Topic: Number LO: Revision - Histograms. PREPARE FOR LEARNING AGREE LEARNING OBJECTIVES Starter Imagine you wanted to draw a Bar Chart to show the following.

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Presentation transcript:

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 ≤ < x ≤ < x ≤ < x ≤ < x ≤ 20020

Starter Height (cm)Frequency 100 < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ Height (cm) Frequency REVIEW

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 PRESENT NEW INFO

Histograms Frequency < x ≤ < x ≤ < x ≤ < x ≤ < 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 = = = = = CONSTRUCT MEANING

Histograms Height (cm)FrequencyFrequency Density 100 < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ Frequency Density Height (cm) CONSTRUCT MEANING

Histograms With a Histogram, area represents Frequency, not the height 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 x 0.5 = 20 so there were 20 people in the group CONSTRUCT MEANING

Histograms To take into account the size of the group, we calculate ‘Frequency Density’ Frequency Density Frequency Classwidth = Frequency Density = = < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ 40 Frequency Density FrequencySpeed (mph) = = = = = CONSTRUCT MEANING

Histograms Speed (mph)FrequencyFrequency Density 0 < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ Frequency Density Speed (mph) CONSTRUCT MEANING

Histograms 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

Your Turn… (4) 33g 103g Frequency Density DEMONSTRATE UNDERSTANDING

Your Turn… DEMONSTRATE UNDERSTANDING EXTENSION: MORE HISTOGRAM QUESTIONS

Plenary 1 Frequency Density Egg Weight (g) REVIEW

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