What is Data Collection and Statistics?

Understand data collection methods, sampling, observational studies vs experiments, and draw valid conclusions from statistical data.

How can I study Data Collection and Statistics effectively?

Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 13 problems provided, checking solutions as you go. Regular review and active practice are key to retention.

Is this Data Collection and Statistics study guide free?

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What course covers Data Collection and Statistics?

Data Collection and Statistics is part of the SAT Prep course on Study Mondo, specifically in the Problem Solving and Data Analysis section. You can explore the full course for more related topics and practice resources.

Are there practice problems for Data Collection and Statistics?

Yes, this page includes 13 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.

Data Collection and Statistics

Measures of Center

Mean: Sum of all values divided by the number of values. Sensitive to outliers.
Median: Middle value when data is ordered. Resistant to outliers.
Mode: Most frequently occurring value.

When to Use Which

Situation	Best Measure
Symmetric data, no outliers	Mean
Skewed data or outliers	Median
Categorical data	Mode

Measures of Spread

Range: Maximum – Minimum

❓ Question:

Find the median of: 12, 8, 15, 10, 9

Solution:

Step 1: Put in order $8, 9, 10, 12, 15$

❓ Question:

A dataset has 5 values with a mean of 20. If a 6th value of 32 is added, what is the new mean?

Solution:

Original sum: $5 \times 20 = 100$

Add new value: $100 + 32 = 132$

New mean: $\frac{132}{6} = 22$

Answer: 22

SAT Tip: Mean × count = sum. Use this to find totals!

❓ Question:

A study found that students who eat breakfast tend to have higher test scores. Which conclusion is valid?

A) Eating breakfast causes higher test scores B) There is an association between eating breakfast and test scores C) Students should be required to eat breakfast D) Skipping breakfast lowers intelligence

Solution:

Key word: "tend to" = correlation/association

Check each:

A) Causes - too strong! Correlation ≠ causation ❌
B) Association - this is what the data shows ✓
C) Should be required - policy decision, not data conclusion ❌
D) Lowers intelligence - causation + extreme claim ❌

Answer: B - There is an association

SAT Tip: Studies show correlation/association. Saying "causes" requires controlled experiments!

❓ Question:

A histogram shows the following frequencies for test scores: 60-69: 3 students 70-79: 8 students 80-89: 12 students 90-100: 7 students

How many students scored below 80?

Step 1: Add the frequencies for intervals below 80: $3 + 8 = 11$

Answer: 11 students scored below 80.

SAT Tip: On histograms, "below 80" includes the 60-69 and 70-79 intervals. Be careful about whether the boundary value is included.

❓ Question:

A histogram shows the following frequencies for test scores: 60-69: 3 students 70-79: 8 students 80-89: 12 students 90-100: 7 students

How many students scored below 80?

Step 1: Add the frequencies for intervals below 80: $3 + 8 = 11$

Answer: 11 students scored below 80.

SAT Tip: On histograms, "below 80" includes the 60-69 and 70-79 intervals. Be careful about whether the boundary value is included.

❓ Question:

The mean of 6 numbers is 15. When a 7th number is added, the mean becomes 17. What is the 7th number?

Step 1: Find the original sum: $6 \times 15 = 90$

Step 2: Find the new sum: $7 \times 17 = 119$

Step 3: The 7th number = $119 - 90 = 29$

Check: $(90 + 29) \div 7 = 119 \div 7 = 17$ ✓

Answer: The 7th number is 29.

❓ Question:

The mean of 6 numbers is 15. When a 7th number is added, the mean becomes 17. What is the 7th number?

Step 1: Find the original sum: $6 \times 15 = 90$

Step 2: Find the new sum: $7 \times 17 = 119$

Step 3: The 7th number = $119 - 90 = 29$

Check: $(90 + 29) \div 7 = 119 \div 7 = 17$ ✓

Answer: The 7th number is 29.

❓ Question:

In a box plot, $Q_1 = 30$ , $\text{Median} = 45$ , $Q_3 = 60$ , $\text{Min} = 10$ , $\text{Max} = 85$ . What is the IQR, and which single value, if added, would most change the mean but least change the median?

IQR: $Q_3 - Q_1 = 60 - 30 = 30$

❓ Question:

IQR: $Q_3 - Q_1 = 60 - 30 = 30$

❓ Question:

A researcher wants to determine if a new teaching method improves test scores. She randomly assigns 50 students to use the new method and 50 to use the traditional method. The new method group has a mean score of 82, while the traditional group has a mean of 78. Can she conclude the new method CAUSES higher scores?

Answer: YES — with appropriate caveats.

Why: This is a randomized controlled experiment, not just an observational study.

Key features that allow a causal conclusion:

Random assignment to treatment groups — this controls for confounding variables
Control group (traditional method) for comparison
Same number in each group

However, she should also consider:

Statistical significance — is the 4-point difference large enough to not be due to chance? (She'd need a p-value or confidence interval.)
Practical significance — is a 4-point difference meaningful in practice?

SAT Rule:

Randomized experiment → CAN conclude causation
Observational study → can only conclude ASSOCIATION

❓ Question:

Answer: YES — with appropriate caveats.

Why: This is a randomized controlled experiment, not just an observational study.

Key features that allow a causal conclusion:

Random assignment to treatment groups — this controls for confounding variables
Control group (traditional method) for comparison
Same number in each group

However, she should also consider:

Statistical significance — is the 4-point difference large enough to not be due to chance? (She'd need a p-value or confidence interval.)
Practical significance — is a 4-point difference meaningful in practice?

SAT Rule:

Randomized experiment → CAN conclude causation
Observational study → can only conclude ASSOCIATION

❓ Question:

Set A has values {10, 12, 14, 16, 18} and Set B has values {12, 13, 14, 15, 16}. Without calculating, which set has the larger standard deviation? Explain.

Set A has the larger standard deviation.

Reasoning: Both sets have the same mean:

Set A: $\frac{10+12+14+16+18}{5} = 14$
Set B: $\frac{12+13+14+15+16}{5} = 14$

Set A has values that are more spread out from 14 (ranging from 10 to 18, each value 2 units apart from the next).

Set B has values that are more tightly clustered around 14 (ranging from 12 to 16, each value only 1 unit apart).

Since standard deviation measures how far values are from the mean on average, Set A has the larger standard deviation.

Answer: Set A

SAT Tip: You don't need to calculate SD on the SAT — just understand that wider spread = larger SD.

❓ Question:

Set A has values {10, 12, 14, 16, 18} and Set B has values {12, 13, 14, 15, 16}. Without calculating, which set has the larger standard deviation? Explain.

Set A has the larger standard deviation.

Reasoning: Both sets have the same mean:

Set A: $\frac{10+12+14+16+18}{5} = 14$
Set B: $\frac{12+13+14+15+16}{5} = 14$

Set A has values that are more spread out from 14 (ranging from 10 to 18, each value 2 units apart from the next).

Set B has values that are more tightly clustered around 14 (ranging from 12 to 16, each value only 1 unit apart).

Since standard deviation measures how far values are from the mean on average, Set A has the larger standard deviation.

Answer: Set A

SAT Tip: You don't need to calculate SD on the SAT — just understand that wider spread = larger SD.

Data Collection and Statistics

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Data Collection and Statistics

Measures of Center

When to Use Which

Measures of Spread

📚 Practice Problems

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