Question from 2020 paper

Mathematics Level 1 1.12 Chance and data
1

Hi there
I have a question from the 2020 paper, Question 2 a iii)

My answer is below
The median for females is 227, greater than the median for males. Females median is well outside the middle 50% of males data. We can see the gap is big enough so that if there is a different sample, there isn’t the concern that medians might overlap.
The data in the graph was collected from Humpbacks found along the west coast of NZ. The claim being made refers to all coasts of NZ. While Female Humpbacks tend to weigh more than males on the west coast of NZ, it wouldn’t be accurate to apply this conclusion to all coasts because different coasts have different landscapes and temperatures, which could affect the data.

So there is no mention of data not being applicable to all coasts in the marking schedule but would my answer still be okay?

Kind Regards
Thanks

2

Hi @11111111

Yes you have covered the key points for the M grade. It is good that you are thinking about if the study is relevant to all of NZ. It could be argued either way with NZ being a relatively small country with the two main coastlines. I would definitely encourage you to think about things like this. Remember the marking schedule just notes the key things they were looking for and other ideas are also valid.

Keep up the great work, you have been doing lots of revision lately!

3

When comparing box and whisker plots you can observe three cases:

  1. Boxes do not overlap so you can claim that 75% of data from group A is greater than 75% of data from group B. That allows you to be confident that group A tends to have higher numbers (for a variable) than group B.

  2. Boxes overlap but at least one of the medians is outside of another group’s box. That is the case in this example. You can claim that 50% of female whales weigh more than 75% of male whales in this sample. That allows you to be reasonably confident that back in the population female whales tend to weigh more than male whales.

  3. Boxes overlap, medians are inside each others’ boxes. In this case you may try to make a claim based on DBM/OVS but your claim won’t be very confident.