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# Histograms

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GCSE Maths Histograms - three examples

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### Histograms

1. 1. Histograms BTEOTSSSBAT draw and interpret histograms
2. 2. Histograms are similar to bar charts but thereare two main differences: There are no gaps between the bars in ahistogram The area of each bar is proportional to thefrequency that it represents. Hence, total areais proportional to the total frequency.The vertical axis islabelled frequencydensity. frequency density = frequency divided by interval width
3. 3. f = 15 f =4 f=6frequency density = frequency divided by interval widthSo, frequency = frequency density x interval width (area of the bars)Frequencies = 1 x 6 = 6 = 3 x 5 = 15 = 2 x 2 = 4
4. 4. frequency density = frequency divided by interval widthSo, frequency = frequency density x interval width
5. 5. Example 1Display the following data as a histogram Mass (g) 0-20 20-40 40-60 60-80 80-100 No of letters 10 18 24 14 18
6. 6. Example 1Display the following data as a histogram Mass (g) 0-20 20-40 40-60 60-80 80-100 No of letters 10 18 24 14 18solutionFirst find the intervals/ widths: NB the interval widths don’t For each one the width/ interval is 20 have to be the same!
7. 7. Example 1Display the following data as a histogram Mass (g) 0-20 20-40 40-60 60-80 80-100 No of letters 10 18 24 14 18solutionFirst find the intervals/ widths: For each one the width/ interval is 20Then find the frequency density using frequency divided by interval/width
8. 8. Example 1Display the following data as a histogram Mass (g) 0-20 20-40 40-60 60-80 80-100 No of letters 10 18 24 14 18solutionFirst find the intervals/ widths: For each one the width/ interval is 20Then find the frequency density using frequency divided by interval/width Mass (g) Interval Frequency Frequency density width = frequency / width 0-20 20 10 0.5 20-40 20 18 0.9 40-60 20 24 1.2 60-80 20 14 0.7 80-100 20 18 0.9
9. 9. Mass (g) Interval Frequency Frequency density width = frequency / width 0-20 20 10 0.5 20-40 20 18 0.9 40-60 20 24 1.2 60-80 20 14 0.780-100 20 18 0.9
10. 10. Finding frequencies from a histogramTo find a frequency in each interval use frequency = interval width × frequency density
11. 11. Example 2 A passengers association conducted survey on punctuality of trains using a particular station. The histogram shows the results. •Construct the frequency distribution •How many trains were there in the survey?Frequency density Time late (mins)
12. 12. Example 2 A passengers association conducted survey on punctuality of trains using a particular station. The histogram shows the results. •Construct the frequency distribution •How many trains were there in the survey? Minutes late Frequency density Frequency = width x freq densityFrequency density 0-5 5-10 10-20 20-30 30-50 50-80 Time late (mins)
13. 13. Example 2 A passengers association conducted survey on punctuality of trains using a particular station. The histogram shows the results. •Construct the frequency distribution •How many trains were there in the survey? Minutes late Frequency density Frequency = width x freq densityFrequency density 0-5 6.4 5-10 8.8 10-20 3 20-30 1.2 30-50 0.6 50-80 0.2 Time late (mins)
14. 14. Example 2 A passengers association conducted survey on punctuality of trains using a particular station. The histogram shows the results. •Construct the frequency distribution •How many trains were there in the survey? Minutes late Frequency density Frequency = width x freq densityFrequency density 0-5 6.4 5 x 6.4 5-10 8.8 5 x 6.4 10-20 3 10 x 3 20-30 1.2 10 x 1.2 30-50 0.6 20 x 0.6 50-80 0.2 30 x 0.2 Time late (mins)
15. 15. Example 2 A passengers association conducted survey on punctuality of trains using a particular station. The histogram shows the results. •Construct the frequency distribution •How many trains were there in the survey? Minutes late Frequency density Frequency = width x freq densityFrequency density 0-5 6.4 5 x 6.4 = 32 5-10 8.8 5 x 6.4 =32 10-20 3 10 x 3 = 30 20-30 1.2 10 x 1.2 = 12 30-50 0.6 20 x 0.6 = 12 50-80 0.2 30 x 0.2 = 6 Time late (mins)
16. 16. Example 2 A passengers association conducted survey on punctuality of trains using a particular station. The histogram shows the results. •Construct the frequency distribution •How many trains were there in the survey? Minutes late Frequency density Frequency = width x freq densityFrequency density 0-5 6.4 5 x 6.4 = 32 5-10 8.8 5 x 6.4 = 32 10-20 3 10 x 3 = 30 20-30 1.2 10 x 1.2 = 12 30-50 0.6 20 x 0.6 = 12 50-80 0.2 30 x 0.2 = 6 Time late (mins) Total trains = 32 + 32 + 30 + 12 + 12 + 6 =
17. 17. 3. Abraham measured the time, inseconds, that birds spent on eachindividual visit to his bird table. Thebirds made a total of 236 individualvisits.The histogram shows some of theresults.(a) Use the information in the histogram to complete the frequency table below.(b) Use the table to complete the histogram Frequency Freq density 0-10 50 10-20 20-25 25-30 20 30-50 Total 236
18. 18. 3. Abraham measured the time, in seconds, that birds spent on each individual visit to his bird table. The birds made a total of 236 individual visits. The histogram shows some of the results. (a) Use the information in the histogram to complete the frequency table below. (b) Use the table to complete the histogram Frequency Freq density 0-10 50 50/ 10 = 5 10-205 20-25 25-30 20 30-50 Total 236
19. 19. 3. Abraham measured the time, in seconds, that birds spent on each individual visit to his bird table. The birds made a total of 236 individual visits. The histogram shows some of the15 results. (a) Use the information in the histogram to complete the frequency table below. (b) Use the table to complete the histogram10 Frequency Freq density 0-10 50 50/ 10 = 5 10-20 70 7 x 10 = 70 5 20-25 25-30 20 30-50 Total 236
20. 20. 3. Abraham measured the time, in seconds, that birds spent on each individual visit to his bird table. The birds made a total of 236 individual visits. The histogram shows some of the15 results. (a) Use the information in the histogram to complete the frequency table below. (b) Use the table to complete the histogram10 Frequency Freq density 0-10 50 50/ 10 = 5 10-20 70 7 x 10 = 70 5 20-25 76 15.2 x 5 25-30 20 30-50 Total 236
21. 21. 3. Abraham measured the time, in seconds, that birds spent on each individual visit to his bird table. The birds made a total of 236 individual visits. The histogram shows some of the15 results. (a) Use the information in the histogram to complete the frequency table below. (b) Use the table to complete the histogram10 Frequency Freq density 0-10 50 50/ 10 = 5 10-20 70 7 x 10 = 70 5 20-25 76 15.2 x 5 25-30 20 20/5= 10 30-50 Total 236
22. 22. 3. Abraham measured the time, in seconds, that birds spent on each individual visit to his bird table. The birds made a total of 236 individual visits. The histogram shows some of the15 results. (a) Use the information in the histogram to complete the frequency table below. (b) Use the table to complete the histogram10 Frequency Freq density 0-10 50 50/ 10 = 5 10-20 70 7 x 10 = 70 5 20-25 76 15.2 x 5 25-30 20 20/5= 10 30-50 Total 236
23. 23. 3. Abraham measured the time, in seconds, that birds spent on each individual visit to his bird table. The birds made a total of 236 individual visits. The histogram shows some of the15 results. (a) Use the information in the histogram to complete the frequency table below. (b) Use the table to complete the histogram10 Frequency Freq density 0-10 50 50/ 10 = 5 10-20 70 7 x 10 = 70 5 20-25 76 15.2 x 5 25-30 20 20/5= 10 30-50 20 20/20 = 1 Total 236
24. 24. 3. Abraham measured the time, in seconds, that birds spent on each individual visit to his bird table. The birds made a total of 237 individual visits. The histogram shows some of the15 results. (a) Use the information in the histogram to complete the frequency table below. (b) Use the table to complete the histogram10 Frequency Freq density 0-10 50 50/ 10 = 5 10-20 70 7 x 10 = 70 5 20-25 76 15.2 x 5 25-30 20 20/5= 10 30-50 20 20/20 = 1 Total 236