Histograms Population data: Lesson 7

Comparing areas instead of heights The bar chart shows the frequencies of the groups of birth rates for Africa. Although the heights correctly represent the frequencies, why could the graph be misleading? These two groups are seen as ‘bigger’. 2

Comparing areas instead of heights 3 As a more appropriate method of comparing the groups, we use the area of each bar to represent the frequencies. Frequency = Class width x ‘Frequency density’ Area = Width x Height Frequency density is placed on the y axis and values for this can be calculated by using the formula: Frequency density = Frequency Class width

Comparing areas instead of heights Birth rate (per 1000 people) Class width FrequencyFrequency density 10 < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ < x ≤

Comparing areas instead of heights The height of the two bars has now been reduced, as the areas represent the frequencies. As these bars are twice as wide, they are now half the height they were in the bar chart. Frequency = Area of bar = 10 x 0.5 = 5 Frequency = Area of bar = 5 x 3 = 15 5

Comparing areas instead of heights 6 Death rate (per 1000 people) Class width FrequencyFrequency density 2 < x ≤ Complete the table below and sketch the associated histogram for African death rates.

Comparing areas instead of heights Death rate (per 1000 people) Class width FrequencyFrequency density 2 < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ < x ≤

African death rates 8

European birth and death rates Use these histograms to compile grouped frequency tables. Compare European birth rates to death rates. 9

Comparing areas instead of heights Birth rate (per 1000 people) Class widthFrequency density Frequency 5 < x ≤ x 1.67 = 5 8 < x ≤ x 10.5 = < x ≤ x 7 = < x ≤ x 1.67 = 5 Death rate (per 1000 people) Class widthFrequency density Frequency 2 < x ≤ x 0.75 = 3 6 < x ≤ x 6 = 12 8 < x ≤ x 8 = < x ≤ x 2.5 = 5 12 < x ≤ x 3 = 9 10

Comparing data in different formats Interpret the following two graphs of birth rates in the Americas and Asia by extracting appropriate data and making comparisons between the two. 11

Comparing data in different formats 12

Comparing areas instead of heights American Birth rates (per 1000 people) Cumulative frequencyFrequency 10 < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ Asian Birth rates (per 1000 people) Class widthFrequency density Frequency 7 < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ < x ≤ < x ≤

Comparing data in different formats  Median: The Americas = 17.5, Asia = 20.  On average, birth rates are higher in Asia than in the Americas.  Range: Americas = 20, Asia = 29.  IQR: Americas = 7.5, Asia = 10.  Asia has a greater spread of birth rates than the Americas. The Americas Asia Note: Raw data values Used for the boxplots 14

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