NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Survey means and medians

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A survey of 100 students in Sydney was conducted to estimate the median number of minutes spent commuting to school each day. The data, arranged in ascending order, shows that the 50th value is 32 minutes and the 51st value is 36 minutes.

What is the exact median number of minutes spent commuting to school for this sample?

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Explanation

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Worked solution

  1. The survey collected data from 100 students in Sydney, and the commuting times are arranged in ascending order.
  2. The median is the middle value in an ordered data set. For an even number of observations, the median is the average of the two central values.
  3. Since there are 100 students (an even number), the median is the average of the 50th and 51st values in the ordered list.
  4. The 50th value is 32 minutes and the 51st value is 36 minutes.
  5. To find the median, calculate the average of 32 and 36: (32 + 36) / 2.
  6. Add the two values: 32 + 36 = 68.
  7. Divide the sum by 2: 68 / 2 = 34.
  8. The result is 34 minutes, which is the median number of minutes spent commuting to school.
  9. The median is a single value that represents the central tendency of the data set, and it is not affected by extreme values.
  10. The data was collected from a sample of students in Sydney, and the median is an estimate of the population median.
  11. The calculation is exact because both values are integers and their average is a whole number.
  12. Therefore, the median number of minutes spent commuting to school for this sample is 34 minutes.

Reference answer: 34 minutes

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