Created by Mr Lafferty Maths Dept Statistics Interpreting / Drawing Graphs Averages and Interpreting Data Mean from Mid-Interval Frequency Table www.mathsrevision.com Scatter Diagrams Frequency Polygons 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Interpreting Graphical Data Learning Intention Success Criteria To revise the various types of graph used to display statistical data. To be able to recognise the various types of graph that can be used to display statistical data. www.mathsrevision.com Interpret graphs. 20-Nov-18 Created by Mr Lafferty Maths Dept

Statistics Bar Chart www.mathsrevision.com Write down a question you could answer using this graph www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Statistics Comparing Line graphs Write down a question you could answer using this graph Statistics Comparing Line graphs www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Statistics Bar Chart www.mathsrevision.com Write down a question you could answer using this graph www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Statistics Pie Chart www.mathsrevision.com Write down a question you could answer using this graph www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Interpreting Graphical Data S4 General Now try Ex 1A Ch5 (page 57) www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions xo 42o www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Averages Learning Intention Success Criteria To explain the terms mean, range, median and mode. Understand the terms mean, range, median and mode. To be able to calculate mean, range, mode and median. www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Finding the mode S4 General The mode or modal value in a set of data is the data value that appears the most often. For example, the number of goals scored by the local football team in the last ten games is: 2, 1, 0, 3, 1. 2, 1, 0, 3, 1. www.mathsrevision.com What is the modal score? 2. Is it possible to have more than one modal value? Yes Is it possible to have no modal value? Yes 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics The mean S4 General The mean is the most commonly used average. To calculate the mean of a set of values we add together the values and divide by the total number of values. Mean = Sum of values Number of values www.mathsrevision.com For example, the mean of 3, 6, 7, 9 and 9 is 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Finding the median S4 General The median is the middle value of a set of numbers arranged in order. For example, Find the median of 10, 7, 9, 12, 8, 6, www.mathsrevision.com Write the values in order: 6, 7, 7, 8, 9, 10, 12. The median is the middle value. 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Finding the median S4 General When there is an even number of values, there will be two values in the middle. For example, Find the median of 56, 42, 47, 51, 65 and 43. The values in order are: www.mathsrevision.com 42, 43, 47, 51, 56, 65. There are two middle values, 47 and 51. 47 + 51 2 = 98 2 = 49 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Finding the range S4 General The range of a set of data is a measure of how the data is spread across the distribution. To find the range we subtract the lowest value in the set from the highest value. Range = highest value – lowest value www.mathsrevision.com When the range is small; the values are similar in size. When the range is large; the values vary widely in size. 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics The range S4 General Here are the high jump scores for two girls in metres. Joanna 1.62 1.41 1.35 1.20 1.15 Kirsty 1.59 1.45 1.30 Find the range for each girl’s results and use this to find out who is consistently better. www.mathsrevision.com Joanna’s range = 1.62 – 1.15 = 0.47 Kirsty’s range = 1.59 – 1.30 = 0.29 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Averages S4 General Now try Ex 2A Ch5 (page 58) www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions 140o xo www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Mean from Mid interval Frequency Table Learning Intention Success Criteria Construct and understand the Key-Points of a various frequency tables. To explain how to calculate the mean from various frequency tables. www.mathsrevision.com 2. Calculate the mean from frequency tables. 20-Nov-18 Created by Mr Lafferty Maths Dept

The mean from a frequency table Here are the results of a survey carried out among university students. Numbers of sports played Frequency 20 1 17 2 15 3 10 4 9 5 6 If you were to write out the whole list of results, what would it look like? What do you think the mean would be? 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics The mean from a frequency table S4 General Numbers of sports Frequency Number of sports × frequency 20 0 × 20 = 0 1 17 1 × 17 = 17 2 15 2 × 15 = 30 3 10 3 × 10 = 30 www.mathsrevision.com 4 9 4 × 9 = 36 5 3 5 × 3 = 15 6 2 6 × 2 = 12 TOTAL 76 140 20-Nov-18 Created by Mr Lafferty Maths Dept Mean = 140 ÷ 76 = 1.84 2 sports (to the nearest whole)

Mid-Interval Frequency Table Example : The test scores for a class are given below. Construct a Frequency Table for the results. Class Intervals Mid Interval Frequency 12 23 41 55 17 15 32 40 51 69 21 12 16 43 56 47 32 19 34 42 55 41 21 20 22 56 10-19 14.5 24.5 34.5 44.5 54.5 64.5 6 5 20-29 30-39 3 Lowest value = 12 40-49 50-59 60-69 6 5 Highest value = 69 1 Group data in 10’s 20-Nov-18

Mid-Interval Frequency Table Class Intervals Mid-Interval Frequency Mid x F 14.5 87 24.5 122.5 34.5 103.5 44.5 267 54.5 272.5 64.5 Total 10-19 6 5 20-29 30-39 3 40-49 6 50-59 5 60-69 1 26 917 Mean = (Class interval 30-39)

Created by Mr Lafferty Maths Dept Statistics Mean from Mid interval Frequency Table S4 General Now try Ex 2B Ch5 (page 59) www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions 138o xo www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Scattergraphs Construction of Scattergraphs Learning Intention Success Criteria Construct and understand the Key-Points of a scattergraph. To construct and interpret Scattergraphs. www.mathsrevision.com 2. Know the term positive and negative correlation. 20-Nov-18 Created by Mr Lafferty Maths Dept

Scattergraphs www.mathsrevision.com Construction of Scattergraph This scattergraph shows the heights and weights of a sevens football team Scattergraphs Write down height and weight of each player. Construction of Scattergraph Bob Tim Joe Sam Gary Dave www.mathsrevision.com Jim 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Scattergraphs Construction of Scattergraph When two quantities are strongly connected we say there is a strong correlation between them. Best fit line x x www.mathsrevision.com Best fit line Strong positive correlation Strong negative correlation 20-Nov-18 Created by Mr Lafferty Maths Dept

Scattergraphs www.mathsrevision.com Construction of Scattergraph Draw in the best fit line Scattergraphs Construction of Scattergraph Is there a correlation? If yes, what kind? Age Price (£1000) 3 1 2 4 5 9 8 7 6 Strong negative correlation www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Relative Frequency S4 General Now try Exercise 3 Ch5 (page 60) www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions 55o xo 80o www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Frequency Polygons Learning Intention Success Criteria To explain frequency polygon graphs. Understand the frequency polygon. Interpret and construct frequency polygon graphs. www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept

Statistics www.mathsrevision.com The frequency table and diagram shows the distribution of weight in a batch of melons. Add mid point zero values either side Join points together and you have made frequency polygon Join mid-point values www.mathsrevision.com 250 300 350 400 450 500 600 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Frequency Polygon Key Points 1. Complete tables. 2. Draw frequency diagram www.mathsrevision.com 3. Plot mid-point values ( remember end mid-point values) 4. Join them together 20-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Statistics Frequency Polygon S4 General Now try Ex 4A & 4B Ch5 (page 61) www.mathsrevision.com 20-Nov-18 Created by Mr Lafferty Maths Dept