Ch. 12 - Data-Based and Statistical Reasoning

What is the arithmetic mean, and how is it affected by outliers?

The arithmetic mean is the average of a data set and is most affected by outliers.

What is the median, and how is it determined?

The median is the middle value of a data set, with 50% of data points above and below it.

What is the mode, and can there be multiple modes in a data set?

The mode is the data point that appears most often, and a data set can have multiple or no modes.

What are the characteristics of a normal distribution?

A normal distribution is symmetrical, with the mean, median, and mode being the same.

What percentage of data points fall within 1, 2, and 3 standard deviations in a standard normal distribution?

• 68% within 1 standard deviation.

• 95% within 2 standard deviations.

• 99% within 3 standard deviations.

What distinguishes a skewed distribution, and how is skew direction defined?

Skewed distributions have differences in mean, median, and mode. The skew direction points to the tail of the distribution.

What is a bimodal distribution, and how should it be analyzed?

A bimodal distribution has multiple peaks, and it may be useful to analyze the groups separately.

What is the range in a data set?

The range is the difference between the largest and smallest values.

How is interquartile range (IQR) calculated, and what is it used for?

IQR is the difference between the third quartile and the first quartile and can be used to identify outliers.

What does standard deviation measure?

Standard deviation measures variability around the mean and can help identify outliers.

What are potential causes of outliers in data?

Outliers may result from true population variability, measurement error, or a non-normal distribution.

What is the difference between independent and dependent events?

• Independent events: Probability does not change based on other outcomes.

• Dependent events: Probability changes based on other outcomes.

What are mutually exclusive and exhaustive outcomes?

• Mutually exclusive: Outcomes cannot occur simultaneously.

• Exhaustive: No other outcomes are possible.

What does a hypothesis test evaluate?

Whether the null hypothesis (no difference) can be rejected.

How is statistical significance determined?

By comparing the p-value to the chosen significance level (α), often set at 0.05

What are confidence intervals, and what is the relationship between interval width and confidence level?

Confidence intervals estimate the population mean; wider intervals are associated with higher confidence levels (e.g., 95%).

What are pie charts and bar charts used for?

To compare categorical data.

What are histograms and box plots used for?

To compare numerical data.

What are maps used for?

To compare up to two demographic indicators.

How can slope be most easily calculated from plots?

From linear plots.

What is the difference between correlation and causation?

• Correlation is a statistical relationship

• Causation implies one variable directly affects another.

What is the distinction between statistical and practical significance?

• Statistical significance: Low likelihood of findings being due to chance.

• Practical significance: The usefulness or importance of findings in context.