Gemma recorded the heights in cm of girls in the same class and constructed a box plot from the data. The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers. Boys cm Girls 1.The girls are taller on average. 2.The boys are taller on average. 130 140 150 160 170 180 190 3.The girls show less variability in height. 4.The smallest person is a girl 5.The boys show less variability in height. 6.The tallest person is a boy

  39. Box Plot Now try Ex 6.1 Ch6 (page 117) Created by Mr. Lafferty Maths Dept.

  40. Starter Questions Created by Mr. Lafferty Maths Dept.

  41. Scattergraphs Construction of Scattergraphs Learning Intention Success Criteria • Construct and understand the Key-Points of a scattergraph. • To construct a scattergraph and answer questions based on it. 2. Know the term positive and negative correlation. Created by Mr. Lafferty Maths Dept.

  42. This scattergraph shows the heights and weights of a sevens football team Scattergraphs Write down height and weight of each player. Construction of Scattergraph Bob Tim Joe Sam Gary Dave Jim Created by Mr. Lafferty Maths Dept.

  43. x x x x x x x x x x x x Scattergraphs Construction of Scattergraph When two quantities are strongly connected we say there is a strong correlation between them. Best fit line Best fit line Strong positive correlation Strong negative correlation Created by Mr. Lafferty Maths Dept.

  44. Draw in the best fit line Car Price (£1000) Age 1 9 1 8 2 8 3 7 3 6 3 5 4 5 4 4 5 2 Scattergraphs Construction of Scattergraph Is there a correlation? If yes, what kind? Strong negative correlation Created by Mr. Lafferty Maths Dept.

  45. Scattergraphs Construction of Scattergraphs Now try Ex 7.1 Ch6 (page 120) Created by Mr. Lafferty Maths Dept.

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