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28-Apr-15Created by Mr. Lafferty Maths Dept. Mean, Median, Mode and Range of a Data Set Line of best fit Statistics www.mathsrevision.com Constructing.

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Presentation on theme: "28-Apr-15Created by Mr. Lafferty Maths Dept. Mean, Median, Mode and Range of a Data Set Line of best fit Statistics www.mathsrevision.com Constructing."— Presentation transcript:

1 28-Apr-15Created by Mr. Lafferty Maths Dept. Mean, Median, Mode and Range of a Data Set Line of best fit Statistics www.mathsrevision.com Constructing Frequency Tables (Tally Tables) Interpreting Graphs. Stem and Leaf Diagram Drawing Graphs Scattergraphs & Codes Nat 4 Range Mode & Median from Frequency Table Mean from a Frequency Table

2 28-Apr-15Created by Mr.Lafferty Maths Dept Starter Questions Starter Questions www.mathsrevision.com Nat 4

3 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 2.Solve problems involving graphs. 1.To explain how to interpret various graphs. 1.Understand key information on various graphs. Nat 4 Interpreting Graphs

4 www.mathsrevision.com What does 1 computer represent You have 1 minute to come up with a question Nat 4

5 Interpreting Graphs 28-Apr-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Nat 4

6 Interpreting Graphs 28-Apr-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com

7 28-Apr-15 Created by Mr. Lafferty Maths Dept. Total300 Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash 30 90 o 108 o 54 o 72 o 36 o Drawing Pie Charts In a survey, 300 people were asked to indicate which one of five sports they liked best. Using the graph calculate the number people who liked each sport. Rugby Football Cricket Ice Hockey Squash

8 Nat 4 28-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 1 Ch12 (page 132) www.mathsrevision.com Interpreting Graphs

9 Nat 4 28-Apr-15Created by Mr.Lafferty Maths Dept Starter Questions Starter Questions www.mathsrevision.com

10 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 2.Solve problems involving scattergraphs and codes. 1.To explain how to interpret a scattergraph and codes. 1.Understand how to interpret a scattergraph and codes. Nat 4 Scattergraphs

11 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Scattergraphs Sam Jim Tim Gary Joe Dave Bob This scattergraph shows the heights and weights of a sevens football team Write down the height and weight of each player.

12 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Break the Code Nat 4 Write down the sentence with the code 13 1 20 8 19 9 19 6 21 14 M A T H S I S F U N

13 28-Apr-15Created by Mr. Lafferty Maths Dept www.mathsrevision.com 13 24 0 -2 1 3 2 (4,3) x - axis y - axis -3 -4 -2 -3 Break the Code Write down the sentence with the code Nat 4 (-3,3) (3,-2) (-2,1) (-2,-4) (2,2) (-4,-4) (1,1) 4 -4 R R W I R G O H N T G R I G H T W A Y W A Y E A

14 28-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 2 Ch12 (page 137) www.mathsrevision.com Scattergraph & Codes Nat 4

15 28-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 10cm 8cm 2cm 6cm Nat 4

16 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 2.Solve problems involving stem leaf diagrams. 1.To explain how to interpret a stem leaf diagrams. 1.Understand how to interpret a stem leaf diagram. Nat 4 Stem Leaf Diagrams

17 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Stem Leaf Graphs 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 Nat 4 You have 1 minute to come up with another question for stem leaf.

18 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Stem Leaf Graphs Back to Back Stem – Leaf Graphs 14026 1534 16016 1716 18144 Rugby Team 2 Heights 14 | 1 represents 141cm Nat 4 78 21 76 4 508 31346 70 n = 15 Rugby Team 1 Heights A back to back stem-leaf helps us to compare two sets of data. Write down a question that can be answered easily from the graph.

19 28-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 3 Ch12 (page 140) www.mathsrevision.com Stem Leaf Diagram Nat 4

20 28-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com Nat 4

21 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria Constructing Graphs 1. To construct various graphs accurately. 1.Understand how to construct various graphs from given information. Nat 4

22 Pictographs www.mathsrevision.com Nat 4 The table below shows the number of internet pages viewed by three pupils. PupilPages viewed Austin55 Chad75 Stephen30 Construct a pictograph to represent this data. Use the following pictures

23 Pictographs www.mathsrevision.com Nat 4 c

24 28-Apr-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Bar Graphs Lets construct a Bar graph for the following table Remember graph has to be labelled and neat ! A survey of S1 pupils asked what their favourite pet was. The results are shown below Nat 4

25 Favourite Pets CatDogRabbitHamsterSnake 0 2 4 6 8 10 12 N u m b e r o f P u p i l s Pets What labels should we use for the Bar Chart Title, Scale, Labels and Units where appropriate

26 28-Apr-15Created by Mr. Lafferty26 Line graphs Line graphs are most often used to show trends over time. If the temperature in Aberdeen, in ºC, over a 12-hour period is plotted, the line graph shows the temperature trend.

27 28-Apr-1527 A hospital nurse recorded a patient’s temperature every hour Time (Hours AM) T e m p e r a t u r e  C Temperature against Time 100 101 678 91011 102 103 Time (Hour)6 am7 am8 am9 am10 am11 am Temperature o C101102102.5103101100.5 Title Labels Units Reasonable Scale

28 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Scattergraphs Construction of Scattergraph Age Price (£1000) 3 1 1 2 3 3 4 4 5 9 8 8 7 6 5 5 4 2 Nat 4

29 28-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 Nat 4

30 28-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 4 Ch12 (page 142) www.mathsrevision.com Constructing Graphs Nat 4

31 28-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 8cm 5cm 2cm 4cm Nat 4

32 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 2.Work out values of Mean, Median, Mode and Range. 1.To define the terms Mean Median, Mode and Range for a set of data. 1.Know the terms Mean, Median, Mode and Range. Different Averages Nat 4

33 28-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 Mean (Average) Nat 4

34 28-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 Nat 4

35 28-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 Nat 4

36 28-Apr-15Created by Mr. Lafferty Maths Dept. Now try Exercise 5 Ch12 (page 144) www.mathsrevision.com Different Averages Nat 4

37 28-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com Nat 4

38 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.To construct a scattergraph and answer questions based on it. 1.Construct and understand the Key-Points of a scattergraph. Scattergraphs Construction of Scattergraphs 2. Know the term positive and negative correlation. Nat 4

39 28-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.

40 28-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. Nat 4

41 28-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 Nat 4

42 28-Apr-15Created by Mr. Lafferty Maths Dept. Now try Extension Booklet 2E (page 53) www.mathsrevision.com Scattergraphs Construction of Scattergraphs Nat 4

43 28-Apr-15Created by Mr. Lafferty43 www.mathsrevision.com Nat 4 Lesson Starter Q1. Q2.How long between 8:40am to 1.20pm Q3.36.9 x 6 Q4.34.7 x 100 Q5.Put these numbers in order 52, 55, 62, 51, 59, 62, 52, 59, 61, 55

44 28-Apr-15Created by Mr. Lafferty44 www.mathsrevision.com Nat 4 Aims of the Lesson 1.Understand the term Frequency Table. 2.Construct a Frequency Table. 3.Interpret information from Frequency Tables.

45 28-Apr-1545 Raw data can often appear untidy and difficult to understand. Organising such data into frequency tables can make it much easier to make sense of (interpret) the data. Frequency tables DataTallyFrequency Sum of Tally is the Frequency llll represents a tally of 5

46 28-Apr-15Created by Mr. Lafferty46 Example 1. 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. 58 59 58 56 62 56 57 60 61 59 57 60 56 59 58 59 56 61 60 56 58 62 59 58 6061596257 5960566160 6258616260 59565862 Frequency tables Lowest number56 Highest number62

47 28-Apr-15Created by Mr. Lafferty47 DiameterTallyFrequency 56 57 58 59 60 61 62 l l l l l l Frequency tables 58 60 58 56 59 57 60 61 59 57 60 56 59 58 59 56 61 60 57 58 62 59 58 6061596257 5960596159 6258615960 5960586062 X X XXXX

48 28-Apr-15Created by Mr. Lafferty48 DiameterTallyFrequency 56 57 58 59 60 61 62 Frequency tables 3 4 9 13 5 10 4 lll llll lll llll 58 60 58 56 59 57 60 61 59 57 60 56 59 58 59 56 61 60 57 58 62 59 58 6061596257 5960596159 6258615960 5960586062 X X XXXX X X XXXX X X XXXX X X XXXX X X XXXX X X XXXX X X XXXX X X XXXX

49 28-Apr-15Created by Mr. Lafferty49 Now try Extension Booklet 5E (page 57) www.mathsrevision.com Nat 4 Frequency Tables

50 28-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com Nat 4

51 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Understand how to work out the range, mode and median from a frequency table. 1. To explain how to work out the range, mode & median from a frequency table. Frequency Tables 2.Solve problems using a frequency Table. Nat 4 Range, Mode & Median

52 28-Apr-15Created by Mr Lafferty Maths Dept www.mathsrevision.com Reminder ! Range : The difference between highest and Lowest values. It is a measure of spread. Median :The middle value of a set of data. When they are two middle values the median is half way between them. Mode :The value that occurs the most in a set of data. Can be more than one value. Nat 4 Frequency Tables Range, Mode & Median

53 Nat 4 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Different Averages Example : Find the median and mode for the set of data. 10, 2, 14, 1, 14, 7

54 28-Apr-15Created by Mr Lafferty Maths Dept Numbers of sports played Frequency 020 117 215 310 49 53 62 Here are the results of a sports survey carried out among university students. 38.5 lies in here Range Mode & Median from Frequency Table Nat 4 Range = 6 Mode = 0 Median harder to calculate 20 + 17 + 15 + 10 + 9 + 3 + 2 = 76 Middle value of 76 is between 38 th and 39 th values 20 + 17 = 37 20 + 17 + 15 = 52 Median = 2 Mode value that occurs the most = 0 High – Low = 6 – 0 = 6

55 Range Mode & Median from Frequency Table Here are the results of a S3 maths exam survey carried out among St. Ninian’s High School students. High – Low = 7 – 1 = 6 Mode value that occurs the most = 5 28-Apr-15Created by Mr Lafferty Maths Dept Grade scored in exam Frequency 125 229 320 420 531 610 75 70.5 lies in here Nat 4 Range = 6 Mode = 5 Median harder to calculate 25 + 29 + 20 + 20 + 31 + 10 + 5 = 140 Middle value of 140 is between the 70 th and 71 th values 25 + 29 = 54 25 + 29 + 20 = 74 Median = 3

56 28-Apr-15Created by Mr. Lafferty Maths Dept. Now try Extension Booklet 6E (page 60) www.mathsrevision.com Frequency Tables Range, Mode & Median Nat 4

57 28-Apr-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com Nat 4

58 28-Apr-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Add a third column to a frequency table. 1. To explain how to work out the mean by adding in a third column to a Frequency Table. Frequency Tables Working Out the Mean 2.Work out the mean from a frequency Table. Nat 4

59 28-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 Nat 4

60 28-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 Nat 4

61 28-Apr-15Created by Mr. Lafferty Maths Dept. Now try Extension Booklet 7E (page 62) www.mathsrevision.com Frequency Tables Working Out the Mean Nat 4


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