91946 – Worked Solutions - 2025
QUESTION ONE
1.3 (AS 91946) – 2025 Answers
Quite often, there are different ways to solve a Mathematics problem.
These solutions/strategies show one possible way to solve them.
Resource 1A
The graph below shows the prices of a random sample of Adidas and Nike sports shoes taken from a New Zealand website selling shoes.
The prices are in New Zealand dollars ($NZ).
Question 1(a)
(a) Using Resource 1A, what percentage of Nike sports shoes cost more than $500?
Question 1(a)
(a) Using Resource 1A, what percentage of Nike sports shoes cost more than $500?
Question 1(a)
(a) Using Resource 1A, what percentage of Nike sports shoes cost more than $500?
Question 1(a)
(a) Using Resource 1A, what percentage of Nike sports shoes cost more than $500?
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Centre
We can see that the median cost of Nike Shoes is $234, compared to the median cost of Adidas shoes which is $131.
This means, typically Nike shoes cost around $100 more than Adidas shoes.
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Centre
We can see that the median cost of Nike Shoes is $234, compared to the median cost of Adidas shoes which is $131.
This means, typically Nike shoes cost around $100 more than Adidas shoes.
Similarly, the mean cost of Nike Shoes is $255.90, compared to the mean cost of Adidas shoes which is $158.39.
This again suggests that Nike shoes cost around $100 more than Adidas shoes.
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Shift
Nike’s middle 50% box for cost of shoes has been shifted slightly to the right of Adidas’ middle 50% box.
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Shift
Nike’s middle 50% box for cost of shoes has been shifted slightly to the right of Adidas’ middle 50% box.
Shift
There is no overlap of these boxes, as the Upper Quartile (UQ) of Adidas is $171, and the Lower Quartile (LQ) of Nike is $183.
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Shift
Nike’s middle 50% box for cost of shoes has been shifted slightly to the right of Adidas’ middle 50% box.
Shift
There is no overlap of these boxes, as the Upper Quartile (UQ) of Adidas is $171, and the Lower Quartile (LQ) of Nike is $183.
Shift
This backs up the idea that Nike shoes tend to be more expensive than Adidas shoes.
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Shape
Both Nike shoes and Adidas distributions for costs of shoes are right skewed.
Most of the data is bunched towards the left-hand side, but with 6 values in Adidas, and 9 values in Nike pulling the tail to the right.
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Spread
The range for the costs of Nike shoes is $810 (900 – 90) and the range for the costs of Adidas shoes is $639 (702 – 63).
This means that there is more variation in the costs of Nike shoes compared to Adidas shoes.
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Spread
The range for the costs of Nike shoes is $810 (900 – 90) and the range for the costs of Adidas shoes is $639 (702 – 63).
This means that there is more variation in the costs of Nike shoes compared to Adidas shoes.
The IQR for the costs of Nike shoes is $115 (298 – 183) and the IQR for the costs of Adidas shoes is $77 (171 – 94).
This also backs up the idea that there is more variation in the costs of the middle 50% of Nike shoes compared to Adidas shoes.
Question 1(b)
Compare the distributions of the cost of Adidas and Nike sports shoes shown in Resource 1A.
• Discuss similarities and differences considering centre, shift, shape, and spread.
• Provide numerical evidence where appropriate.
• In your answer, describe at least TWO different features, in context.
• What conclusion about Adidas and Nike sports shoes can you make about which brand of shoe is more expensive, based on this sample?
• Use evidence from the graph to support your answer.
Conclusion
As there is no overlap of the middle 50% of each group, we can make a claim that Nike sports shoes tends to be more epxensive than Adidas sports shoes, and Nike sports shoes also tend to have more variation in the prices.
Question 1(c)
(c) Give at least one justified reason why Resource 1A may not be reliable for comparing the cost of Adidas and Nike sports shoes.
Question 1(c)
(c) Give at least one justified reason why Resource 1A may not be reliable for comparing the cost of Adidas and Nike sports shoes.
This data comes from only one website.
There is a large number of sport-shoes website with a wide variety in the cost of sports shoes, so we would need to be very careful, as this website might not represent the costs of sports shoes on all website prices.
We don’t know if this was including sale prices or the original retail prices. This could mislead people on the cost of shoes, if they include sale prices, showing a cheaper price.
This website is based in New Zealand, for women. It again may not represent all shoes for both genders.
Question 1(c)
(c) Give at least one justified reason why Resource 1A may not be reliable for comparing the cost of Adidas and Nike sports shoes.
This data comes from only one website.
There is a large number of sport-shoes website with a wide variety in the cost of sports shoes, so we would need to be very careful, as this website might not represent the costs of sports shoes on all website prices.
We don’t know if this was including sale prices or the original retail prices. This could mislead people on the cost of shoes, if they include sale prices, showing a cheaper price.
This website is based in New Zealand, for women. It again may not represent all shoes for both genders.
Question 1(c)
(c) Give at least one justified reason why Resource 1A may not be reliable for comparing the cost of Adidas and Nike sports shoes.
This data comes from only one website.
There is a large number of sport-shoes website with a wide variety in the cost of sports shoes, so we would need to be very careful, as this website might not represent the costs of sports shoes on all website prices.
We don’t know if this was including sale prices or the original retail prices. This could mislead people on the cost of shoes, if they include sale prices, showing a cheaper price.
This website is based in New Zealand, for women. It again may not represent all shoes for both genders.
Resource 1B
The graph below shows the amount of money spent (millions of $NZ) on clothing and footwear each quarter, between the years 2010 and 2024. Each quarter is a group of 3 months. Quarter 1 is January to March; Quarter 2 is April to June; Quarter 3 is July to September; Quarter 4 is October to December. The blue line is the long-term trend for the data shown.
Question 1(d)
(d) What trends, repeating patterns, and unusual features do you notice in the spending shown in the graph?
• Support your statements with evidence from the graph.
• Give at least two reasons to support and explain your answer.
Question 1(d)
(d) What trends, repeating patterns, and unusual features do you notice in the spending shown in the graph?
• Support your statements with evidence from the graph.
• Give at least two reasons to support and explain your answer.
We can see that the long-term trend of the amount of spending is steadily increasing from approximately $790 million NZD in 2010 to approximately $1090 million NZD in 2024. This could be because the population of NZ is increasing and prices are rising .
Question 1(d)
(d) What trends, repeating patterns, and unusual features do you notice in the spending shown in the graph?
• Support your statements with evidence from the graph.
• Give at least two reasons to support and explain your answer.
There seems to be a repeating pattern. Spending generally looks like it peaks in Quarter 4 of each year, when it is close to Christmas. Spending is likely to increase then because people tend to spend more buying presents for families and colleagues and partners etc, as well as buying clothes and footwear for the summer activities.
Question 1(d)
(d) What trends, repeating patterns, and unusual features do you notice in the spending shown in the graph?
• Support your statements with evidence from the graph.
• Give at least two reasons to support and explain your answer.
The appears to be a few outliers, that do not follow the repeating trend;
*In 2017 Q2, we have an unusual peak in spending, of approximately $1400 million NZD.
Question 1(d)
(d) What trends, repeating patterns, and unusual features do you notice in the spending shown in the graph?
• Support your statements with evidence from the graph.
• Give at least two reasons to support and explain your answer.
The appears to be a few outliers, that do not follow the repeating trend;
*In 2017 Q2, we have an unusual peak in spending, of approximately $1400 million NZD.
*And in 2021, there appears to be a dip in spending during the entire year, likely due to the Covid pandemic and less people out and about in shops.
Question 1(e)
(e) Using Resource 1B, make a prediction about future spending on clothing and footwear in New Zealand. Explain your prediction, and discuss how confident you are in it.
Question 1(e)
(e) Using Resource 1B, make a prediction about future spending on clothing and footwear in New Zealand. Explain your prediction, and discuss how confident you are in it.
Question 1(e)
(e) Using Resource 1B, make a prediction about future spending on clothing and footwear in New Zealand. Explain your prediction, and discuss how confident you are in it.
I predict that in the future the amount of spending on clothes and shoes will continue to rise, even though there is a drop of money spent since mid 2022.
This follows the long-term trend, which has increased since 2010 from approx. $800 million NZD to approx. $1100 million NZD.
I would be reasonably confident with this prediction for the next few years, as it is too difficult to predict further than this due a variety of factors. The drop in spending due to Covid in 2021 and a second drop in spending during 2022-2024, which could be still related to Covid or due to other factors, does make any future predictions a little less reliable in case an external factor like this happens again.
Question 1(e)
(e) Using Resource 1B, make a prediction about future spending on clothing and footwear in New Zealand. Explain your prediction, and discuss how confident you are in it.
Valid comment regarding future predictions made
AND
Justifies how confident they would be with the predictions for the next few years.
I predict that in the future the amount of spending on clothes and shoes will continue to rise, even though there is a drop of money spent since mid 2022.
This follows the long-term trend, which has increased since 2010 from approx. $800 million NZD to approx. $1100 million NZD.
I would be reasonably confident with this prediction for the next few years, as it is too difficult to predict further than this due a variety of factors. The drop in spending due to Covid in 2021 and a second drop in spending during 2022-2024, which could be still related to Covid or due to other factors, does make any future predictions a little less reliable in case an external factor like this happens again.