T Madas Discrete or Continuous T Madas Cumulative

Cumulative Frequency Graphs for Discrete Data Exam marks Test marks 0 - 19 20

Cumulative Frequency Graphs for Discrete Data Exam marks Test marks cf Frequency Cumulative frequency

Cumulative Frequency Graphs for Discrete Data cf Exam marks Test marks Frequency Cumulative frequency

Cumulative Frequency Graphs for Discrete Data cf Exam marks Test marks 0 - 19

Cumulative Frequency Graphs for Continuous Data Car speeds on A 404 Speed (mph) 20≤s<30

Cumulative Frequency Graphs for Continuous Data Car speeds on A 404 Speed (mph) cf

Cumulative Frequency Graphs for Continuous Data cf Car speeds on A 404 Speed (mph)

Cumulative Frequency Graphs for Continuous Data cf Estimating the cumulative frequency reading at 72:

a final important point cf Can you criticise the graph opposite? 120 Try to

0 10 20 30 40 50 3 0 10 20 30 40 50 frequency

Slides: 21

Download presentation

Discrete or Continuous © T Madas

Cumulative Frequency Graphs for Discrete Data Exam marks Test marks 0 - 19 20 - 39 40 - 59 60 - 79 80 - 100 Frequency Cumulative frequency (f) 5 8 9 16 8 5 13 22 38 46 Next we need another column in our table for the cumulative frequency Test 020 40 60 80 100 marks © T Madas

Cumulative Frequency Graphs for Discrete Data Exam marks Test marks cf Frequency Cumulative frequency (f) 0 - 19 5 5 20 - 39 8 13 Frequency 40 - 59 Cumulative 9 22 60 - 79 16 always 38 gets plotted on the y axis 80 - 100 8 46 Test 020 40 60 80 100 marks © T Madas

Cumulative Frequency Graphs for Discrete Data cf Exam marks Test marks Frequency Cumulative frequency (f) 0 - 19 20 - 39 40 - 59 60 - 79 80 - 100 5 8 9 16 8 5 13 22 38 46 Note where the points are plotted 48 44 40 36 32 28 24 20 16 12 8 4 0 Test 020 40 60 80 100 marks © T Madas

Cumulative Frequency Graphs for Discrete Data cf Exam marks Test marks 0 - 19 20 - 39 40 - 59 60 - 79 80 - 100 Frequency Cumulative frequency (f) 5 8 9 16 8 5 13 22 38 46 We can use a C. F. G for estimates Smallest possible value 48 44 40 36 32 28 24 20 16 12 8 4 0 Test 020 40 60 80 100 marks © T Madas

Cumulative Frequency Graphs for Discrete Data cf Exam marks Test marks 0 - 19 20 - 39 40 - 59 60 - 79 80 - 100 Frequency Cumulative frequency (f) 5 8 9 16 8 5 13 22 38 46 We can use a C. F. G How many pupils got for estimates less than 55 marks? 19 pupils 48 44 40 36 32 28 24 19 20 16 12 8 4 0 Test 020 40 60 80 100 marks © T Madas

Cumulative Frequency Graphs for Discrete Data cf Exam marks Test marks 0 - 19 20 - 39 40 - 59 60 - 79 80 - 100 Frequency Cumulative frequency (f) 5 8 9 16 8 5 13 22 38 46 48 44 40 36 30 32 28 24 20 16 12 How many pupils got more than 70 marks? 16 pupils 8 4 0 Test 020 40 60 80 100 marks © T Madas

Cumulative Frequency Graphs for Discrete Data cf Exam marks Test marks 0 - 19 20 - 39 40 - 59 60 - 79 80 - 100 Frequency Cumulative frequency (f) 5 8 9 16 8 5 13 22 38 46 The bottom 10 pupils will move down a set. Which is the decisive mark? ≈ 31% 48 44 40 36 32 28 24 20 16 12 8 4 0 Test 020 40 60 80 100 31 marks © T Madas

Cumulative Frequency Graphs for Continuous Data Car speeds on A 404 Speed (mph) 20≤s<30 30≤s<40 40≤s<50 50≤s<60 60≤s<70 70≤s<90 Frequency Cumulative (f) Frequency 10 46 36 18 8 2 10 56 92 110 118 120 Next we need another column in our table for the cumulative frequency mph 020 40 60 80 100 © T Madas

Cumulative Frequency Graphs for Continuous Data Car speeds on A 404 Speed (mph) cf Frequency Cumulative (f) Frequency 20≤s<30 10 10 30≤s<40 46 56 Cumulative Frequency 40≤s<50 36 92 always 50≤s<60 gets plotted 18 on 110 the y axis 60≤s<70 8 118 70≤s<90 2 120 mph 020 40 60 80 100 © T Madas

Cumulative Frequency Graphs for Continuous Data cf Car speeds on A 404 Speed (mph) 20≤s<30 30≤s<40 40≤s<50 50≤s<60 60≤s<70 70≤s<90 Frequency Cumulative (f) Frequency 10 46 36 18 8 2 10 56 92 110 118 120 110 100 90 80 70 60 50 40 30 20 Note where the points are plotted 10 0 mph 020 40 60 80 100 © T Madas

Cumulative Frequency Graphs for Continuous Data cf Car speeds on A 404 Speed (mph) 20≤s<30 30≤s<40 40≤s<50 50≤s<60 60≤s<70 70≤s<90 Frequency Cumulative (f) Frequency 10 46 36 18 8 2 10 56 92 110 118 120 110 100 90 80 70 60 50 40 30 20 10 We can use a C. F. G Smallest possible value 0 for estimates mph 020 40 60 80 100 © T Madas

Cumulative Frequency Graphs for Continuous Data cf Car speeds on A 404 Speed (mph) 20≤s<30 30≤s<40 40≤s<50 50≤s<60 60≤s<70 70≤s<90 Frequency Cumulative (f) Frequency 10 46 36 18 8 2 10 56 92 110 118 120 We What can use a C. F. G of percentage for estimates cars travels at less 120 110 100 90 72 80 70 60 50 40 30 20 10 0 mph 020 40 60 80 100 than 45 mph © T Madas

Cumulative Frequency Graphs for Continuous Data cf Car speeds on A 404 Speed (mph) 20≤s<30 30≤s<40 40≤s<50 50≤s<60 60≤s<70 70≤s<90 Frequency Cumulative (f) Frequency 10 46 36 18 8 2 10 56 92 110 118 120 110 100 90 72 80 70 60 50 40 30 20 What percentage of cars travels at less than 45 mph 10 0 mph 020 40 60 80 100 © T Madas

Cumulative Frequency Graphs for Continuous Data cf Estimating the cumulative frequency reading at 72: 120 110 100 90 or use a calculator: 72 80 70 60 50 40 30 20 What percentage of cars travels at less than 45 mph 10 0 mph 020 40 60 80 100 © T Madas

a final important point cf Can you criticise the graph opposite? 120 Try to draw your graph as large as possible. 80 The extra detail will produce a better estimate. 110 100 90 72 70 60 50 40 30 20 What percentage of cars travels at less than 45 mph 10 0 mph 020 40 60 80 100 © T Madas

0 10 20 30 40 50 3 0 10 20 30 40 50 frequency 0 10 20 30 40 50 D 0 10 20 30 40 50 4 0 10 20 30 40 50 E 0 10 20 30 40 50 cum frequency 2 C cum frequency 1 0 10 20 30 40 50 cum frequency 0 10 20 30 40 50 B cum frequency A frequency 10 graphs are shown below. Each frequency polygon shows the same information as one of the cumulative frequency graphs. Match each of the letters A-E with the numbers 1 -5 5 0 10 20 30 40 50 © T Madas