Transcript Slide 1
Statistics Level 3 / 4 www.mathsrevision.com Mean, Median, Mode and Range of Data Set Class Intervals Frequency Tables Mean from a Frequency Table Cumulative Frequency Tables and Median Pie-Chart Stem and Leaf Diagrams Scatter Graphs Probability 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions Level 3 / 4 www.mathsrevision.com 1. A v id e o h a s b e r e d u c e d in t h e s a le b y 1 0 % . I t w a s £ 2 4 0 . H o w m u c h is it n o w . 2. S im p lif y t h e r a t io 7 : 5 6 4cm 3. 3 .5 % of 6 0 0 p 4. T id y u p t h e e x p r e s s io n 5w + 3y + 4w + 10w 5. 2 5cm F in d t h e a r e a a n d p e r im e t e r o f t h e s h a p e . 2cm 21-Jul-15 Created by Mr. Lafferty Maths Dept. 8cm Different Averages www.mathsrevision.com Level 3 / 4 Learning Intention Success Criteria 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. 2. Calculate values for the Mean, Median, Mode and Range in a context. 21-Jul-15 Created by Mr. Lafferty Maths Dept. Different Averages www.mathsrevision.com Level 3 / 4 T he M ean = S um o f a ll th e d a ta va lue s h o w m a n y d a ta va lue s Find the mean of the set of data 1, 1, 1, 1, 2, 3, 26 T he M ean = 1 + 1 + 1 + 1 + 2 + 3 + 26 7 =5 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 21-Jul-15 Created by Mr. Lafferty Maths Dept. Different Averages www.mathsrevision.com Level 3 / 4 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 21-Jul-15 Created by Mr. Lafferty Maths Dept. Different Averages Level 3 / 4 www.mathsrevision.com Example : Find the mean, median, mode and range for the set of data. Range = Highest number – Lowest Number 10, 2, 14, 1, 14, 7 M ean = 48 6 =8 M od e = 14 R a n g e = 14 - 1 = 13 21-Jul-15 M edian = 1, 2, 7, 10 , 14 , 14 M e d ia n = Created by Mr. Lafferty Maths Dept. 7 + 10 2 = 17 2 = 8 .5 Different Averages www.mathsrevision.com Level 3 / 4 Now try Exercise 1 Ch17 (page 73) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions Level 3 / 4 www.mathsrevision.com 1. F in d t h e p e r im e t e r a n d a r e a o f t h e s h a p e . 2a 6h 2. C a lc u la t e (a ) (-3 m ) x (-4 m ) 3. ( b ) (2 b ) x (3 a ) F in d t h e m e a n o f t h e d a t a s e t 3 ,5 ,5 , 7 ,1 0 21-Jul-15 Created by Mr. Lafferty Maths Dept. Class Intervals Frequency Tables www.mathsrevision.com Level 3 / 4 Learning Intention Success Criteria 1. We are learning how to construct and interpret Frequency Tables. 21-Jul-15 1. Be able to Construct Frequency Table 2. Be able to Interpret information contained in a Frequency Table. Created by Mr. Lafferty Maths Dept. Class Intervals Frequency Tables www.mathsrevision.com Level 3 / 4 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 We will now construct a Frequency Table 21-Jul-15 Created by Mr. Lafferty Maths Dept. Choose suitable Class interval Class Intervals Frequency Tables www.mathsrevision.com Level 3 / 4 Example : The test scores for a class Class are given below. Construct a Frequency Intervals Table for the results. 10-19 12 15 21 71 55 56 78 21-Jul-15 23 32 12 32 76 41 17 41 40 16 75 21 19 55 51 43 34 73 20 77 69 56 42 22 47 Created by Mr. Lafferty Maths Dept. Tally Frequency 6 20-29 5 30-39 3 40-49 6 50-59 5 60-69 1 70-79 6 Statistics Working Out Statistics www.mathsrevision.com Level 3 / 4 Now try Exercise 2 Ch17 (page 76) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions Level 3 / 4 www.mathsrevision.com 1. A C D p la y e r h a s b e r e d u c e d in t h e s a le b y 4 0 % . I t w a s £ 3 6 0 . H o w m u c h is it n o w . 2. S im p lif y t h e r a t io 6 : 2 8 3. 10% of £ 22 4. T id y u p t h e e x p r e s s io n (- 5 ) - (- 6 ) x 2 21-Jul-15 Created by Mr. Lafferty Maths Dept. Frequency Tables Working Out the Mean www.mathsrevision.com Level 3 / 4 Learning Intention Success Criteria 1. We are learning to work out the mean from a Frequency Table. 21-Jul-15 1. Be able to add a third column to a frequency table. 2. Calculate the mean from a frequency Table. Created by Mr. Lafferty Maths Dept. Frequency Tables Working Out the Mean www.mathsrevision.com Level 3 / 4 Example : This table shows the number No of of coins in the pockets of some children. Coins (c) Adding a third column to this table will help us find the total number of coins and the ‘Mean’. M ean N um b er of coins = 21-Jul-15 40 16 Freq. (f) fxC 1 5 5 x 1 =5 2 5 5 x 2 = 10 3 1 1x3=3 4 3 3 x 4 = 12 5 2 2 x 5 = 10 Totals 16 40 = 2 .5 c o in s Created by Mr. Lafferty Maths Dept. Frequency Tables Working Out the Mean www.mathsrevision.com Level 3 / 4 Example : This table shows the number No of of brothers and sisters of pupils in an Sibling s (S) S2 class. Adding a third column to this table 0 will help us find the total number of siblings and the ‘Mean’. 1 M e a n N um b e r o f sib lin g s = 33 30 = 1.1 sib lin g s Created by Mr. Lafferty Maths Dept. 9 Sxf 0 x 9 =0 13 1 x 13 = 13 2 6 2 x 6 = 12 3 1 3x1=3 5 1 5x1=5 Totals 21-Jul-15 Freq. (f) 30 33 Frequency Tables Working Out the Mean www.mathsrevision.com Level 3 / 4 Now try Exercise 3 Ch17 (page 78) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions Level 3 / 4 www.mathsrevision.com 1. A C D p la y e r h a s b e r e d u c e d in t h e s a le b y 4 0 % . I t w a s £ 3 6 0 . H o w m u c h is it n o w . 2. S im p lif y t h e r a t io 8 6 : 2 2 3. 30% of £ 90 4. T id y u p t h e e x p r e s s io n (4 ) x (- 9 ) 2 21-Jul-15 Created by Mr. Lafferty Maths Dept. Cumulative Frequency Tables Working Out The Median www.mathsrevision.com Level 3 / 4 Learning Intention Success Criteria 1. We are learning how to calculate the median Frequency Table. 1. Be able to add a third cumulative column to a frequency table. 2. Be able to calculate the median from a Cumulative Frequency Table. 21-Jul-15 Created by Mr. Lafferty Maths Dept. Cumulative Frequency Tables Working Out The Median www.mathsrevision.com Level 3 / 4 Example : This table shows the number of eggs laid by a clutch of chickens each day over a seven day period. A third column is added to keep a running total. This makes it easier to get the total number of items. You have 1 minute to come up with a question you can easily answer from the table. When was the Median egg collected. Collected on Day 5 21-Jul-15 Created by Mr. Lafferty Maths Dept. Day Freq. (f) C. Freq. Total so far 1 2 2 2 3 5 3 1 6 4 6 12 5 5 17 6 8 25 7 4 29 Frequency Tables Working Out the Mean www.mathsrevision.com Level 3 / 4 Now try Exercise 4 Ch17 (page 80) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions Level 3 / 4 www.mathsrevision.com 1. W h a t is t h e m e a n o f t h e n u m b e r s 16, 10, 8, 18 5 of 360 2. C a lc u la t e 3. C a lc u la t e 3 a x 8 a 4. H o w m a n y d e g r e e s in 21-Jul-15 6 1 2 , 1 3 , 1 4 , 1 , 1 6 10 Created by Mr. Lafferty Maths Dept. o f a c ir c le . Pie Charts Constructing Pie Charts www.mathsrevision.com Level 3 / 4 Learning Intention Success Criteria 1. We are learning to display data in the form of a PieChart. 21-Jul-15 1. Be able to calculate a fraction of 360o. 2. Understand the process of constructing a Pie Chart. Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Favourite Sport Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 R u g b y a n g le = F o o tb a ll a n g le = C ric k e t a n g le = 75 300 90 300 45 300 Ic e H o c k e y a n g le = S q u a s h a n g le = 21-Jul-15 x 360 90o x 3 6 0 1 0 8o x 360 54o 60 300 30 300 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. x 360 72 o x 360 36o Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Favourite Sport Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 R u g b y a n g le = F o o tb a ll a n g le = C ric k e t a n g le = 75 300 90 300 45 300 Ic e H o c k e y a n g le = S q u a s h a n g le = 21-Jul-15 x 360 90o x 3 6 0 1 0 8o x 360 54o 60 300 30 300 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. x 360 72 o x 360 36o Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Favourite Sport Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 R u g b y a n g le = F o o tb a ll a n g le = C ric k e t a n g le = 75 300 90 300 45 300 Ic e H o c k e y a n g le = S q u a s h a n g le = 21-Jul-15 x 360 90o x 3 6 0 1 0 8o x 360 54o 60 300 30 300 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. x 360 72 o x 360 36o Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Favourite Sport Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 R u g b y a n g le = F o o tb a ll a n g le = C ric k e t a n g le = 75 300 90 300 45 300 Ic e H o c k e y a n g le = S q u a s h a n g le = 21-Jul-15 x 360 90o x 3 6 0 1 0 8o x 360 54o 60 300 30 300 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. x 360 72 o x 360 36o Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Favourite Sport Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 R u g b y a n g le = F o o tb a ll a n g le = C ric k e t a n g le = 75 300 90 300 45 300 Ic e H o c k e y a n g le = S q u a s h a n g le = 21-Jul-15 x 360 90o x 3 6 0 1 0 8o x 360 54o 60 300 30 300 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. x 360 72 o x 360 36o Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Favourite Sport Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 R u g b y a n g le = F o o tb a ll a n g le = C ric k e t a n g le = 75 300 90 300 45 300 Ic e H o c k e y a n g le = S q u a s h a n g le = 21-Jul-15 x 360 90o x 3 6 0 1 0 8o x 360 54o 60 300 30 300 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. x 360 72 o x 360 36o Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Favourite Sport Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 R u g b y a n g le = F o o tb a ll a n g le = C ric k e t a n g le = 75 300 90 300 45 300 Ic e H o c k e y a n g le = S q u a s h a n g le = 21-Jul-15 x 360 90o x 3 6 0 1 0 8o x 360 54o 60 300 30 300 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. x 360 72 o x 360 36o Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Favourite Sport Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 R u g b y a n g le = F o o tb a ll a n g le = C ric k e t a n g le = 75 300 90 300 45 300 Ic e H o c k e y a n g le = S q u a s h a n g le = 21-Jul-15 x 3 6 0 1 0 8o x 360 54o 300 300 Squash x 360 90o 60 30 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. x 360 72 o x 360 36o Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Favourite Sport Rugby 75 Football 90 Cricket 45 Ice Hockey 60 Squash 30 Total 300 R u g b y a n g le = F o o tb a ll a n g le = C ric k e t a n g le = 75 300 90 300 45 300 Ic e H o c k e y a n g le = S q u a s h a n g le = 21-Jul-15 x 360 90o x 3 6 0 1 0 8o x 360 54o 60 300 30 300 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. x 360 72 o 108o 90 36o 54o 72o o x 360 36o Created by Mr. Lafferty Maths Dept. Worksheet Constructing a Pie Chart 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. Total 21-Jul-15 Created by Mr. Lafferty Maths Dept. Drawing Pie Charts Musical Instrument Guitar 35 Violin 10 Recorder 15 Drum 5 Keyboard 25 Total 90 G u ita r a n g le = V io lin a n g le = 35 90 10 90 R e c o rd e r a n g le = D ru m a n g le = x 360 40o 15 90 5 90 K e y b o a rd a n g le = x 360 140o x 360 60o x 360 20o 25 90 x 360 100o 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. Drawing Pie Charts Musical Instrument Guitar 35 Violin 10 Recorder 15 Drum 5 Keyboard 25 Total 90 G u ita r a n g le = V io lin a n g le = 35 90 10 90 R e c o rd e r a n g le = D ru m a n g le = x 360 40o 15 90 5 90 K e y b o a rd a n g le = x 360 140o x 360 60o x 360 20o 25 90 x 360 100o 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. Drawing Pie Charts Musical Instrument Guitar 35 Violin 10 Recorder 15 Drum 5 Keyboard 25 Total 90 G u ita r a n g le = V io lin a n g le = 35 90 10 90 R e c o rd e r a n g le = D ru m a n g le = x 360 40o 15 90 5 90 K e y b o a rd a n g le = x 360 140o x 360 60o x 360 20o 25 90 x 360 100o 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. Drawing Pie Charts Musical Instrument Guitar 35 Violin 10 Recorder 15 Drum 5 Keyboard 25 Total 90 G u ita r a n g le = V io lin a n g le = 35 90 10 90 R e c o rd e r a n g le = D ru m a n g le = x 360 40o 15 90 5 90 K e y b o a rd a n g le = x 360 140o x 360 60o x 360 20o 25 90 x 360 100o 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. Drawing Pie Charts Musical Instrument Guitar 35 Violin 10 Recorder 15 Drum 5 Keyboard 25 Total 90 G u ita r a n g le = V io lin a n g le = 35 90 10 90 R e c o rd e r a n g le = D ru m a n g le = x 360 40o 15 90 5 90 K e y b o a rd a n g le = x 360 140o x 360 60o x 360 20o 25 90 x 360 100o 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. Drawing Pie Charts Musical Instrument Guitar 35 Violin 10 Recorder 15 Drum 5 Keyboard 25 Total 90 G u ita r a n g le = V io lin a n g le = 35 90 10 90 R e c o rd e r a n g le = D ru m a n g le = x 360 40o 15 90 5 90 K e y b o a rd a n g le = x 360 140o x 360 60o x 360 20o 25 90 x 360 100o 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. Drawing Pie Charts Musical Instrument Guitar 35 Violin 10 Recorder 15 Drum 5 Keyboard 25 Total 90 G u ita r a n g le = V io lin a n g le = 35 90 10 90 R e c o rd e r a n g le = D ru m a n g le = x 360 40o 15 90 5 90 K e y b o a rd a n g le = x 360 140o x 360 60o x 360 20o 25 90 x 360 100o 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. Drawing Pie Charts Musical Instrument Guitar 35 Violin 10 Recorder 15 Drum 5 Keyboard 25 Total 90 G u ita r a n g le = V io lin a n g le = 35 90 10 90 R e c o rd e r a n g le = D ru m a n g le = x 360 40o 90 90 K e y b o a rd a n g le = x 360 140o 15 5 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. x 360 60o x 360 20o 25 90 x 360 100o Drum Drawing Pie Charts Musical Instrument Guitar 35 Violin 10 Recorder 15 Drum 5 Keyboard 25 Total 90 G u ita r a n g le = V io lin a n g le = 35 90 10 90 R e c o rd e r a n g le = D ru m a n g le = x 360 40o 90 90 K e y b o a rd a n g le = x 360 140o 15 5 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. x 360 60o x 360 20o 25 90 x 360 100o 40o 140o 60o 100o 20o Drawing Pie Charts Ice-cream Sales Vanilla 13 Banana 22 Chocolate 28 Strawberry 57 Total 120 V a n illa a n g le = B a n a n a a n g le = C h o c o la te a n g le = S tra w b e rry a n g le = 13 120 22 120 x 360 39o x 360 66o 28 120 57 120 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. x 360 84 o x 360 171 o Drawing Pie Charts Ice-cream Sales Vanilla 13 Banana 22 Chocolate 28 Strawberry 57 Total 120 V a n illa a n g le = B a n a n a a n g le = C h o c o la te a n g le = S tra w b e rry a n g le = 13 120 22 120 x 360 39o x 360 66o 28 120 57 120 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. x 360 84 o x 360 171 o Drawing Pie Charts Ice-cream Sales Vanilla 13 Banana 22 Chocolate 28 Strawberry 57 Total 120 V a n illa a n g le = B a n a n a a n g le = C h o c o la te a n g le = S tra w b e rry a n g le = 13 120 22 120 x 360 39o x 360 66o 28 120 57 120 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. x 360 84 o x 360 171 o Drawing Pie Charts Ice-cream Sales Vanilla 13 Banana 22 Chocolate 28 Strawberry 57 Total 120 V a n illa a n g le = B a n a n a a n g le = C h o c o la te a n g le = S tra w b e rry a n g le = 13 120 22 120 x 360 39o x 360 66o 28 120 57 120 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. x 360 84 o x 360 171 o Drawing Pie Charts Ice-cream Sales Vanilla 13 Banana 22 Chocolate 28 Strawberry 57 Total 120 V a n illa a n g le = B a n a n a a n g le = C h o c o la te a n g le = S tra w b e rry a n g le = 13 120 22 120 x 360 39o x 360 66o 28 120 57 120 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. x 360 84 o x 360 171 o Drawing Pie Charts Ice-cream Sales Vanilla 13 Banana 22 Chocolate 28 Strawberry 57 Total 120 V a n illa a n g le = B a n a n a a n g le = C h o c o la te a n g le = S tra w b e rry a n g le = 13 120 22 120 x 360 39o x 360 66o 28 120 57 120 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. x 360 84 o x 360 171 o Drawing Pie Charts Ice-cream Sales Vanilla 13 Banana 22 Chocolate 28 Strawberry 57 Total 120 V a n illa a n g le = B a n a n a a n g le = C h o c o la te a n g le = S tra w b e rry a n g le = 13 120 22 120 x 360 39o x 360 66o 28 120 57 120 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. x 360 84 o x 360 171 o 84o 66o 171o 39o Statistics Working Out Statistics www.mathsrevision.com Level 3 / 4 Now try Exercise 5 Ch17 (page 81) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com Level 3 / 4 1. W h a t is t h e m e a n o f t h e n u m b e r s 2,3, 4, 5 2. C a lc u la t e 6 0 % o f 3 6 0 3. C a lc u la t e 7 b x 9 b 4. 21-Jul-15 H o w m a n y d e g r e e s in 1 12 , 1 20 Created by Mr. Lafferty Maths Dept. , o f a c ir c le . Stem Leaf Graphs Construction of Stem-Leaf www.mathsrevision.com Level 3 / 4 Learning Intention Success Criteria 1. We are learning to display data in the form of a StemLeaf Graph. 1. Be able Construct and understand the Key-Points of a Stem-Leaf Graph. 2. Answer questions based on the graph. 21-Jul-15 Created by Mr. Lafferty Maths Dept. 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 n = 20 Class Maths Marks 1 0 2 2 6 8 2 3 4 5 9 9 3 0 0 2 6 8 9 9 4 0 4 5 2 / 3 means a mark of 23 Stem Leaf Graphs Construction of Stem and Leaf www.mathsrevision.com Level 3 / 4 A Stem – Leaf graph is another way of displaying information : Ages This stem and leaf graph shows 2 4 6 8 the ages of people waiting in a 3 0 1 3 queue at a post office 4 4 4 5 6 7 9 5 0 3 4 9 How many people in the queue? 20 6 1 4 5 6 How many people in their forties? 6 leaves stem n = 20 Key : 2 4 means 24 21-Jul-15 Created by Mr. Lafferty Maths Dept. 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 Pocket money Note this gives us the same diagram as the previous example. This shows the importance of the title and key. 5 6 8 8 9 6 0 1 2 2 3 6 7 9 7 2 2 4 n = 15 6 / 2 means £6.20 Stem Leaf Graphs Construction of Stem and Leaf www.mathsrevision.com Level 3 / 4 Example : Construct a stem and leaf graphs for the following weights in (kgs) : Weight (kgs) 1 2 2 3 5 5 2 1 3 9 3 2 2 4 0 0 1 1 12 12 40 13 57 15 54 15 55 21 13 23 55 29 15 32 32 55 40 32 40 15 41 41 21 51 40 54 23 55 41 55 29 55 51 57 12 5 stem 1 4 5 5 5 7 leaves n = 20 Key : 2 3 means 23 21-Jul-15 Created by Mr. Lafferty Maths Dept. 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. Maths marks for class 1A 9 8 0 Maths marks for class 1B 6 8 9 8 5 3 1 1 2 2 2 5 5 8 9 4 4 5 2 0 2 0 0 1 1 6 7 6 4 3 1 1 0 3 3 7 7 7 3 3 4 1 n = 20 3/2 means a mark of 32 n = 20 How many students in 1A had a mark of 31? 2 How many students in 1B had a mark of 12? 3 Which class appears to be best at Maths? 1A Statistics Stem Leaf www.mathsrevision.com Level 3 / 4 Now try Exercise 6 Ch17 (page 83) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com Level 3 / 4 1. W h a t is t h e H C F o f 6 4 , 3 6 2. W h a t is L C M o f 4 a n d 5 3. C a lc u la t e 3 z x 1 2 b 4. 21-Jul-15 H o w m a n y d e g r e e s in 1 30 , 1 40 Created by Mr. Lafferty Maths Dept. , o f a c ir c le . Scattergraphs Construction of Scattergraphs www.mathsrevision.com Level 3 / 4 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. 2. Know the term positive and negative correlation. 21-Jul-15 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Level 3 / 4 This scattergraph shows the heights and weights of a sevens football team Write down height and Scattergraphs weight of each player. Construction of Scattergraph Bob Tim Sam Joe Gary Jim 21-Jul-15 Created by Mr. Lafferty Maths Dept. Dave Scattergraphs Construction of Scattergraph www.mathsrevision.com Level 3 / 4 When two quantities are strongly connected we say there is a strong correlation between them. Best fit line x x x x x x Strong positive correlation 21-Jul-15 x x x x x x Best fit line Strong negative correlation Created by Mr. Lafferty Maths Dept. Draw in the best fit line Scattergraphs Construction of Scattergraph Price Age (£1000) 1 1 9 8 2 3 3 3 4 4 5 8 7 6 5 5 4 2 21-Jul-15 12 Is there a correlation? If yes, what kind? 10 Car prices (£1000) www.mathsrevision.com Level 3 / 4 8 6 4 2 0 0 2 4 6 Ages (Years) Created by Mr. Lafferty Maths Dept. 8 10 12 Scattergraphs Construction of Scattergraphs www.mathsrevision.com Level 3 / 4 Now try Exercise 7 Ch17 (page 85) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com Level 3 / 4 1. F in d th e va lue o f x if 4x = 48 o 47 o 55 o x o 2. C a lc ula te x : 3. C h a n g e 2 3 .3 k m to m 4. F in d th e a ve r a g e o f th e n um b e r s 1 5 , 2 5 , 2 0 ? 21-Jul-15 Created by Mr. Lafferty Maths Dept. Probability Likelihood Line www.mathsrevision.com Level 3 / 4 Learning Intention Success Criteria 1. We are learning how a likelihood line helps to understand probability. 1. Understand the term likelihood line and probability. 2. Decide where certain events should lie on the likelihood line. 3. Calculate simple probabilities. 21-Jul-15 Created by Mr. Lafferty Maths Dept. Probability Likelihood Line www.mathsrevision.com Level 3 / 4 0 Impossible Seeing a butterfly In July 21-Jul-15 0.5 Not very likely School Holidays Evens Winning the Lottery Created by Mr. Lafferty Maths Dept. 1 Very likely Baby Born A Boy Certain Go back in time Probability Likelihood Line www.mathsrevision.com Level 3 / 4 0 Impossible It will Snow in winter 21-Jul-15 0.5 Not very likely Evens Homework Everyone getting Every week 100 % in test Created by Mr. Lafferty Maths Dept. 1 Very likely Certain Toss a coin Going without That land Food Heads for a year. Statistics and Probability www.mathsrevision.com Level 3 / 4 Now Round the Class Exercise 8 Ch17 (page 87) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Probability Calculating Probability Level 3 / 4 www.mathsrevision.com 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) Pro b a b ility o f a n e ve n t h a ppe n in g = 21-Jul-15 n um b e r o f f a vo ura b le o utco m e s n um b e r o f po ssib le o utco m e s Created by Mr. Lafferty Maths Dept. Probability Calculating Probability www.mathsrevision.com Level 3 / 4 Example : A boy tossed a coin. What is the probability that it is heads. P( heads ) 1 2 Example : There are 3 red and 4 green balls in a bag. What is the probability a green ball is picked. P( green ) 21-Jul-15 4 34 Created by Mr. Lafferty Maths Dept. 4 7 Probability Calculating Probability www.mathsrevision.com Level 3 / 4 Now try Exercise 9 Ch17 (page 87) 21-Jul-15 Created by Mr. Lafferty Maths Dept.