AP Statistics Unit One Summary

These flashcards cover key terms and concepts from the AP Statistics Unit One summary.

Statistical Analysis

The process of collecting, exploring, and interpreting data to make decisions and understand phenomena.

Categorical Data

Data that can be divided into groups or categories, such as eye color or car brands.

Quantitative Data

Numerical data that can be measured or counted, such as height or weight.

Statistic

A summary value that describes a sample.

Parameter

A summary value that describes an entire population.

Frequency Table

A table that displays the number of occurrences of each category of data.

Relative Frequency

The proportion of observations in a category relative to the total number of observations.

Distribution

The way in which data is spread out or arranged, showing how often each value occurs.

Discrete Variable

A quantitative variable that takes on countable values, such as the number of students in a class.

Continuous Variable

A quantitative variable that can take on an infinite number of values, such as the height of individuals.

Histogram

A graphical representation of the distribution of quantitative data using bars to show frequency distributions.

Box Plot

A graphical representation that displays the five-number summary of a dataset: minimum, first quartile, median, third quartile, and maximum.

Outlier

A data point that is significantly different from other observations, either much higher or much lower.

Mean

The average value of a dataset, calculated by summing all values and dividing by the count.

Median

The middle value of a dataset when arranged in order.

Standard Deviation

A measure of the dispersion of a dataset, indicating how much values deviate from the mean.

Percentile

A value below which a certain percentage of data falls; for example, the 25th percentile is the value below which 25% of the data lies.

Normal Distribution

A probability distribution that is symmetric about the mean, with most observations clustering near the central peak.

Z-score

A measure indicating how many standard deviations an element is from the mean of the dataset.

Empirical Rule

A statistical rule stating that for a normal distribution, approximately 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations.

Interquartile Range (IQR)

The range of the middle 50% of a dataset, calculated as the difference between the third and first quartiles.

Fence Method

A method to identify outliers by calculating upper and lower fences based on the IQR.

What is the formula for the z-score?

The z-score is calculated as z = \frac{(X - \mu)}{\sigma} where X is the value, \mu is the mean, and \sigma is the standard deviation.

How do you calculate the mean?

The mean is calculated as \text{Mean} = \frac{\sum X}{N} where \sum X is the sum of all values and N is the number of values.

What is the formula for the median?

To find the median, sort the numbers in ascending order and use: - If N (number of values) is odd, median = value at position \frac{N + 1}{2}. - If N is even, median = average of values at positions \frac{N}{2} and \frac{N}{2} + 1.

What is the formula for standard deviation?

Standard deviation is calculated as \sigma = \sqrt{\frac{\sum (X - \mu)^2}{N}} where X represents each value, \mu is the mean, and N is the number of values