60 potato plants produce 5 to 10 potatoes each. The mass of potatoes produced by each plant were measured. The cumulative frequency curve below shows the distribution of the masses of the potatoes produced by each plant.

((i))
Use the curve to estimate
1. ((a))
  the median mass,
  
  Answer ... kg
2. ((b))
  the interquartile range.
  
  Answer ... kg
((ii))
It was stated that 20% of the potato plants were considered premium plants as they produced greater mass of potatoes.

Find the least mass of potatoes produced for the plant to be 'premium'.

Answer ... kg
((iii))
The potatoes produced by another group of 60 plants have the same median but smaller interquartile range.

Describe how the cumulative frequency curve will differ from the given curve.

Answer ...

...

Analysis interpretation Quartiles percentiles 中文

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Worked solution

9((iii))

1. Relate the same median and smaller interquartile range to the shape of the cumulative frequency curve.

For $60$ plants, the median is read at cumulative frequency $30$ .
Same median: the new curve has the same mass value at cumulative frequency $30$ .
Smaller interquartile range: the mass difference between cumulative frequencies $45$ and $15$ is smaller, so the curve is more concentrated and steeper around the middle.

Answer

The new cumulative frequency curve passes through the same median point at cumulative frequency $30$ , but is steeper around the median, so that the horizontal distance between the points at cumulative frequencies $15$ and $45$ is smaller.

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60 potato plants produce 5 to 10 potatoes each. The mass of potatoes produced by each plant were measured. The cumulative frequency curve below shows the distribution of the masses of the potatoes produced by each plant.

Worked solution

9((iii))

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