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Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts www.mathsrevision.com Constructing Pie Charts Cumulative Frequency Tables Dot Plots Cumulative Frequency Graphs Five Figure Summary Box Plots S5 Int2

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Starter Questions 3-Jun-14Created by Mr Lafferty Maths Dept www.mathsrevision.com S5 Int2 1Factorize 3x 3 – 9 2A car depreciates at 15% per year. How much is it worth after 3 years, if it cost £12000 initially? 3Write 85% as a common fraction in its simplest form.

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Tables Charts & Graphs 3-Jun-14Created by Mr Lafferty Maths Dept Learning Intention Success Criteria 1.Know the term relative frequency. 1.To understand the term relative frequency. 2.Calculate relative frequency from data given. www.mathsrevision.com Relative Frequency S5 Int2

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Tables Charts & Graphs 3-Jun-14Created by Mr Lafferty Maths Dept www.mathsrevision.com Relative Frequency How often an event happens compared to the total number of events.CountryFrequency Relative Frequency France180 Italy90 Spain90 Total Example : Wine sold in a shop over one week 180 ÷ 360 = 90 ÷ 360 = 90 ÷ 360 = 360 0.25 0.25 0.5 1 Relative Frequency always added up to 1 S5 Int2

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Tables Charts & Graphs 3-Jun-14Created by Mr Lafferty Maths Dept www.mathsrevision.com Relative Frequency How often an event happens compared to the total number of events.BoysGirlsTotalFrequency300200 Relative Frequency Example Calculate the relative frequency for boys and girls born in the Royal Infirmary hospital in December 2007. Relative Frequency 500 0.6 0.4 1 Relative Frequency adds up to 1 S5 Int2

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Question 1 Page 138 Created by Mr. Lafferty Maths Dept. This question gives a breakdown of 5 hours on watching sport on TV. The time is recorded to the nearest 5 minutes. First, we create a table of values and work out the frequencies. SPORTFREQUENCY (M) REL. FREQCY Football120 Golf60 Swimming45 Athletics30 Equestrian15 Others30 TOTAL Tables Charts & Graphs www.mathsrevision.com S5 Int2

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Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. We add the frequencies to get a total SPORTFREQUENCY (M) REL. FREQCY Football120 Golf60 Swimming45 Athletics30 Equestrian15 Others30 TOTAL www.mathsrevision.com S5 Int2 300

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SPORTFREQUENCY (M) REL. FREQCY Football120120 ÷ 300 = 0.4 Golf60 60 ÷ 300 = 0.2 Swimming45 45 ÷ 300 = 0.15 Athletics30 30 ÷ 300 = 0.1 Equestrian15 15 ÷ 300 = 0.05 Others30 TOTAL300 SPORTFREQUENCY (M) REL. FREQCY Football120 Golf60 Swimming45 Athletics30 Equestrian15 Others30 TOTAL300 3-Jun-14Created by Mr. Lafferty Maths Dept. Then we work out the fraction of time each sport takes SPORTFREQUENCY (M) REL. FREQCY Football120120 ÷ 300 = 0.4 Golf60 Swimming45 Athletics30 Equestrian15 Others30 TOTAL300 SPORTFREQUENCY (M) REL. FREQCY Football120120 ÷ 300 = 0.4 Golf60 60 ÷ 300 = 0.2 Swimming45 Athletics30 Equestrian15 Others30 TOTAL300 SPORTFREQUENCY (M) REL. FREQCY Football120120 ÷ 300 = 0.4 Golf60 60 ÷ 300 = 0.2 Swimming45 45 ÷ 300 = 0.15 Athletics30 Equestrian15 Others30 TOTAL300 SPORTFREQUENCY (M) REL. FREQCY Football120120 ÷ 300 = 0.4 Golf60 60 ÷ 300 = 0.2 Swimming45 45 ÷ 300 = 0.15 Athletics30 30 ÷ 300 = 0.1 Equestrian15 Others30 TOTAL300 SPORTFREQUENCY (M) REL. FREQCY Football120120 ÷ 300 = 0.4 Golf60 60 ÷ 300 = 0.2 Swimming45 45 ÷ 300 = 0.15 Athletics30 30 ÷ 300 = 0.1 Equestrian15 15 ÷ 300 = 0.05 Others30 30 ÷ 300 = 0.1 TOTAL300 Tables Charts & Graphs www.mathsrevision.com S5 Int2

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3-Jun-14Created by Mr Lafferty Maths Dept Now try Exercise 1 Ch10 (page 138) www.mathsrevision.com Tables Charts & Graphs Relative Frequency S5 Int2

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Starter Questions Starter Questions 3-Jun-14 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria Pie Charts Reading Pie Charts 1. To interpret information from Pie Charts. 1.Find the relative frequency for an angle with in a Pie Chart. 2.Use relative frequency to interpret Pie Chart information. S5 Int2

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3-Jun-14Created by Mr. Lafferty12 Pie charts can be thought of as circle graphs. Reading Pie Charts 1.Work out relative frequency of each angle. 2.Then multiply by the total amount that the circle represents. Two step process

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3-Jun-14Created by Mr. Lafferty13 A drinks machine dispenses 500 drinks on a Monday. The information is displayed in the pie chart. Use the information to find the number of each drink sold. Tea 72 o 36 o Milk Squash 144 o 108 o Coffee Pie Charts Milk Squash Use the two step process Coffee Tea

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3-Jun-14Created by Mr Lafferty Maths Dept Now try Exercise 2 Ch10 (page 140) www.mathsrevision.com Tables Charts & Graphs Reading Pie Charts S5 Int2

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Starter Questions Starter Questions 3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2 A B C 8cm 53 o 70 o 4cm 2cm 3cm 29 o

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria Pie Charts Constructing Pie Charts 1. To construct an accurate Pie-Chart from a given table using fractions of 360 o. 1.Find fractions of 360 o. 2.Use these fractions to construct a Pie Chart given in a table. S5 Int2

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3-Jun-14Created by Mr. Lafferty Maths Dept. 75 ÷ 300 × 360 = 90° Relative Frequency 90 ÷ 300 × 360 = 108° 45 ÷ 300 × 360 = 54° 60 ÷ 300 × 360 = 72° 30 ÷ 300 × 360 = 36° Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 Total300

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3-Jun-14 Created by Mr. Lafferty Maths Dept. Total300 Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30

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3-Jun-14 Created by Mr. Lafferty Maths Dept. Total300 Rugby Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30

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3-Jun-14 Created by Mr. Lafferty Maths Dept. Total300 Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 Rugby

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3-Jun-14Created by Mr. Lafferty Maths Dept. Total300 Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 Football Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby

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3-Jun-14Created by Mr. Lafferty Maths Dept. Total300 Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 Rugby Football

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3-Jun-14 Created by Mr. Lafferty Maths Dept. Total300 Cricket Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 Rugby Football

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3-Jun-14 Created by Mr. Lafferty Maths Dept. Total300 Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket

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3-Jun-14 Created by Mr. Lafferty Maths Dept. Total300 Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 Ice Hockey Squash Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket

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3-Jun-14 Created by Mr. Lafferty Maths Dept. Total300 Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 90 o 108 o 54 o 72 o 36 o Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket Ice Hockey Squash

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3-Jun-14 Created by Mr. Lafferty Maths Dept. Total Drawing Pie Charts In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart. Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 Worksheet Constructing a Pie Chart

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3-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 3 Ch10 (page 141) www.mathsrevision.com Constructing Pie Charts S5 Int2

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Starter Questions Starter Questions 3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Add a third cumulative column to a frequency table. 1. To explain how to construct a cumulative Frequency Table. Cumulative Frequency Tables S5 Int2

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3-Jun-14Created by Mr. Lafferty Maths Dept. You have 1 minute to come up with a question you can easily answer from the table. www.mathsrevision.comDayFreq.(f) Example : This table shows the number of cars sold by a motor dealership each day over a seven day period. 2 1 5 6 3 1 2 3 4 5 A third column is added to keep a running total. This makes it easier to get the total number of items. 2 6 17 12 5 Cum. Freq. Total so far Cumulative Frequency Tables 7 68 4 25 29 S5 Int2

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3-Jun-14 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Cumulative Frequency Tables S5 Int2 Construct a cumulative frequency table for this data FrequencyC. Freq. Total 1 2 3 4 5 6 Shoe Size 1 4 5 14 2 4 1 5 10 24 26 30 30 1 minute to come up with a question

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3-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 4 Ch10 (page 143) www.mathsrevision.com Cumulative Frequency Tables S5 Int2

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Starter Questions Starter Questions 3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2 Waist SizesFrequency 287 3012 3223 3414

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Be able to construct a cumulative frequency graph. 1. To show how to construct a cumulative frequency graph from cumulative frequency table. Cumulative Frequency Tables S5 Int2

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Cumulative Frequency Graphs How to draw a cumulative frequency graph www.mathsrevision.com S5 Int2

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Km travelled on 1 gallon (mpg) Frequency Cumulative Frequency 2033 25811 301930 352353 401669 45776 50480 How to construct a Cumulative Frequency Graph Plot www.mathsrevision.com S5 Int2

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Write down a question you could ask about this graph. Cumulative Frequency Graphs Sometimes called an S – curve graph www.mathsrevision.com S5 Int2

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3-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 5 Ch10 (page 145) www.mathsrevision.com S5 Int2 Cumulative Frequency Graphs

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Starter Questions Starter Questions 3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2 10cm 90 o

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Be able to construct a dot and identify the key features of various plots. 1. To show how to construct a dot plot and identify key feature.. Dot Plot S5 Int2

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Dot Plot Dot plots are a very simple yet useful way of getting a feel for data using the number line. www.mathsrevision.com S5 Int2

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Dot Plot www.mathsrevision.com S5 Int2 Example :A group of students measure their pulse rates when resting. The rates are 66, 69, 62, 58, 74, 56, 67, 72, 61, 62, 59 50607080 Write down as many key points that you can deduce from the plot. 1.Lowest value is 56 BPM. 2.Highest value is 74 BPM. 3.Mode is 62. 4.Median is also 62. 5.Distribution is fairly flat.

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Dot Plot www.mathsrevision.com S5 Int2 Common expressions for various dot plots. Symmetrical distributionWidely spread out distribution Uniform distributionTightly clustered distribution Skewed to the right distributionSkewed to the left distribution By looking at the shape of the distribution try and describe the 6 types we have.

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3-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 6 Ch10 (page 147) www.mathsrevision.com S5 Int2 Dot Plot

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Starter Questions Starter Questions 3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2 33 o

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Understand the terms L, H, Q 1, Q 2 and Q 3. 1. To explain the meaning and show how to workout the five summary information for a set of data. S5 Int2 Five Figure Summary 2.Be able to work L, H, Q 1, Q 2 and Q 3 For a set of data

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When a set of numbers are put in ORDER, it can be summarised by quoting five figures. www.mathsrevision.com S5 Int2 Five Figure Summary 1. The highest number(H) 2. The lowest number(L) 3. The median, the number that halves the list (Q 2 ) 4. The upper quartile, the median of the upper half (Q 3 ) 5. The lower quartile, the median of the lower half (Q 1 )

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2 Five Figure Summary Example Find the five figure summary for the data. 2, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10 L = Q 3 = 24556 7 778910 Q 2 = Median (middle value) Q 2 = H = Q 1 = 102 785 The 11 numbers are already in order ! Q 3 = upper middle value Q 1 = lower middle value

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2 Five Figure Summary Example Find the five figure summary for the data. 2, 4, 5, 5, 6, 7, 7, 8, 9, 10 L = Q 3 = 24556778910 Q 2 = Median (middle value) Q 2 = H = Q 1 = 10 2 6.5 8 5 The 10 numbers are already in order ! Q 3 = upper middle value Q 1 = lower middle value

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2 Five Figure Summary Example Find the five figure summary for the data. 2, 4, 5, 5, 6, 7, 8, 9, 10 L = Q 3 = 2455 6 78910 Q 2 = Median (middle value) Q 2 = H = Q 1 = 10 2 68.5 4.5 The 9 numbers are already in order ! Q 3 = upper middle value Q 1 = lower middle value

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3-Jun-14Created by Mr. Lafferty Maths Dept. Now try Exercise 7 Ch10 (page 150) www.mathsrevision.com S5 Int2 Five Figure Summary

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Starter Questions Starter Questions 3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com S5 Int2

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3-Jun-14Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.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. S5 Int2 Box Plot

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Two middle values so take the mean. 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 Median drive = 90 yards 50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 135, 140 Ordered data

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Finding the median, quartiles and inter-quartile range. 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Order the data Inter- Quartile Range = 9 - 5½ = 3½ Example 1: Find the median and quartiles for the data below. Lower Quartile = 5½ Q1Q1 Upper Quartile = 9 Q3Q3 Median = 8 Q2Q2

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Upper Quartile = 10 Q3Q3 Lower Quartile = 4 Q1Q1 Median = 8 Q2Q2 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Finding the median, quartiles and inter-quartile range. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Order the data Inter- Quartile Range = 10 - 4 = 6 Example 2: Find the median and quartiles for the data below.

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456789101112 Median Lower Quartile Upper Quartile Lowest Value Highest Value Box Whisker 130140150160170180190 Boys Girls cm 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.

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Lower Quartile = 5½ Q1Q1 Upper Quartile = 9 Q3Q3 Median = 8 Q2Q2 456789101112 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Example 1: Draw a Box plot for the data below Drawing a Box Plot.

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Upper Quartile = 10 Q3Q3 Lower Quartile = 4 Q1Q1 Median = 8 Q2Q2 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Example 2: Draw a Box plot for the data below Drawing a Box Plot. 34567891011 1213 1415

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Upper Quartile = 180 Q3Q3 Lower Quartile = 158 Q1Q1 Median = 171 Q2Q2 Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data. Drawing a Box Plot. 137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186 130140150160170180190cm

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2. The boys are taller on average. 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. Drawing a Box Plot. 130140150160170180190 Boys Girls cm 1. The girls are taller on average. 3. The girls show less variability in height. 4. The boys show less variability in height. 5. The smallest person is a girl 6. The tallest person is a boy

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3-Jun-14Created by Mr. Lafferty Maths Dept. Now try Ex 8 & 9 Ch10 (page 152) www.mathsrevision.com S5 Int2 Box Plot

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