Presenting Logical & Reasoned Arguments (AQA Level 3 Mathematical Studies (Core Maths))
Revision Note
Author
Jamie WoodExpertise
Maths
Criticising Arguments & Claims
How do I criticise an argument or claim mathematically?
A thorough argument should be backed by mathematical or statistical evidence, with clear reasoning linking to the conclusion
However, this is not always the case for claims or arguments that are made
In an exam, you may be asked to do any of the following:
Critically analyse
Look for and identify errors, suggest improvements and evaluate
whether a claim is justified
Comment on
Describe one or more notable feature(s) of the situation in the
question
Comment on the validity of
Determine if there is evidence to support the claim
Justify
Give working or reasons to support your answers
When criticising a claim or argument you must be as objective as possible
Use the data or information in front of you only
Quote the data accurately to help justify your own argument
Consider the limitations and scope of the data
If something is true in this sample, is it necessarily true for the population?
Worked Example
Basil, a hotel manager, is investigating the number of different drinks consumed each day at breakfast. The hotel serves breakfast every day and Basil conducts a survey on Friday, Saturday, and Sunday.
Basil produces the composite bar chart below, showing the number of cups of coffee, tea, and fruit juice consumed on Friday, Saturday, and Sunday.
(a) Basil claims that the most popular drink consumed on Sunday is coffee.
Comment on his claim.
Use the evidence from the composite bar chart, only considering Sunday
The lowest section of the graph in grey, shows the number of cups of tea consumed
150 cups of tea
The height of the middle (striped) section shows the number of cups of fruit juice consumed
350 - 150 = 200 cups of fruit juice
The height of the top (black) section shows the number of cups of coffee consumed
500 - 350 = 150 cups of coffee
Calculate a statistic to help evidence your argument
E.g. Coffee as a percentage of all drinks on Sunday
150 ÷ (150 + 150 + 200) = 0.3 = 30%
And for fruit juice
200 ÷ (150 + 150 + 200) = 0.4 = 40%
Comparing the figures for Sunday, coffee only represents 30% of drinks consumed, which is the same percentage as tea
Fruit juice however is the most popular, with 40% of drinks consumed on Sunday
(b) Sybil, another manager at the hotel, claims that
"According to the data, fruit juice is the most popular drink each week".
Assess the validity of Sybil's claim.
Calculate the total number of drinks consumed of each type for Friday, Saturday, and Sunday
Tea: 100 + 150 + 150 = 400
Fruit Juice: 150 + 200 + 200 = 550
Coffee: 100 + 100 + 150 = 350
Sybil's claim is true for Friday, Saturday, and Sunday, this week
However, her claim is further-reaching than this
She claims it is true "each week" which we do not have data for
Whilst Sybil's claim is valid for the sample shown, 3 days across one particular week, it does not have statistical evidence for the rest of this week, nor multiple weeks
So the claim that fruit juice is the most popular drink every week is not valid with the data provided
However, more samples, for more days and weeks, could be collected to investigate this claim
Exam Tip
The majority of marks on these questions are for the mathematical methods, rather than the final conclusion or assessment made about the claim.
So make sure your working is clear, and label what it is you are working out.
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