# Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Statistics Mean, Median, Mode and Range of Data Set Class Intervals Frequency Tables www.mathsrevision.com.

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Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Statistics Mean, Median, Mode and Range of Data Set Class Intervals Frequency Tables www.mathsrevision.com Mean from a Frequency Table Cumulative Frequency Tables and Median Stem and Leaf Diagrams Pie-Chart Scatter Graphs Probability

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 8cm 5cm 2cm 4cm

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 2.Calculate values for the Mean, Median, Mode and Range in a context. 1.We are learning the terms Mean Median, Mode and Range for a set of data. 1.Understand the differences between the terms Mean, Median, Mode and Range. Different Averages

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Find the mean of the set of data 1, 1, 1, 1, 2, 3, 26 Can you see that this is not the most suitable of averages since five out of the six numbers are all below the mean of 5 Different Averages

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com An average should indicate a “measure of central tendency” but should also indicate what the distribution of data looks like. This is why we have 3 different types of averages to consider 1.The Mean 2.The Median (put the data in order then find the MIDDLE value) 3.The Mode (the number that appears the most) For the above data the Median or Mode is a better average = 1 Different Averages

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Different Averages Example : Find the mean, median, mode and range for the set of data. Range = Highest number – Lowest Number 10, 2, 14, 1, 14, 7

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 1 Ch17 (page 73) www.mathsrevision.com Different Averages

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 6h 2a

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Be able to Construct Frequency Table 1. We are learning how to construct and interpret Frequency Tables. Class Intervals Frequency Tables 2.Be able to Interpret information contained in a Frequency Table.

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Class Intervals When a set of data is large, the numbers have to be grouped into “class intervals”. Each interval must have the same number of values Ideally, there should be between 6 to 10 intervals Frequency Tables We will now construct a Frequency Table

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Class Intervals Frequency Tables Class Intervals TallyFrequency 1223415577 1532405169 2112164356 7132753442 5576217322 5641192047 7817 Example : The test scores for a class are given below. Construct a Frequency Table for the results. 1 6 3 5 6 6 5 10-19 20-29 30-39 40-49 50-59 60-69 70-79 Choose suitable Class interval

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 2 Ch17 (page 76) www.mathsrevision.com Statistics Working Out Statistics

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Be able to add a third column to a frequency table. 1. We are learning to work out the mean from a Frequency Table. Frequency Tables Working Out the Mean 2.Calculate the mean from a frequency Table.

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com No of Coins ( c ) Freq.(f) Example : This table shows the number of coins in the pockets of some children. 5 1 2 16 3 5 1 2 3 4 5 Totals Frequency Tables Working Out the Mean Adding a third column to this table will help us find the total number of coins and the ‘Mean’. 5 x 1 =5 1 x 3 = 3 2 x 5 = 10 3 x 4 = 12 5 x 2 = 10 40 f x C

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com No of Sibling s ( S ) Freq.(f) Example : This table shows the number of brothers and sisters of pupils in an S2 class. 9 6 1 30 1 13 0 1 2 3 5 Totals Frequency Tables Working Out the Mean Adding a third column to this table will help us find the total number of siblings and the ‘Mean’. 0 x 9 =0 2 x 6 = 12 5 x 1 = 5 3 x 1 = 3 1 x 13 = 13 33 S x f

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 3 Ch17 (page 78) www.mathsrevision.com Frequency Tables Working Out the Mean

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Be able to add a third cumulative column to a frequency table. 1. We are learning how to calculate the median Frequency Table. Cumulative Frequency Tables 2.Be able to calculate the median from a Cumulative Frequency Table. Working Out The Median

Level 3 / 4 17-Apr-15Created 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 eggs laid by a clutch of chickens 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 C. Freq. Total so far Cumulative Frequency Tables Working Out The Median 7 68 4 25 29 When was the Median egg collected. Collected on Day 5

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 4 Ch17 (page 80) www.mathsrevision.com Frequency Tables Working Out the Mean

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria Pie Charts Constructing Pie Charts 1. We are learning to display data in the form of a Pie- Chart. 1.Be able to calculate a fraction of 360 o. 2.Understand the process of constructing a Pie Chart.

17-Apr-15Created 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

17-Apr-15Created 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

17-Apr-15Created 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

17-Apr-15Created 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

17-Apr-15Created 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

17-Apr-15Created 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

17-Apr-15Created 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

17-Apr-15Created 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

17-Apr-15Created 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

17-Apr-15Created 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

Total90 Drawing Pie Charts In a survey, people were asked to indicate which one of five musical instruments they played. The information is given in the table. Display the information in a pie chart. Guitar Violin Recorder Drum 35 10 15 5 Musical Instrument Keyboard25

Total90 Guitar Drawing Pie Charts In a survey, people were asked to indicate which one of five musical instruments they played. The information is given in the table. Display the information in a pie chart. Guitar Violin Recorder Drum 35 10 15 5 Musical Instrument Keyboard25

Total90 Drawing Pie Charts In a survey, people were asked to indicate which one of five musical instruments they played. The information is given in the table. Display the information in a pie chart. Guitar Violin Recorder Drum 35 10 15 5 Musical Instrument Keyboard25 Guitar

Total90 Drawing Pie Charts In a survey, people were asked to indicate which one of five musical instruments they played. The information is given in the table. Display the information in a pie chart. Guitar Violin Recorder Drum 35 10 15 5 Musical Instrument Keyboard25 Guitar Violin

Total90 Drawing Pie Charts In a survey, people were asked to indicate which one of five musical instruments they played. The information is given in the table. Display the information in a pie chart. Guitar Violin Recorder Drum 35 10 15 5 Musical Instrument Keyboard25 Guitar Violin

Total90 Drawing Pie Charts In a survey, people were asked to indicate which one of five musical instruments they played. The information is given in the table. Display the information in a pie chart. Guitar Violin Recorder Drum 35 10 15 5 Musical Instrument Keyboard25 Guitar Violin Recorder

Total90 Drawing Pie Charts In a survey, people were asked to indicate which one of five musical instruments they played. The information is given in the table. Display the information in a pie chart. Guitar Violin Recorder Drum 35 10 15 5 Musical Instrument Keyboard25 Guitar Violin Recorder

Total90 Drawing Pie Charts In a survey, people were asked to indicate which one of five musical instruments they played. The information is given in the table. Display the information in a pie chart. Guitar Violin Recorder Drum 35 10 15 5 Musical Instrument Keyboard25 Guitar Violin Recorder Drum Keyboard

Total90 Drawing Pie Charts In a survey, people were asked to indicate which one of five musical instruments they played. The information is given in the table. Display the information in a pie chart. Guitar Violin Recorder Drum 35 10 15 5 Musical Instrument Keyboard25 Guitar Violin Recorder Drum Keyboard 140 o 100 o 60 o 40 o 20 o

Drawing Pie Charts Total120 Vanilla Banana Chocolate Strawberry 13 22 28 57 Ice-cream Sales The information in the table shows sales of ice-cream from an ice-cream van one Saturday afternoon in the summer. Display the information in a pie chart.

Drawing Pie Charts Total120 Vanilla Banana Chocolate Strawberry 13 22 28 57 Ice-cream Sales The information in the table shows sales of ice-cream from an ice-cream van one Saturday afternoon in the summer. Display the information in a pie chart. Vanilla

Drawing Pie Charts Total120 Vanilla Banana Chocolate Strawberry 13 22 28 57 Ice-cream Sales The information in the table shows sales of ice-cream from an ice-cream van one Saturday afternoon in the summer. Display the information in a pie chart. Vanilla

Drawing Pie Charts Total120 Vanilla Banana Chocolate Strawberry 13 22 28 57 Ice-cream Sales The information in the table shows sales of ice-cream from an ice-cream van one Saturday afternoon in the summer. Display the information in a pie chart. Vanilla Banana

Drawing Pie Charts Total120 Vanilla Banana Chocolate Strawberry 13 22 28 57 Ice-cream Sales The information in the table shows sales of ice-cream from an ice-cream van one Saturday afternoon in the summer. Display the information in a pie chart. Banana Vanilla

Drawing Pie Charts Total120 Vanilla Banana Chocolate Strawberry 13 22 28 57 Ice-cream Sales The information in the table shows sales of ice-cream from an ice-cream van one Saturday afternoon in the summer. Display the information in a pie chart. Banana Vanilla Chocolate Strawberry

Drawing Pie Charts Total120 Vanilla Banana Chocolate Strawberry 13 22 28 57 Ice-cream Sales The information in the table shows sales of ice-cream from an ice-cream van one Saturday afternoon in the summer. Display the information in a pie chart. Banana Vanilla Chocolate Strawberry 39 o 66 o 84 o 171 o

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 5 Ch17 (page 81) www.mathsrevision.com Statistics Working Out Statistics

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.We are learning to display data in the form of a Stem- Leaf Graph. 1. Be able Construct and understand the Key-Points of a Stem-Leaf Graph. Stem Leaf Graphs Construction of Stem-Leaf 2. Answer questions based on the graph.

Stem and Leaf Diagrams Stem and leaf diagrams are a pictorial way of showing statistics The important parts of a stem and leaf diagram are The Title The stem The leaves in order starting from the stem The number of items The key Class Maths Marks 12341234 0 2 2 6 8 3 4 5 9 9 0 0 2 6 8 9 9 0 4 5 n = 20 2 / 3 means a mark of 23

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Stem Leaf Graphs Construction of Stem and Leaf A Stem – Leaf graph is another way of displaying information : This stem and leaf graph shows the ages of people waiting in a queue at a post office 2468 3013 4445679 50349 61456 stem leaves Ages n = 20 Key : 2 4 means 24 How many people in the queue? How many people in their forties? 20 6

A group of students were asked how much pocket money they get. The results were. £6.60 £6.90 £6.20 £5.80 £7.40 £5.60 £6.70 £7.20 £6.10 £6.20 £5.90 £6.00 £7.20 £5.80 £6.30 Draw a Stem and Leaf diagram to show this 6 8 8 9 0 1 2 2 3 6 7 9 2 2 4 n = 156 / 2 means £6.20 567567 Pocket money Note this gives us the same diagram as the previous example. This shows the importance of the title and key.

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Stem Leaf Graphs Construction of Stem and Leaf Example : Construct a stem and leaf graphs for the following weights in (kgs) : 12 2 3 4 5 stem leaves Weight (kgs) n = 20 Key : 2 3 means 23 2 1 0 3 39 22 011 1455 55 57 12405754551355153255 3215412140 2341295112 12121315152123293232 4040414151 5455555557

Stem and Leaf diagrams can be used to compare 2 sets of data. To do this we draw a back to back stem and leaf diagram. 0123401234 9 8 8 5 3 9 4 4 5 2 0 6 4 3 1 1 0 7 3 3 6 8 9 1 2 2 2 5 5 8 0 0 1 1 6 7 3 7 7 1 Maths marks for class 1AMaths marks for class 1B n = 20 3/2 means a mark of 32 How many students in 1A had a mark of 31? How many students in 1B had a mark of 12? Which class appears to be best at Maths? 2 3 1A

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 6 Ch17 (page 83) www.mathsrevision.com Statistics Stem Leaf

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.We are learning to display data in the form of a scattergraph. 1.Be able to construct and understand the Key-Points of a scattergraph. Scattergraphs Construction of Scattergraphs 2. Know the term positive and negative correlation.

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Scattergraphs Construction of Scattergraph Sam Jim Tim Gary Joe Dave Bob This scattergraph shows the heights and weights of a sevens football team Write down height and weight of each player.

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Scattergraphs Construction of Scattergraph x x x x x x Strong positive correlation x x x x x x Strong negative correlation Best fit line Best fit line When two quantities are strongly connected we say there is a strong correlation between them.

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Scattergraphs Construction of Scattergraph Is there a correlation? If yes, what kind? Age Price (£1000) 3 1 1 2 3 3 4 4 5 9 8 8 7 6 5 5 4 2 S t r o n g n e g a t i v e c o r r e l a t i o n Draw in the best fit line

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 7 Ch17 (page 85) www.mathsrevision.com Scattergraphs Construction of Scattergraphs

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com 55 o xoxo 47 o

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Understand the term likelihood line and probability. likelihood line and probability. 1.We are learning how a likelihood line helps to understand probability. 2.Decide where certain events should lie on the likelihood line. likelihood line. www.mathsrevision.com Probability Likelihood Line 3.Calculate simple probabilities.

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 10.50 CertainEvensImpossible Not very likely Very likely Winning the Lottery School Holidays Baby Born A Boy Seeing a butterfly In July Go back in time Probability Likelihood Line

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 10.50 CertainEvensImpossible Not very likely Very likely Everyone getting 100 % in test Homework Every week Toss a coin That land Heads It will Snow in winter Going without Food for a year. Probability Likelihood Line

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Now Round the Class Exercise 8 Ch17 (page 87) www.mathsrevision.com Statistics and Probability

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Probability Calculating Probability Probability can be thought of as a simple fraction or decimal. It always lies between 0 and 1. 0 meaning impossible ( could not happen) 1 meaning certain ( will definitely happen)

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Probability Calculating Probability Example : A boy tossed a coin. What is the probability that it is heads. Example : There are 3 red and 4 green balls in a bag. What is the probability a green ball is picked.

Level 3 / 4 17-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 9 Ch17 (page 87) www.mathsrevision.com Probability Calculating Probability

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