SAT Math Flashcards: Inferences And Claims From Statistics

What this deck covers

This deck focuses on Inferences And Claims From Statistics, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the purpose of a confidence interval in statistics?

Answer: Estimate range for population parameter. Provides likely bounds where true population value falls with given confidence.

Flashcard 2: What is a skewed distribution?

Answer: A distribution that is not symmetric. Data is pulled more toward one tail than the other.

Flashcard 3: What is the mode of the data set: 4, 4, 6, 8, 8, 8?

Answer: The mode is 8. The value 8 appears most frequently (3 times).

Flashcard 4: What is the mean of the data set: 4, 5, 7, 10?

Answer: Mean = 6.5. Sum all values and divide by count: $(4+5+7+10) ÷ 4 = 6.5$.

Flashcard 5: What is a scatter plot?

Answer: A graph showing the relationship between two variables. Each point represents one observation with two variable values.

Flashcard 6: What is the mean of the data set: 3, 7, 8, 10, 15?

Answer: The mean is 8.6. Sum all values and divide by count: $(3+7+8+10+15)/5 = 43/5 = 8.6$.

Flashcard 7: What is a statistical inference?

Answer: A conclusion about a population based on a sample. Uses sample data to make generalizations about the entire population.

Flashcard 8: What is the interquartile range (IQR)?

Answer: IQR = Q3 - Q1. Measures the spread of the middle 50% of data values.

Flashcard 9: What is the range of the data set: 3, 6, 9, 12, 15?

Answer: The range is 12. $15 - 3 = 12$; difference between largest and smallest values.

Flashcard 10: What does a histogram display?

Answer: The frequency distribution of a data set. Shows how often different values or ranges occur in data.

Flashcard 11: What is the central limit theorem?

Answer: The distribution of sample means approximates normality. For large samples, sample means follow a normal distribution pattern.

Flashcard 12: Define 'sample' in statistics.

Answer: A subset of the population used for analysis. Representative portion selected from the larger population for study.

Flashcard 13: What does a 95% confidence interval mean?

Answer: 95% of samples contain the true population parameter. Indicates the reliability of the interval estimation method.

Flashcard 14: Define 'population' in statistics.

Answer: The entire set of individuals or items of interest. All possible subjects or objects being studied in research.

Flashcard 15: Define 'null hypothesis' in statistics.

Answer: A statement that there is no effect or difference. The baseline assumption that researchers try to reject or fail to reject.

Flashcard 16: What is the range of the data set: 3, 6, 9, 12, 15?

Answer: The range is 12. $15 - 3 = 12$; difference between largest and smallest values.

Flashcard 17: What does correlation measure?

Answer: The strength and direction of a linear relationship. Values closer to -1 or 1 indicate stronger linear relationships.

Flashcard 18: What type of claim is made when stating a cause-and-effect relationship?

Answer: Causal claim. Asserts one variable directly influences or causes changes in another.

Flashcard 19: What is the critical value for a 95% confidence interval with a z-distribution?

Answer: The critical value is 1.96. Marks the boundary for 95% of the standard normal distribution.

Flashcard 20: What is the correlation coefficient range?

Answer: From -1 to 1. Perfect positive correlation is 1, perfect negative is -1.

Flashcard 21: Calculate the confidence interval: mean = 50, SD = 10, n = 25, 95% CI.

Answer: The confidence interval is (46.08, 53.92). $50 \pm 1.96 \times \frac{10}{\sqrt{25}} = 50 \pm 3.92$.

Flashcard 22: Calculate the z-score for $x = 85$, $\text{mean} = 80$, $\text{SD} = 5$.

Answer: The z-score is 1. $(85-80)/5 = 1$; standardizes the value relative to the distribution.

Flashcard 23: What is a box plot?

Answer: A graphical summary of data distribution using quartiles. Shows median, quartiles, and potential outliers in data distribution.

Flashcard 24: Define 'sample' in statistics.

Answer: A subset of the population used for analysis. Representative portion selected from the larger population for study.

Flashcard 25: Identify the median of the following numbers: 5, 2, 9, 4, 7.

Answer: The median is 5. Sort values first: 2, 4, 5, 7, 9; middle value is 5.

Flashcard 26: What is the mode of the data set: 4, 4, 6, 8, 8, 8?

Answer: The mode is 8. The value 8 appears most frequently (3 times).

Flashcard 27: What is a statistic in statistics?

Answer: A numerical characteristic of a sample. Calculated value describing a sample (used to estimate parameters).

Flashcard 28: What does a histogram display?

Answer: The frequency distribution of a data set. Shows how often different values or ranges occur in data.

Flashcard 29: Which graph type is best for displaying frequency distributions?

Answer: Histogram. Shows distribution shape and frequency of values across intervals or bins.

Flashcard 30: What is the purpose of a confidence interval in statistics?

Answer: Estimate range for population parameter. Provides likely bounds where true population value falls with given confidence.

Flashcard 31: What is sampling bias?

Answer: Bias due to non-random sample selection. Systematic error that makes samples unrepresentative of the population.

Flashcard 32: Identify the median of the following numbers: 5, 2, 9, 4, 7.

Answer: The median is 5. Sort values first: 2, 4, 5, 7, 9; middle value is 5.

Flashcard 33: Find and correct the claim: 'The sample result proves the hypothesis.'

Answer: Correct: 'The sample result supports the hypothesis.'. 'Supports' is proper; samples provide evidence but never absolute proof.

Flashcard 34: What type of claim is made when stating a cause-and-effect relationship?

Answer: Causal claim. Asserts one variable directly influences or causes changes in another.

Flashcard 35: What is statistical significance?

Answer: Results unlikely due to chance, given a threshold. Indicates results are unlikely to occur by random chance alone.

Flashcard 36: What is the central limit theorem?

Answer: The distribution of sample means approximates normality. For large samples, sample means follow a normal distribution pattern.

Flashcard 37: What does a p-value indicate in hypothesis testing?

Answer: Probability of observed result under null hypothesis. Lower p-values suggest stronger evidence against the null hypothesis.

Flashcard 38: What is sampling bias?

Answer: Bias due to non-random sample selection. Systematic error that makes samples unrepresentative of the population.

Flashcard 39: Identify the claim in the statement: 'The average height is over 6 feet.'

Answer: The claim is that the mean height > 6 feet. States that the population mean exceeds 6 feet.

Flashcard 40: What is a skewed distribution?

Answer: A distribution that is not symmetric. Data is pulled more toward one tail than the other.

Flashcard 41: Which statistical measure is most affected by outliers?

Answer: Mean. Extreme values pull the mean away from the center more than median or mode.

Flashcard 42: What is a parameter in statistics?

Answer: A numerical characteristic of a population. Fixed value describing an entire population (usually unknown).

Flashcard 43: What is a statistical inference?

Answer: A conclusion about a population based on a sample. Uses sample data to make generalizations about the entire population.

Flashcard 44: What is the formula for variance?

Answer: Variance = $\frac{\text{sum of squared deviations}}{n-1}$. Measures how spread out data points are from the mean.

Flashcard 45: Define 'null hypothesis' in statistics.

Answer: A statement that there is no effect or difference. The baseline assumption that researchers try to reject or fail to reject.

Flashcard 46: Identify the stronger correlation: $r = 0.7$ or $r = -0.7$.

Answer: Both are equally strong. Both have the same absolute value, so equal strength.

Flashcard 47: Which statistical measure is most affected by outliers?

Answer: Mean. Extreme values pull the mean away from the center more than median or mode.

Flashcard 48: Choose the correct alternative hypothesis: $H_0: \text{mean} = 50$

Answer: $H_a: \text{mean} \neq 50$. Alternative hypothesis claims the parameter is not equal to the null value.

Flashcard 49: What is the interquartile range (IQR)?

Answer: IQR = Q3 - Q1. Measures the spread of the middle 50% of data values.

Flashcard 50: What is a Type II error in hypothesis testing?

Answer: Failure to reject a false null hypothesis. Accepting a null hypothesis when the alternative is actually true.

Flashcard 51: Identify the claim in the statement: 'The average height is over 6 feet.'

Answer: The claim is that the mean height > 6 feet. States that the population mean exceeds 6 feet.

Flashcard 52: What does 'margin of error' describe?

Answer: The range of error in sample estimate of population. Quantifies the uncertainty in survey or poll results.

Flashcard 53: What is a normal distribution?

Answer: A bell-shaped distribution symmetric about the mean. Most data falls within a predictable range around the center.

Flashcard 54: Calculate the z-score for $x = 85$, $\text{mean} = 80$, $\text{SD} = 5$.

Answer: The z-score is 1. $(85-80)/5 = 1$; standardizes the value relative to the distribution.

Flashcard 55: Identify the outlier in the set: 2, 4, 4, 5, 100.

Answer: The outlier is 100. Value that falls far outside the typical range of the data.

Flashcard 56: What does a p-value indicate in hypothesis testing?

Answer: Probability of observed result under null hypothesis. Lower p-values suggest stronger evidence against the null hypothesis.

Flashcard 57: What is the critical value for a 95% confidence interval with a z-distribution?

Answer: The critical value is 1.96. Marks the boundary for 95% of the standard normal distribution.

Flashcard 58: Which graph type is best for displaying frequency distributions?

Answer: Histogram. Shows distribution shape and frequency of values across intervals or bins.

Flashcard 59: Identify the null hypothesis in a statistical test.

Answer: Null hypothesis: no effect or difference. Default assumption that treatment has no impact; what we test against.

Flashcard 60: What is a box plot?

Answer: A graphical summary of data distribution using quartiles. Shows median, quartiles, and potential outliers in data distribution.

Flashcard 61: Find the range of the data set: 2, 8, 15, 22.

Answer: Range = 20. Difference between maximum and minimum: $22 - 2 = 20$.

Flashcard 62: What does a 95% confidence interval mean?

Answer: 95% of samples contain the true population parameter. Indicates the reliability of the interval estimation method.

Flashcard 63: Calculate the confidence interval: mean = 50, SD = 10, n = 25, 95% CI.

Answer: The confidence interval is (46.08, 53.92). $50 \pm 1.96 \times \frac{10}{\sqrt{25}} = 50 \pm 3.92$.

Flashcard 64: Define 'population' in statistics.

Answer: The entire set of individuals or items of interest. All possible subjects or objects being studied in research.

Flashcard 65: What is a Type II error in hypothesis testing?

Answer: Failure to reject a false null hypothesis. Accepting a null hypothesis when the alternative is actually true.

Flashcard 66: What is the definition of a statistical inference?

Answer: Drawing conclusions about a population based on a sample. Uses sample data to make educated guesses about the entire population.

Flashcard 67: What is the correlation coefficient range?

Answer: From -1 to 1. Perfect positive correlation is 1, perfect negative is -1.

Flashcard 68: Identify the formula for calculating the median of a data set.

Answer: Arrange data, find middle value(s). For odd $n$, middle value; for even $n$, average of two middle values.

Flashcard 69: State the formula for calculating the range of a data set.

Answer: Range = Maximum - Minimum. Range measures the spread by finding the difference between extremes.

Flashcard 70: What does 'margin of error' describe?

Answer: The range of error in sample estimate of population. Quantifies the uncertainty in survey or poll results.

Flashcard 71: Identify the formula for calculating the median of a data set.

Answer: Arrange data, find middle value(s). For odd $n$, middle value; for even $n$, average of two middle values.

Flashcard 72: What does correlation measure?

Answer: The strength and direction of a linear relationship. Values closer to -1 or 1 indicate stronger linear relationships.

Flashcard 73: What is a parameter in statistics?

Answer: A numerical characteristic of a population. Fixed value describing an entire population (usually unknown).

Flashcard 74: What is the mean of the data set: 3, 7, 8, 10, 15?

Answer: The mean is 8.6. Sum all values and divide by count: $(3+7+8+10+15)/5 = 43/5 = 8.6$.

Flashcard 75: What is a normal distribution?

Answer: A bell-shaped distribution symmetric about the mean. Most data falls within a predictable range around the center.

Flashcard 76: State the formula for calculating the range of a data set.

Answer: Range = Maximum - Minimum. Range measures the spread by finding the difference between extremes.

Flashcard 77: State the formula for standard deviation in a sample data set.

Answer: $s = \sqrt{\frac{1}{n-1} \sum (x_i - \bar{x})^2}$. Measures spread by calculating square root of variance with $n-1$ denominator.

Flashcard 78: Identify the stronger correlation: $r = 0.7$ or $r = -0.7$.

Answer: Both are equally strong. Both have the same absolute value, so equal strength.

Flashcard 79: Identify the null hypothesis in a statistical test.

Answer: Null hypothesis: no effect or difference. Default assumption that treatment has no impact; what we test against.

Flashcard 80: Find the range of the data set: 2, 8, 15, 22.

Answer: Range = 20. Difference between maximum and minimum: $22 - 2 = 20$.

Flashcard 81: What is the mode of the data set: 3, 3, 4, 5, 6?

Answer: Mode = 3. The value that appears most frequently in the data set.

Flashcard 82: What is the formula for variance?

Answer: Variance = $\frac{\text{sum of squared deviations}}{n-1}$. Measures how spread out data points are from the mean.

Flashcard 83: What is the mode of the data set: 3, 3, 4, 5, 6?

Answer: Mode = 3. The value that appears most frequently in the data set.

Flashcard 84: What is statistical significance?

Answer: Results unlikely due to chance, given a threshold. Indicates results are unlikely to occur by random chance alone.

Flashcard 85: What is the mean of the data set: 4, 5, 7, 10?

Answer: Mean = 6.5. Sum all values and divide by count: $(4+5+7+10) ÷ 4 = 6.5$.

Flashcard 86: What is a scatter plot?

Answer: A graph showing the relationship between two variables. Each point represents one observation with two variable values.

Flashcard 87: Choose the correct alternative hypothesis: $H_0: \text{mean} = 50$

Answer: $H_a: \text{mean} \neq 50$. Alternative hypothesis claims the parameter is not equal to the null value.

Flashcard 88: What is a statistic in statistics?

Answer: A numerical characteristic of a sample. Calculated value describing a sample (used to estimate parameters).

Flashcard 89: Identify the outlier in the set: 2, 4, 4, 5, 100.

Answer: The outlier is 100. Value that falls far outside the typical range of the data.

Flashcard 90: Identify the term: The likelihood that a result is due to chance.

Answer: P-value. Measures probability that observed results occurred by random chance alone.