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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 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 Nat 4

3 28-Apr-15Created by Mr. Lafferty Maths Dept. 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 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 Nat 4

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

7 28-Apr-15 Created by Mr. Lafferty Maths Dept. Total300 Rugby Football Cricket Ice Hockey Favourite Sport Squash 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) Interpreting Graphs

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

10 28-Apr-15Created by Mr. Lafferty Maths Dept. 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. 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. Break the Code Nat 4 Write down the sentence with the code M A T H S I S F U N

13 28-Apr-15Created by Mr. Lafferty Maths Dept (4,3) x - axis y - axis 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) Scattergraph & Codes Nat 4

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

16 28-Apr-15Created by Mr. Lafferty Maths Dept. 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. 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 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. Stem Leaf Graphs Back to Back Stem – Leaf Graphs Rugby Team 2 Heights 14 | 1 represents 141cm Nat 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) Stem Leaf Diagram Nat 4

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

21 28-Apr-15Created by Mr. Lafferty Maths Dept. 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 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 Nat 4 c

24 28-Apr-15Created by Mr.Lafferty Maths Dept 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 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 Time (Hour)6 am7 am8 am9 am10 am11 am Temperature o C Title Labels Units Reasonable Scale

28 28-Apr-15Created by Mr. Lafferty Maths Dept. Scattergraphs Construction of Scattergraph Age Price (£1000) Nat 4

29 28-Apr-15Created by Mr. Lafferty Maths Dept. Stem Leaf Graphs Construction of Stem and Leaf Example : Construct a stem and leaf graphs for the following weights in (kgs) : stem leaves Weight (kgs) n = 20 Key : 2 3 means Nat 4

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

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

32 28-Apr-15Created by Mr. Lafferty Maths Dept. 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. 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. 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. 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) Different Averages Nat 4

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

38 28-Apr-15Created by Mr. Lafferty Maths Dept. 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. 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. 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. Scattergraphs Construction of Scattergraph Is there a correlation? If yes, what kind? Age Price (£1000) 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) Scattergraphs Construction of Scattergraphs Nat 4

43 28-Apr-15Created by Mr. Lafferty43 Nat 4 Lesson Starter Q1. Q2.How long between 8:40am to 1.20pm Q x 6 Q 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 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 Frequency tables Lowest number56 Highest number62

47 28-Apr-15Created by Mr. Lafferty47 DiameterTallyFrequency l l l l l l Frequency tables X X XXXX

48 28-Apr-15Created by Mr. Lafferty48 DiameterTallyFrequency Frequency tables lll llll lll llll 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) Nat 4 Frequency Tables

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

51 28-Apr-15Created by Mr. Lafferty Maths Dept. 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 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. 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 Here are the results of a sports survey carried out among university students lies in here Range Mode & Median from Frequency Table Nat 4 Range = 6 Mode = 0 Median harder to calculate = 76 Middle value of 76 is between 38 th and 39 th values = = 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 lies in here Nat 4 Range = 6 Mode = 5 Median harder to calculate = 140 Middle value of 140 is between the 70 th and 71 th values = = 74 Median = 3

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

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

58 28-Apr-15Created by Mr. Lafferty Maths Dept. 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. No of Coins ( c ) Freq.(f) Example : This table shows the number of coins in the pockets of some children 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 = f x C Nat 4

60 28-Apr-15Created by Mr. Lafferty Maths Dept. No of Sibling s ( S ) Freq.(f) Example : This table shows the number of brothers and sisters of pupils in an S2 class 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 = S x f Nat 4

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


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