1. Topic: Number LO: Revision - Histograms. PREPARE FOR LEARNING AGREE LEARNING OBJECTIVES Starter Imagine you wanted to draw a Bar Chart to show the following information; Height (cm)Frequency 100 < x ≤ 12020 120 < x ≤ 14025 140 < x ≤ 15030 150 < x ≤ 16025 160 < x ≤ 20020

3. Starter Height (cm)Frequency 100 < x ≤ 12020 120 < x ≤ 14025 140 < x ≤ 15030 150 < x ≤ 16025 160 < x ≤ 20020 Height (cm) Frequency 0 5 20 15 10 100 25 120180160140 200 REVIEW

4. Starter Problems 1) The data is continuous so there should be no gaps 2) 150 – 160 has the same height as 120 – 140, even though it represents a smaller range A Histogram will correct both of these problems! Height (cm) Frequency 0 5 20 15 10 100 25 120180160140 200 PRESENT NEW INFO

5. Histograms 20 25 30 25 20 Frequency 0.5160 < x ≤ 200 2.5150 < x ≤ 160 3140 < x ≤ 150 1.25120 < x ≤ 140 1100 < x ≤ 120 Frequency Density Height (cm) To take into account the size of the group, we calculate ‘Frequency Density’ Frequency Density Frequency Classwidth = Frequency Density 20 = 1 = 30 10 3 = 25 20 1.25 = 20 40 0.5 = 25 10 2.5 = CONSTRUCT MEANING

6. Histograms Height (cm)FrequencyFrequency Density 100 < x ≤ 120 201 120 < x ≤ 140 251.25 140 < x ≤ 150 303 150 < x ≤ 160 252.5 160 < x ≤ 200 200.5 100140130120150160180170110200190 1 2 3 0 Frequency Density Height (cm) CONSTRUCT MEANING

7. Histograms With a Histogram, area represents Frequency, not the height 100140130120150160180170110200190 1 2 3 0 Frequency Density Height (cm) eg)The first group is a rectangle measuring 20 by 1 20 x 1 = 20 so there were 20 people in the group eg)The fifth group is a rectangle measuring 40 by 0.5 40 x 0.5 = 20 so there were 20 people in the group CONSTRUCT MEANING

8. Histograms To take into account the size of the group, we calculate ‘Frequency Density’ Frequency Density Frequency Classwidth = Frequency Density = 10 40 0.25 = 220 70 < x ≤ 80 735 65 < x ≤ 70 420 60 < x ≤ 65 1.818 50 < x ≤ 60 1.515 40 < x ≤ 50 0.2510 0 < x ≤ 40 Frequency Density FrequencySpeed (mph) 18 10 1.8 = 35 5 7 = 20 5 4 = 15 10 1.5 = 20 10 2 = CONSTRUCT MEANING

9. Histograms Speed (mph)FrequencyFrequency Density 0 < x ≤ 40 100.25 40 < x ≤ 50 151.5 50 < x ≤ 60 181.8 60 < x ≤ 65 204 65 < x ≤ 70 357 70 < x ≤ 80 202 08040302010605070 10 2 8 6 4 0 Frequency Density Speed (mph) CONSTRUCT MEANING

10. Histograms 08040302010605070 10 2 8 6 4 0 Frequency Density Speed (mph) Group 1 is a 40 by 0.25 rectangle 40 x 0.25 = 10 So 10 people in the group Remember that Area represents Frequency! Group 5 is a 5 by 7 rectangle 5 x 7 = 35 So 35 people in the group CONSTRUCT MEANING

11. Your Turn… (4) 33g 103g Frequency Density 0.5 2.2 5.3 0.5 DEMONSTRATE UNDERSTANDING

12. Your Turn… DEMONSTRATE UNDERSTANDING EXTENSION: MORE HISTOGRAM QUESTIONS

13. Plenary 1 Frequency Density 6 5 4 3 2 Egg Weight (g) REVIEW

14. Summary We have learnt how to plot Histograms of sets of data We have seen how they are different to Bar Charts We have learnt what is meant by ‘Frequency Density’ We have shown that on a Histogram, area represents Frequency, not height! REVIEW