## **Learning Outcomes**

After reading this article, you will be able to approach LSAT logical reasoning questions involving quantitative data, statistics, and sampling. You will be able to identify and analyze arguments that use statistical evidence, recognize flawed reasoning with numbers or percentages, and distinguish common errors such as unrepresentative samples and mistaken correlations. You will also know the best techniques for strengthening or weakening statistics-based arguments.

## **LSAT Syllabus**

For LSAT, you are required to understand how quantitative reasoning and statistics are used in arguments, and how to critically assess them. In your preparation, focus especially on:

- recognizing and evaluating the use of statistical data and quantitative claims
- identifying arguments that rely on surveys, studies, or samples, and assessing if these are representative
- understanding how percentages, proportions, and raw numbers are used in reasoning
- analyzing arguments that imply causation from correlation or statistical evidence
- using statistical flaws to strengthen or weaken LSAT arguments, especially in critical questions

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. When a logical reasoning question presents survey results as evidence, which one of the following issues is most relevant for evaluating the argument?  
   a) whether the argument contains a contrapositive  
   b) whether the sample is representative of the group discussed in the conclusion  
   c) whether the argument uses formal logic  
   d) whether the survey asked only yes/no questions

2. Which is a common statistical flaw?  
   a) assuming that correlation proves causation  
   b) confusing a necessary with a sufficient condition  
   c) attacking the author's motivation  
   d) using a syllogism

3. True or false? In LSAT arguments, a raw number difference always implies a percentage difference.

4. In a weaken question with a statistical study, which answer type is most likely to be correct?  
   a) one that identifies an unrepresentative sample  
   b) one that challenges a definition  
   c) one that uses extreme language  
   d) one that restates the conclusion

## **Introduction**

Arguments on the LSAT often use statistics or quantitative evidence to persuade. These can include studies, percentages, averages, and survey results. For the exam, you must be able to spot flaws in statistical reasoning, know how quantitative evidence can (and cannot) support a conclusion, and apply exam techniques for arguments involving numbers or data.

Many LSAT questions—particularly strengthen and weaken types—expect you to analyze whether data is reliable, the sample is appropriate, and if the statistics actually support the conclusion. Poor arguments may use unrepresentative samples, confuse correlation with causation, or manipulate numbers to mislead.

> **Key Term: statistical evidence**  
> Quantitative data used to support an argument, such as rates, averages, percentages, or survey results.
>
> **Key Term: sample**  
> The group or set used as the basis for a statistical generalization to a wider population.
>
> **Key Term: representative**  
> A sample or subset that matches the characteristics of the whole population relevant to the argument.
>
> **Key Term: correlation**  
> A statistical relationship between two variables. Correlation does not on its own establish causation.
>
> **Key Term: causation**  
> A causal relationship, where one factor directly brings about another. Arguments often mistakenly infer causation from evidence of correlation.

## **Quantitative Evidence in Arguments**

On the LSAT, arguments frequently cite data—surveys, polls, experimental results, or raw numbers—to draw conclusions. To analyze such arguments, focus on how the evidence connects to the claim: Is the statistical evidence interpreted correctly? Does it justify the jump from sample to population? Are alternative explanations possible?

### Common Flaws in Quantitative Reasoning

Familiarize yourself with these flaws, as they appear frequently on the exam:

- **Unrepresentative samples:** If a study surveys only a subgroup but makes conclusions about the general population, the result may be biased.
- **Small or biased samples:** Arguments may base claims on too little data, or on data collected from individuals not relevant to the larger group.
- **Confusing correlation and causation:** Just because two variables change together does not mean one causes the other.
- **Ambiguity in percentages or rates:** A claim about “50% more” could mean different things—examine if the numbers actually support the conclusion.
- **Percentages versus raw numbers:** Large percentages of small groups, or small percentages of large groups, can mislead. Clarity about context is essential.

> **Key Term: bias**  
> A sample or method that systematically favors a particular outcome over others, leading to skewed results.

### **Worked Example 1.1**

A company claims, “Our survey found that 80% of people who use our product saw improvements. Therefore, our product is effective for everyone.” What is the main flaw?

> **Answer:** The argument assumes the survey group represents all possible users. It does not account for the possibility that only satisfied customers responded, introducing bias and making the result unrepresentative of everyone.

### Evaluating Surveys and Studies

Every time you see an argument based on data or a study, ask:

- Who or what was included in the sample?
- Does the sample represent all groups mentioned in the conclusion?
- Was participation self-selected (introducing bias)?
- Could other factors explain the result?

If the sample is not representative, the statistics may not justify the conclusion.

### **Worked Example 1.2**

Study: “A survey of 200 gym members found that 90% are in good health. Hence, joining a gym leads to good health.”

What is a flaw in this argument?

> **Answer:** The sample includes only current gym members, who may already be healthy for reasons unrelated to gym membership. The argument fails to consider that correlation does not prove causation, and the sample may not represent the general population.

### Causation Versus Correlation

Many LSAT arguments use data to suggest cause and effect. However, even if two variables are correlated, there may be a third factor, or the relationship may be coincidental. Always ask whether the argument has unjustifiably leapt from correlation to causation.

### **Worked Example 1.3**

Argument: “Areas with more libraries have higher literacy rates. Therefore, building libraries causes higher literacy.”

What exam-relevant flaw can you identify?

> **Answer:** The argument confuses correlation with causation. Higher literacy might attract libraries, or both may result from greater community investment. The evidence does not prove that libraries cause increased literacy.

### Statistical Strengthening and Weakening

On the LSAT, strengthen questions often validate the representativeness of the sample, show high response rates, or rule out confounding variables. Weaken questions often highlight poor sampling, show other explanations, or find contradictions in the data. Correct answers typically attack (for weaken) or defend (for strengthen) the link between evidence and conclusion.

### **Worked Example 1.4**

Argument: “A poll found that only 30% of dog owners favor a new law. Thus, most city residents oppose the law.”

What weakens this argument?

> **Answer:** Showing that dog owners are not representative of all city residents would weaken the argument. The conclusion goes beyond the sample to the wider public.

### **Exam Warning**

> On weaken questions, don't simply select an answer that introduces any new fact. Instead, ask: Would this new information directly attack the statistical support or the sample?

### Reasoning with Raw Numbers and Percentages

- Be cautious with claims involving changes in percentages—always check the denominators.
- A higher percentage of a small group does not always mean a higher raw number.
- Percentages cannot be substituted for actual numbers without knowing the group size.

### **Worked Example 1.5**

Argument: “Company A doubled its sales last year, while Company B increased by only 10%. Company A must have earned more revenue than Company B.”

Is the argument justified?

> **Answer:** No. Without knowing the starting figures, “doubled” may not lead to a higher amount than a 10% increase if Company B’s base was much larger.

### **Revision Tip**

> When a question involves data, always note who was surveyed, who is included in the numbers, and whether the argument makes a jump from the data to a broader claim.

## **Summary**

| Flaw Type             | Description                               | Weakening Approach             | Strengthening Approach              |
| --------------------- | ----------------------------------------- | ------------------------------ | ----------------------------------- |
| Poor sample           | Sample too small or unrepresentative      | Show bias or lack of diversity | Show sample covers whole population |
| Correlation/causation | Assumes cause from correlation            | Show alternative explanations  | Rule out other factors              |
| Percentages/numbers   | Confuses rates with totals, or vice versa | Change denominators, context   | Clarify totals and group sizes      |

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Arguments using statistics must have representative samples to support broader conclusions
- Sample bias and unrepresentative groups are common LSAT flaws
- Correlation does not establish causation; watch for arguments that imply causes from statistical relationships
- Percentages and raw numbers should not be confused; always check group sizes
- Correct answers on strengthen/weaken questions often address sample size, representativeness, or alternative causes

## **Key Terms and Concepts**

- statistical evidence
- sample
- representative
- correlation
- causation
- bias

Logical reasoning strategies and techniques - Quantitative reasoning and statistics in arguments