Air-quality readings and grouped representation

Air-quality readings and grouped representation

Secondary 2
11 marks
TGM Original Questions

Core stretch

The air-pollution index measures air pollution; a lower reading indicates better air quality. The 30 daily readings for June are 22, 28, 35, 40, 45, 48, 52, 58, 61, 65, 70, 74, 78, 80, 84, 90, 96, 102, 110, 118, 125, 132, 140, 148, 155, 160, 168, 175, 184, 195.

  1. Using classes \(0<x\le40,40<x\le80\), and so on to 200, construct a frequency table.[3]
  2. Draw a histogram.[3]
  3. Give one advantage of a histogram for comparing the frequencies in the stated ranges.[1]
  4. Values above 80 are unhealthy; find the percentage of unhealthy days.[2]
  5. In July, the mean index was 72. Assess whether the average air quality improved from June to July. Explain why this comparison alone does not determine whether July had fewer unhealthy days.[2]

Solution:

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Answer:(i) \(4,10,6,6,4\) (ii) See worked solution (iii) compact comparison of frequencies in the stated ranges (iv) \(53.3\%\) (v) improvement is suggested because \(72<97.9\), but the mean alone does not determine July’s unhealthy-day percentage.

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