AP Statistics Basics Practice Quiz

The mean is calculated by adding all values in a dataset and dividing by the total number of values. It represents the average and is commonly used to describe the center of numerical data. However, it is sensitive to extreme values, which can shift the mean significantly.

Quartiles divide a dataset into four equal parts. The middle 50 percent of the data lies between the first quartile (Q1) and third quartile (Q3), making quartiles useful for understanding data spread.

The interquartile range focuses on the middle 50 percent of data values. By excluding extreme values, it provides a more reliable measure of spread when outliers are present.

An outlier is defined as a data point that lies more than 1.5 times the IQR above Q3 or below Q1. This rule helps identify unusually large or small values.

The five number summary consists of the minimum, first quartile, median, third quartile, and maximum. These values describe the overall distribution of a dataset.

A modified boxplot visually displays the five number summary. It highlights the median, quartiles, and potential outliers, helping identify skewness and variability.

Variance measures how far data points spread from the mean by averaging squared deviations. Squaring ensures all differences are positive and emphasizes larger deviations.

Standard deviation indicates how much data values typically differ from the mean. A larger standard deviation means greater variability in the dataset.

Back-to-back stemplots are effective for comparing the shapes of two small datasets. They help identify similarities or differences in distribution patterns.

The range is calculated by subtracting the minimum value from the maximum value. It provides a simple measure of overall spread but is affected by outliers.

The median is resistant to outliers because it depends on position rather than magnitude. Extreme values do not significantly affect it.

The mean works best for symmetric datasets without outliers because it accurately reflects the center when values are evenly distributed.

Q1 represents the 25th percentile, meaning 25 percent of the data values lie below it. It helps define the lower boundary of the middle spread.

Q3 represents the 75th percentile, indicating that 75 percent of the data lies below this value. It defines the upper boundary of the middle spread.

The IQR is calculated by subtracting Q1 from Q3. This measures the spread of the middle half of the data and helps identify outliers.