Histograms
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Histograms

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Histograms Presentation Transcript

  • 1. Histograms 8 7 6 5 4 3 2 1 0 1-10 11-20 21-30 31-40 41-50 51+ © T Madas
  • 2. How do we present Continuous Data?Continuous Data can only be presented in groupsWe can only present Grouped Continuous DataThe main graph for Grouped Continuous Data is:A Histogram © T Madas
  • 3. Response Times to a Maths Question 14 f Class Frequenc interval y 12(seconds) f0 ≤ t < 10 12 1010 ≤ t < 20 14 820 ≤ t < 30 7 630 ≤ t < 40 8 440 ≤ t < 50 5 2 t50 ≤ t < 60 4 0 0 10 20 30 40 50 60 © T Madas
  • 4. Response Times to a Maths Question 14 f 12A histogram looks 10like a bar chart but: 8Continuous Data 6 Histogrammeans NO GAPS 4between bars 2 t 0 0 10 20 30 40 50 60 © T Madas
  • 5. This seems a small differencebetween a bar chart and aHistogram. Is that it? NO © T Madas
  • 6. The real difference between Bar Chartsand Histograms is:In a Bar Chart the lengths of the bars areproportional to the frequency they represent.In a Histogram the areas of the rectangles areproportional to the frequency they represent. © T Madas
  • 7. Response Times to a Maths Question 14 f 12 10The heights of the bars 8represent frequency onlyif the groups are of equal 6intervals 4 2 t 0 0 10 20 30 40 50 60 © T Madas
  • 8. Histograms withunequal width intervals © T Madas
  • 9. Reaction Times in a Chemistry Experiment ? Frequency Class Frequency Density interval Frequency density(seconds) f0 ≤ t < 4 3 0.754 ≤ t < 5 8 85 ≤ t < 6 9 9 Frequency Frequency Density =6 ≤ t < 7 13 13 Class width7 ≤ t < 8 5 5 t 0 1 2 3 4 5 6 7 8 98 ≤ t < 10 6 3 10 © T Madas
  • 10. Reaction Times in a Chemistry Experiment Frequency Class Frequency 14 Density interval Frequency density(seconds) 12 10 f0 ≤ t < 4 3 0.75 84 ≤ t < 5 8 8 65 ≤ t < 6 9 9 46 ≤ t < 7 13 13 27 ≤ t < 8 5 5 t 0 0 1 2 3 4 5 6 7 8 98 ≤ t < 10 6 3 10 © T Madas
  • 11. AnotherExample © T Madas
  • 12. Lengths of a certain Plant’s Leaves ? Frequency Class Frequency Densityinterval Frequency density (cm) f 0≤ L <4 8 2 4≤ L <6 10 5 6≤ L <8 12 6 Frequency Frequency Density = 8≤ L <9 13 13 Class width9≤ L <11 14 7 L 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1511≤ L <15 6 1.5 © T Madas
  • 13. Lengths of a certain Plant’s Leaves Frequency Class Frequency 14 Densityinterval Frequency density (cm) 12 10 f 0≤ L <4 8 2 8 4≤ L <6 10 5 6 6≤ L <8 12 6 4 8≤ L <9 13 13 29≤ L <11 14 7 L 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1511≤ L <15 6 1.5 © T Madas
  • 14. Exam Question © T Madas
  • 15. The histogram below gives information about the times120 pupils spent on their last Maths homework.Use the histogram to complete the frequency table. 5 Time Frequenc (t min) yFrequency density 4 0 < t ≤ 10 20 The area of the rectangles of a 3 10 < t ≤ 15 25 histogram represent frequency 15 < t ≤ 30 45 2 30 < t ≤ 60 30 1 0 10 20 30 40 50 60 Time, in minutes © T Madas
  • 16. Exam Question © T Madas
  • 17. The histogram and the table below gives informationabout the weights of 120 pupils in Year 11Complete the histogram and the frequency table. The area of the rectangles of a 5 Weight Frequenc histogram represents frequency (w kg) yFrequency density 4 30 < w ≤ 40 10 3 40 < w ≤ 55 45 55 < w ≤ 60 20 2 60 < w ≤ 90 45 1 0 30 40 50 60 70 80 90 Weight, in kg © T Madas
  • 18. © T Madas
  • 19. The histogram below shows the age distribution of accident and emergency admissions in the Colby City Hospital for a particular month. Given that there were 90 admissions for the 20-25 age group, calculate the number of admissions for all the other age groups. 30 The area of the rectangles of a 27 histogram represents 24 frequencyfrequency density 21 18 18 15 12 9 225 225 135 120 6 90 5 3 90 45 30 0 10 20 30 40 50 60 70 80 90 age © T Madas
  • 20. © T Madas
  • 21. The histogram below shows the age distribution of accident and emergency admissions in the Colby City Hospital for a particular month. Given that there were 90 admissions for the 20-25 age group, calculate the number of admissions for all the other age groups. The area of the rectangles of a histogram represents frequency Squares : Datafrequency density 12 : 90 4 : 30 90 6 : 45 30 : 225 18 : 135 225 225 135 120 90 16 : 120 90 45 30 0 10 20 30 40 50 60 70 80 90 age © T Madas
  • 22. © T Madas