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0580/43 May/Jun 2024, Question 3: Averages from Frequency Tables

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 11 marks

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The question, in short

From a 60-roll dice frequency table, work out mode, median and mean; from a grouped table of 100 car speeds, estimate the mean and find histogram bar heights given one bar is 3 cm.

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Part (a) · 5 marks

Using the six scores and their frequencies, determine the mode, the median and the mean of the 60 rolls.

  1. 1Mode = 5 (highest frequency 14)
  2. 2Cumulative: 10, 16, 27, 40 → 30th and 31st values are both 4, median = 4
  3. 3Σfx = 10 + 12 + 33 + 52 + 70 + 36 = 213
  4. 4Mean = 213 ÷ 60 = 3.55

Answermode = 5, median = 4, mean = 3.55

Part (bi) · 4 marks

Using class midpoints for the three speed groups, work out an estimated mean speed for the 100 cars.

  1. 1Midpoints 25, 40, 62.5
  2. 2Σfx = 10 × 25 + 72 × 40 + 18 × 62.5 = 250 + 2880 + 1125 = 4255
  3. 3Mean = 4255 ÷ 100 = 42.55 km/h

Answer42.55 or 42.6

Part (bii) · 2 marks

With the 20 < v ≤ 30 bar drawn 3 cm tall, work out the heights of the 30 < v ≤ 50 and 50 < v ≤ 75 bars.

  1. 1Frequency densities: 10 ÷ 10 = 1, 72 ÷ 20 = 3.6, 18 ÷ 25 = 0.72
  2. 2Density 1 is 3 cm, so heights are 3.6 × 3 = 10.8 cm and 0.72 × 3 = 2.16 cm

Answer30 < v ≤ 50: 10.8 cm; 50 < v ≤ 75: 2.16 cm

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