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**S5 Int2**Relative Frequency Tables Charts & Graphs Reading Pie Charts Constructing Pie Charts Cumulative Frequency Tables Cumulative Frequency Graphs www.mathsrevision.com Dot Plots Five Figure Summary Box Plots Created by Mr. Lafferty Maths Dept.**S5 Int2**Starter Questions • Factorize 3x3 – 9 • A car depreciates at 15% per year. How much is it worth after 3 years, if it cost £12000 initially? • Write 85% as a common fraction in its simplest form. www.mathsrevision.com Created by Mr Lafferty Maths Dept**Relative Frequency**S5 Int2 Tables Charts & Graphs Learning Intention Success Criteria • Know the term relative frequency. • To understand the term relative frequency. • Calculate relative frequency from data given. www.mathsrevision.com Created by Mr Lafferty Maths Dept**Relative Frequency always added up to 1**Relative Frequency S5 Int2 Relative Frequency How often an event happens compared to the total number of events. Tables Charts & Graphs Example : Wine sold in a shop over one week www.mathsrevision.com 0.5 180 ÷ 360 = 0.25 90 ÷ 360 = 0.25 90 ÷ 360 = 1 360 Created by Mr Lafferty Maths Dept**Relative Frequency**S5 Int2 Relative Frequency How often an event happens compared to the total number of events. Tables Charts & Graphs Example Calculate the relative frequency for boys and girls born in the Royal Infirmary hospital in December 2007. www.mathsrevision.com Relative Frequency adds up to 1 500 1 0.4 0.6 Created by Mr Lafferty Maths Dept**Question 1 Page 138**Tables Charts & Graphs S5 Int2 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. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Tables Charts & Graphs**S5 Int2 We add the frequencies to get a total www.mathsrevision.com 300 Created by Mr. Lafferty Maths Dept.**Tables Charts & Graphs**S5 Int2 Then we work out the fraction of time each sport takes www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Tables Charts & Graphs**Relative Frequency S5 Int2 Now try Exercise 1 Ch10 (page 138) www.mathsrevision.com Created by Mr Lafferty Maths Dept**S5 Int2**Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Pie Charts**Reading Pie Charts S5 Int2 Learning Intention Success Criteria • Find the relative frequency for an angle with in a Pie Chart. • 1. To interpret information from Pie Charts. • 2. Use relative frequency to interpret Pie Chart information. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Reading Pie Charts**Pie charts can be thought of as circle graphs. Two step process • 1. Work out relative frequency of each angle. • 2. Then multiply by the total amount that the circle represents. Created by Mr. Lafferty**Tea**Coffee Tea 72o Squash 144o Milk 108o Coffee Squash 36o Milk Pie Charts 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. Use the two step process Created by Mr. Lafferty**Tables Charts & Graphs**Reading Pie Charts S5 Int2 Now try Exercise 2 Ch10 (page 140) www.mathsrevision.com Created by Mr Lafferty Maths Dept**S5 Int2**Starter Questions 2cm 3cm 29o 4cm www.mathsrevision.com A C 70o 53o 8cm B Created by Mr. Lafferty Maths Dept.**Pie Charts**Constructing Pie Charts S5 Int2 Learning Intention Success Criteria • Find fractions of 360o. • 1. To construct an accurate Pie-Chart from a given table using fractions of 360o. • 2. Use these fractions to construct a Pie Chart given in a table. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Favourite Sport**Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 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. Relative Frequency 75 ÷ 300 × 360 = 90° 90 ÷ 300 × 360 = 108° 45 ÷ 300 × 360 = 54° 60 ÷ 300 × 360 = 72° 30 ÷ 300 × 360 = 36° Total 300 Created by Mr. Lafferty Maths Dept.**Drawing Pie Charts**Favourite Sport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 Created by Mr. Lafferty Maths Dept.**Drawing Pie Charts**Favourite Sport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 Rugby Created by Mr. Lafferty Maths Dept.**Drawing Pie Charts**Favourite Sport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Rugby Total 300 Created by Mr. Lafferty Maths Dept.**Drawing Pie Charts**Favourite Sport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Rugby Total 300 Football Created by Mr. Lafferty Maths Dept.**Drawing Pie Charts**Favourite Sport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Rugby Football Total 300 Created by Mr. Lafferty Maths Dept.**Drawing Pie Charts**Favourite Sport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Rugby Football Total 300 Cricket Created by Mr. Lafferty Maths Dept.**Drawing Pie Charts**Favourite Sport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Rugby Football Total 300 Cricket Created by Mr. Lafferty Maths Dept.**Drawing Pie Charts**Favourite Sport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Rugby Football Total 300 Cricket Squash Ice Hockey Created by Mr. Lafferty Maths Dept.**Drawing Pie Charts**Favourite Sport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Football Rugby Total 300 90o 108o 36o 54o 72o Squash Cricket Ice Hockey Created by Mr. Lafferty Maths Dept.**Worksheet Constructing a Pie Chart**Drawing Pie Charts FavouriteSport 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 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total Created by Mr. Lafferty Maths Dept.**Constructing Pie Charts**S5 Int2 Now try Exercise 3 Ch10 (page 141) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**S5 Int2**Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Cumulative Frequency Tables**S5 Int2 Learning Intention Success Criteria • Add a third cumulative column to a frequency table. • 1. To explain how to construct a cumulative Frequency Table. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Cumulative Frequency Tables**S5 Int2 Example : This table shows the number of cars sold by a motor dealership 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. This makes it easier to get the total number of items. 2 3 5 3 1 6 You have 1 minute to come up with a question you can easily answer from the table. www.mathsrevision.com 4 6 12 5 5 17 6 8 25 7 4 29 Created by Mr. Lafferty Maths Dept.**Cumulative Frequency Tables**1 minute to come up with a question S5 Int2 Construct a cumulative frequency table for this data Shoe Size 1 1 1 4 5 2 5 10 3 www.mathsrevision.com 14 24 4 2 26 5 4 30 6 30 Created by Mr. Lafferty Maths Dept.**Cumulative Frequency Tables**S5 Int2 Now try Exercise 4 Ch10 (page 143) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**S5 Int2**Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Cumulative Frequency Tables**S5 Int2 Learning Intention Success Criteria • Be able to construct a cumulative frequency graph. • 1. To show how to construct a cumulative frequency graph from cumulative frequency table. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**How to draw a cumulative frequency graph**Cumulative Frequency Graphs S5 Int2 www.mathsrevision.com**Plot**How to construct a Cumulative Frequency Graph S5 Int2 www.mathsrevision.com**Cumulative**Frequency Graphs S5 Int2 Sometimes called an S – curve graph Write down a question you could ask about this graph. www.mathsrevision.com**Cumulative**Frequency Graphs S5 Int2 Now try Exercise 5 Ch10 (page 145) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**S5 Int2**Starter Questions 10cm www.mathsrevision.com 90o Created by Mr. Lafferty Maths Dept.**Dot Plot**S5 Int2 Learning Intention Success Criteria • 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.. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**Dot plots are a very simple yet useful way of getting a feel**for data using the number line. Dot Plot S5 Int2 www.mathsrevision.com**Write down as many key points that you can deduce from the**plot. Lowest value is 56 BPM. Highest value is 74 BPM. Mode is 62. Median is also 62. Distribution is fairly flat. Dot Plot 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 www.mathsrevision.com 50 60 70 80**By looking at the shape of the distribution try and describe**the 6 types we have. Dot Plot S5 Int2 Common expressions for various dot plots. Symmetrical distribution Widely spread out distribution www.mathsrevision.com Uniform distribution Tightly clustered distribution Skewed to the right distribution Skewed to the left distribution**Dot Plot**S5 Int2 Now try Exercise 6 Ch10 (page 147) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.**S5 Int2**Starter Questions www.mathsrevision.com 33o Created by Mr. Lafferty Maths Dept.**Five Figure Summary**S5 Int2 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 summary information for a set of data. www.mathsrevision.com • Be able to work • L , H, Q1, Q2 and Q3 • For a set of data Created by Mr. Lafferty Maths Dept.**When a set of numbers are put in ORDER,**it can be summarised by quoting five figures. Five Figure Summary S5 Int2 1. The highest number (H) 2. The lowest number (L) www.mathsrevision.com 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)**Five Figure Summary**Q2 = Median (middle value) Q1 = lower middle value S5 Int2 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 www.mathsrevision.com 7 L = 2 H = 10 2 4 5 6 7 7 9 10 Created by Mr. Lafferty Maths Dept.**Five Figure Summary**Q2 = Median (middle value) Q1 = lower middle value S5 Int2 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 www.mathsrevision.com 7 7 8 L = H = 10 2 2 4 5 6 9 10 Created by Mr. Lafferty Maths Dept.