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1) Mathematics uses more of deductive reasoning, logic and evidence and we solve to jump to a certain conclusion using proof where as statistics utilises inductive reasoning by creating groups, gaining data and there is always seems to be some uncertainty in the conclusion.

2) Statistics is very easy to be misinterpreted or think that it is misled because of sampling bias when gathering data, maybe because of using different techniques and proportions than what the investigation and use of statistics require. There could be selective biases like cherry picking data and overgeneralisation of one data point to make it seem much bigger than it is. Manipulation of the visuals and graphs. An example of this is:

The Literary Digest, a well-known journal, incorrectly predicted Alfred Landon's election victory. Despite a track record of accuracy, the 1936 forecast failed because of skewed factors. 1) selective bias- The poll used telephone and vehicle registration databases to reach out to people in a specified socioeconomic category. 2) Furthermore, there was a bias because Landon supporters were more likely to participate in the poll, resulting in a major distortion of general sentiment. In the end, Franklin D. Roosevelt won convincingly, emphasising the need of extensive and fair polling methodology.

3) It is not justifiable to use statistics with the intention to mislead others as it can cause many problems such as deception, incorrect conclusions and low reliability and confidence which is not fair and honest.

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1. Statistics often does not produce definitive conclusions whereas mathematics usually does. Measurement plays different roles and is treated differently in mathematics and statistics. This is because Mathematics have a definitive answer whereas stats is up to interpretation.

2. Factors contributing to misleading statistics include selective bias, neglected sample size, faulty correlations, and causations, and the use of manipulative graphs and visuals. These issues can arise from intentional manipulation or unintentional errors in data handling and interpretation.

3. I do not think that it is justifiable to purposely use statistics to mislead someone as the person can interpret the data differently or the data can be manipulated to be interpreted differently.

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I do not think that mathematics and statistics are treated as separate subjects. statistics is a part of mathematics and uses other aspects such as probability to be solved in some cases which is also a part of mathematics altogether.

Statistics can be mislead due to the different types of data collection. Demographics need to be cross checked and verified effectively to not be mislead by statistical data.

It is incorrect to use statistics to mislead others with data provided since people make decisions and analyse situations through statistics and a faulty statistical report can cause more damage than benefits. An example of misleading statistics that caused deceptions is the statistics China uploaded about their Covid-19 cases in 2020. They intentionally deceived other countries by hiding the actual number of cases and reducing them while providing statistics. This was damaging for China since, it portrayed to countries that they cannot trust their government and there were data based conflicts globally.

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Despite their connection, statistics and mathematics have generally been taught as separate subjects. While theoretical connections and structures are covered by mathematics, statistics focuses only on the gathering, analysing, and interpreting of data. Sample bias, confusion about correlation and causation, limited sample sizes, selective data collection, and confounding variable omission are some of the ways that statistics may be abused. It is generally seen to be unethical to deliberately utilise statistics to deceive others since it undermines confidence and can have negative effects. Transparency, truthfulness, and correct data representation are prioritised in ethical statistical practices to guarantee responsible and trustworthy information distribution.

Cherry-picking Data: To give the appearance that crime rates have dramatically grown during the current administration, a political candidate may use crime figures from a certain time period. The candidate might skew the statistics to fit their story by utilising a small timeframe or disregarding past tendencies.

Correlation versus Causation: Let's say a study discovers a positive relationship between the quantity of ice cream sold and the frequency of drownings in swimming pools. Drawing the conclusion that increasing ice cream purchases cause an increase in drownings would be erroneous. As warm weather really affects both variables, it is important to take confounding factors into account.

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1)Math and statistics may be considered as different subjects as generally statistics has uncertain answers and conclusions to a problem while on the other hand math always has a definitive answer and cannot have inconclusive answers.

2) There are many factors that lead to misleading statistics such as selective bias and the manipulation of graphs and visuals this is widely used by politicians and the government to manipulate the general public into thinking that the country has taken up a good path although in reality these graphs and data is manipulated to make it look better to the public's eye.

3) Personally I think it is not justified to use statistics to mislead others this does not only provide false information on important topics but it also brings down the credibility of the source that is providing this data. Half-truths are not fair towards the general public because the blind faith they have on this data and statistics can cause a lot of false information to dpread in the world.

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1) I believe that statistics is a part of maths as a whole- as statistics branches from concepts of maths such as probability. Without statistical data, I do not think there is a way to analyse any concept using mathematical understanding. However statistics utilizes inductive reasoning and conclusions are always uncertain, and subjective to the perspective that is being looked at, as compared to maths concepts in general which is objective in nature.

2) I think that it is very easy to be mislead by statistics, as they can be manipulated by anyone, and as humans are cognitive misers- we would not look into statistics we see, and be content with the values we see without feeling the need to further investigate. According to DataPine, there are many examples of misleading COVID statistics- some countries felt the need to look better by manipulating the statistics based on the death rate from COVID 19.

3) No, deliberately using data to mislead someone is unethical and dishonest. It breaks trust, gives the wrong idea about the reality of a situation, and can have serious consequences- especially in business and bigger organizations. It hampers informed decision-making.

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1) The study of mathematics is a vast field that includes theorems, abstract structures, and mathematical reasoning. It covers foundational ideas that are relevant to many different domains. In contrast, statistics focuses on the collection, analysis, and interpretation of data, providing methods for making inferences about populations.

2) It is relatively easy to be misled by statistics if one is not vigilant and critical in their interpretation. Statistics can be manipulated or presented in a biased manner, leading to false conclusions. Common pitfalls include selecting a non-representative sample, misusing statistical tests, or presenting data without proper context. Additionally, the misinterpretation of correlation as causation and reliance on small sample sizes can contribute to erroneous conclusions. Therefore, statistical literacy and a nuanced understanding of data are essential for individuals to navigate the complex landscape of statistical information.

3) It is never justifiable to purposely use statistics to mislead others. Deliberate manipulation of statistical information for deceptive purposes, known as statistical deception, is considered unethical. Ethical guidelines in research stress transparency, honesty, and accuracy in reporting findings. Intentionally distorting statistics can erode trust in data, compromise the integrity of research, and have far-reaching consequences. Maintaining the credibility of statistical information is crucial for informed decision-making, policy development, and public trust in various domains, including science, business, and governance. Ethical considerations dictate that statisticians and researchers should prioritise truthfulness and integrity in their use and presentation of statistical data.

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1. Why have mathematics and statistics sometimes been treated as separate subjects?

Mathematics and statistics have sometimes been treated as separate subjects due to their distinct nature and the perception that they deal with different aspects of data analysis. Mathematics focuses on the theory, formulas, and calculations behind numerical data, while statistics deals with the collection, organization, and interpretation of data to draw conclusions and make decisions

2. How easy is it to be misled by statistics?

It is possible to be misled by statistics due to several reasons, including selective data display, neglected sample size, wrong correlations and causations, and manipulative graphs and visuals. Misleading statistics can lead to incorrect conclusions and poor decisio making

3. Is it ever justifiable to purposely use statistics to mislead others?

It is never justifiable to purposely use statistics to mislead others, as it can lead to confusion and misinformation, in data and its applications. Particularly in the age of social media and online content. It is essential to critically evaluate sources of information and consider the context when interpreting statistics and data.

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1.There are educational and historical justifications for the division of mathematics and statistics. The history of mathematics, as an abstract and fundamental field that includes algebra, geometry, and calculus, is extensive. These mathematical concepts are frequently presented in a more theoretical context in educational settings, with an emphasis on the improvement of logical reasoning and problem-solving abilities. In contrast, statistics developed as a field of study to deal with real-world problems involving the gathering, analysing, and interpreting of data. The creation of distinct statistics departments and courses resulted from this pragmatic approach.

2.Those who lack statistical literacy or critical thinking abilities are easily tricked by misleading statistics. Inaccurate conclusions can arise from the selective use of data or the presentation of statistics out of context. Using biassed samples, relying on small sample sizes, and mistaking correlation for causation are common mistakes. People need to be sceptical of methodology, sources, and potential biases when consuming statistical information in order to avoid being mislead in a world where data is abundant.

3.Using statistics to intentionally mislead people is never ethically acceptable. Such activities have far-reaching effects, compromise the reliability of information sources, and compromise the integrity of data. Transparency, honesty, and accuracy in the communication of research findings are prioritised by ethical guidelines in data reporting and research. Deliberate statistical manipulation, also referred to as statistical deception, is widely condemned and can happen in a variety of settings, including political discourse and advertising. Ensuring that information is used responsibly and truthfully in decision-making processes is a shared obligation of society, as much as it is for statisticians and researchers to uphold the ethical use of statistics.

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1. Mathematics covers algebra, geometry, calculus, and more, focused on abstract structures and forms. Statistics focuses on data collection, analysis, interpretation, presentation, and organisation. Both subjects use maths, but they emerged separately with different focuses and applications. Mathematical solving gives certain solutions whereas statistics provides uncertainty since it is based on interpretations.

2. Misleading by statistics can lead to false conclusions because statistics is a helpful method and concept in understanding as well as interpreting a data. Misleading would be through selective graphs and a major one is sampling bias where researcher purposely chooses a certain sample to either prove/disprove their hypothesis when collecting data. Other factors include confounding variables, selective reporting, correlation vs causation and more.

3. It is unethical to purposely mislead someone to interpret data in a designated direction. Transparency is required and ethical practice requires truthfulness about data and findings.

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The field of mathematics is vast and it therefore deals with quantities, numbers, shapes, and abstract reasoning. It is more theoretical in nature and concentrates on comprehending and substantiating underlying  principles. As opposed to this, statistics is a subfield of mathematics that focuses only on gathering, evaluating, interpreting, and presenting empirical data. It is relatively easy to be misled by statistics due to many factors like biased sampling, misleading graphs, cherry-picking data, and misuse of statistical significance. Additional, the presentation and interpretation of the data can lead to a misleading understanding as well. Lastly, it is not justifiable to use statistics to mislead others as it is deceptive, manipulating information to create false impressions or conclusions undermine the integrity of information, leading to misinformed decisions and eroding trust in data-driven knowledge

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1. Statistics can often have bias as it uses inductive reasoning and the conclusions formed are not certain. Whereas, mathematics unlike statistics is not based on the interpretation of data.

2. there can be errors in handling the data and interpretation can be biased.

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1) For different reasons, mathematics and statistics have been viewed as separate subjects at times. While statistics is founded on mathematical ideas, it has evolved its own body of knowledge and methodologies, earning it recognition as a distinct subject.

Mathematics and statistics have a complicated relationship. Because of its reliance on mathematical concepts and procedures, statistics is frequently seen as a branch of mathematics. Statistics, on the other hand, has emerged as a distinct science with its own theories, methodology, and applications. This has sparked controversy over whether statistics should be considered a part of mathematics or a separate discipline.

2) Statistics can be deceptive, resulting in inaccurate conclusions, poor decision-making, and a false sense of certainty in particular views or assumptions. Misuse of statistics happens when a statistical argument claims a falsehood, whether mistakenly or on purpose for the perpetrator's benefit. Misleading statistics can provide people with inaccurate information that deceives them rather than informs them, and when taken out of context, they can lead to inaccurate conclusions. Statistics can be misleading in a variety of ways, including selective bias, inadequate sample size, inaccurate correlations and causations, and the use of manipulative graphs and visualisations since most viewers tend to accept information as credible when presented with statistics without verifying the information for themselves.

3)In my opinion, using statistics to deceive others is never justified. Statistics that are misleading might be used to build a false narrative about an issue, influencing public opinion and decision-making. This can be observed in advertising, politics, and news, as inaccurate facts are utilised to persuade the public to support a specific product, candidate, or cause. Misleading data can be used to conceal the truth about a product's, service's, or idea's usefulness or performance, making it difficult for consumers to make informed decisions. Presenting inaccurate statistics can assist individuals or organisations to avoid accountability for their actions or decisions by shifting the focus away from the underlying issues and towards the misleading facts.

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Mathematics and statistics have sometimes been treated as separate subjects due to their different focuses. Mathematics deals with the study of numbers, quantities, shapes, and patterns, while statistics involves the collection, analysis, interpretation, and presentation of data. However, they are closely related, as statistical methods often rely on mathematical principles for their foundation.It is easy to be misled by statistics due to the potential for misuse of numerical data, either intentionally or by error. Misleading statistics can create false narratives around a topic, leading to misunderstandings. Examples of misleading statistics include the misuse of graphs, faulty polling, and the intentional omission of data. It is crucial to critically evaluate statistical information to avoid being misled.Purposely using statistics to mislead others is unethical and can have serious consequences. Misuse of statistics, whether accidental or intentional, can lead to false conclusions and misinform the public. It is important to promote ethical and accurate use of statistics to maintain the integrity of data and information.Misleading statistics can be identified through careful analysis of graphical displays, ensuring that the data is represented accurately and without bias. This involves examining the labeling, scaling, and presentation of data to detect any potential misinterpretation

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1. Even though statistics is a subset of mathematics, it has sometimes been treated as separate subject because of the distinct methodologies used in the field of statistics in comparison with the other sub-fields. While fields like calculus and trigonometry use more algebraic approaches and can be theoretical in nature, statistics inherently requires the application of real life contexts to reach conclusions.

2. It is easy to be misled by statistics due to their ability to persuade audiences. Sometimes statistics can have biases, mathematical inaccuracies, etc. which can cause a statistic to be inaccurate, and thereby mislead those who have been persuaded.

3. It is never justified to purposely mislead someone with statistics because it is unethical. This is since statistics are used in fields like economics, psychology, etc. to reach conclusions, and if they are intentionally inaccurate, then it could lead to false conclusions and cause larger errors in reports.

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1) The study of mathematics has historically involved theoretical ideas and abstract reasoning with an emphasis on the establishment of proofs. On the other hand, statistics deals with data collection, analysis, interpretation, and presentation; it is frequently linked to empirical observations and inductive reasoning. Although both disciplines make use of mathematical concepts, their main goals and uses are different.

2)First of all, sampling bias happens when a study's sample isn't representative of the total population, which makes it impossible to generalise the findings. Although this logical mistake is frequently made, correlation does not imply causation, which can lead to incorrect assumptions about cause-and-effect relationships. By altering the way that data is visually represented, misleading graphs and charts have the power to skew perceptions. Biassed interpretations can also result from cherry-picking data, which is the selective presentation of information to favour a particular position while disregarding contradicting information.

3) It is unethical and unacceptable to purposefully mislead others with data. Intentionally tampering with data or statistical analysis compromises the reliability of scientific findings, and can have detrimental effects on understanding. Transparency, honesty, and the appropriate application of statistical methods are prioritised by ethical rules and standards. These values forbid deception of others by the use of statistics, and those caught doing so risk moral and legal consequences.

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1. I think that Maths and stats have been treated as separate topics due to their application. Traditional math topics such as geometry and algebra are more often use in natural sciences such as astrophysics and chemistry, whereas stats is used more often in the human sciences such as biology, and psychology

2. I think it is very easy to be misled by statistics due to inherent biases. One example of this is people often assuming that correlation means causation. Other examples include biases such as the framing effect where stats can be framed in a particular way to prove a person's main argument

3. I don't believe it is ethically justifiable to use statistics to mislead people since it can cause harm to the individual. For example, in the medical field, if a company frames statistics in a certain way to sell their medicines which aren't actually very effective, it could cost people their lives.

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Despite their connections, statistics and mathematics have frequently been treated as separate subjects because of their different approaches and areas of focus.  The main goals of mathematics are the proof of theories and the establishment of consistency.  It is a discipline that uses logical reasoning and proof to arrive at absolute truths and definitive conclusions.  On the other hand, the organization, interpretation, collection, analysis, and presentation of data are all covered by the mathematical field of statistics.  Although it is based on the mathematical discipline of probability, its main goal is to comprehend and analyze uncertainties.  Statistical interpretation is contingent upon context, unlike mathematics, which is generally context-independent.  Practical experience and real-world application are essential to its application. Statistical errors in interpretation or application can quickly result in incorrect conclusions.  Erroneous polling, flawed correlations, data fishing—the practice of choosing results that confirm a particular conclusion while disregarding those that do not—and misleading data visualization can all lead to this.  It is possible to manipulate statistics in order to present false narratives, deceive casual observers, and assert falsehoods.  This misuse frequently takes place in a variety of industries, including politics, journalism, advertising, and media, where information can be twisted to support a specific viewpoint or agenda. The deliberate manipulation of statistics to deceive others is typically regarded as unethical.  False beliefs, incorrect decisions, and negative outcomes are possible outcomes.  For example, in medical science, the dissemination of false information based on misleading statistics can have serious consequences and even result in the loss of lives.  Correcting such an untruth could require decades.  However, some could contend that there might be circumstances. There are situations in which it is acceptable to use misleading statistics, such as when attempting to protect sensitive data or achieve greater good.  Regardless, it is always important to carefully consider the ethical ramifications of using misleading statistics, as the potential harm frequently outweighs any benefits.

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1) The distinct goals of statistics and mathematics have in the past contributed to their separation. While statistics focuses on practical applications and provides the tools required to analyse, interpret, and draw conclusions from real-world data, mathematics is concerned with abstract structures and theoretical concepts.

2) Although statistics is an effective tool for drawing conclusions from data, there is always a chance that results will be misinterpreted. Critical interpretation is crucial because incorrect interpretations can be caused by biased data selection, selective sampling results, correlation-causation errors, small sample size constraints, and misleading visual representations.

3) When statistics tend to be intentionally misused, it can have a negative ethical impact on society and the economy, reduce trust, compromise scientific integrity, compromise one's reputation, and interfere with democratic processes. To ensure responsible and credible use of statistical tools, an ethical approach involves transparency, caution in data representation, and a commitment to truthfulness.

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The separation of mathematics and statistics in educational and professional contexts often stems from differences in focus and application, despite the inherent connections between the two disciplines.

Mathematics, as a broader field, involves the study of abstract structures, patterns, and relationships using logic and deductive reasoning. It encompasses a wide range of areas, including algebra, geometry, calculus, and number theory. In contrast, statistics primarily deals with the collection, analysis, interpretation, presentation, and organisation of data. While statistics relies on mathematical principles, it is more focused on the practical application of these principles to real-world problems.

The distinction between mathematics and statistics is somewhat artificial and varies across educational systems. In many cases, they are intertwined, with statistics courses often incorporating mathematical concepts, and mathematical research frequently involving statistical methods.

Regarding the potential for being misled by statistics, it's crucial to recognise that statistics can be manipulated or misinterpreted to convey a particular narrative.