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GCSE Maths Statistics & Probability S 14 Histograms with Unequal Class Intervals Subject Content Reference: S3.2h A histogram with unequal class intervals uses the notion of frequency density . . learn Frequency Density = Frequency ÷ Class Interval Example The following table shows the time (in minutes) taken for 100 athletes to complete a marathon. Draw up a histogram and from it, estimate the number of athletes who took between 2 1/2 and 3 hours to finish: Time (t) in minutes 125 ≤ t < 140 140 ≤ t < 160 160 ≤ t < 170 170 ≤ t < 195 195 ≤ t < 235 235 ≤ t < 285 Frequency 6 16 28 35 10 5 Frequency Density 0.4 (6 ÷ 15) 0.8 (16 ÷ 20) 2.8 (28 ÷ 10) 1.4 (35 ÷ 25) 0.25 (10 ÷ 40) 0.1 (5 ÷ 50) Step 1: Draw the axes for time and frequency density . . Step 2: Draw in the bars . . Frequency Density 3 Step 3: Shade in the parts of the histogram between 21/2 and 3 hours (150 and 180 mins) . . 2 . . and calculate the frequency represented = 1/2(16) + 28 + 2/5(35) 1 = 8 + 28 + 14 = 50 answer It’s important to realise that the area of each rectangle represents the frequency (frequency density x time) 50 100 150 200 250 Time in minutes Exercise 1 1) The following table shows the time taken for members of a cycling club to finish a 100 km charity ride: Time (t) in minutes 120 ≤ t < 140 140 ≤ t < 155 155 ≤ t < 170 170 ≤ t < 195 195 ≤ t < 205 205 ≤ t < 285 Frequency 6 30 45 55 28 16 Frequency Density a) Complete the table by calculating frequency densities: b) Draw a histogram to show this information: c) Use the histogram to estimate the number of cyclists completing the ride between 21/2 and 31/2 hours: Exercise 1 (cont’d) 2) The following table shows the distance covered by cars in a 24 hour race: Distance (d) in 1000 km 2.25 ≤ d < 2.4 2.4 ≤ d < 2.5 2.5 ≤ d < 2.75 2.75 ≤ d < 2.95 2.95 ≤ d < 3.25 3.25 ≤ d < 3.5 Frequency 3 5 15 18 12 8 Frequency Density a) Complete the table by calculating frequency densities: b) Draw a histogram to show this information: c) Use the histogram to estimate the number of cars covering between 2650 and 3150 km: