AP Statistics Unit 1 Review : Exploring One Variable Data Flashcards | Quizlet

Statistics

The art of distilling meaning from data.

Data

Values, along with their context.

Categorical Variables

Variables that name categories, labels, or groupings. Usually in the form of words but can be numerals.

Quantitative Variables

Variables in which the numbers act as a numerical value for a measurement, always have units.

Two "W's" that always must be known in order to analyze data

"Who" and "What".

Frequency Table vs. Relative Frequency Table

A frequency table lists categories and how many cases (#) belong to each one, whereas a relative frequency table displays percentages/proportions rather than counts by category.

Area Principle - Bar Chart

Bars have equal width to obey the area principle.

SOCV

Shape, Outliers/Unusual Features, Center, Variability/Spread; the method used to describe or compare the distributions of a quantitative variable.

Left Skew

$\text{Mean} < \text{Median}$; the mean is dragged down towards the tail.

Right Skew

$\text{Mean} > \text{Median}$; the mean is dragged up towards the tail.

Median Position

Given $n$ values, the median is in the $\frac{n+1}{2}$ position.

Five Number Summary

Minimum, $Q_1$ (Quartile 1), Median, $Q_3$ (Quartile 3), Maximum.

Interquartile Range (IQR)

$Q_3 - Q_1$ ($\text{Quartile } 3 - \text{Quartile } 1$).

Equation to Determine Outliers using IQR

$\text{Outlier} < Q_1 - (1.5 \times \text{IQR})$ or $\text{Outlier} > Q_3 + (1.5 \times \text{IQR})$.

Equation to Determine Outliers using Standard Deviation

$\text{Outlier} \le \bar{x} - 2(\text{Standard Deviation})$ or $\text{Outlier} \ge \bar{x} + 2(\text{Standard Deviation})$.

Discrete Variables

Variables that are countable in a finite amount of time.

Continuous Variables

Variables that can take on unlimited values from the lowest and highest points of measurement.

z-score Formula

$$\frac{\text{value} - \text{mean}}{\text{standard deviation}}$$

Effect of adding/subtracting a constant on center and spread

For measures of center (e.g., Mean, Median), add/subtract the same constant value; for measures of spread (e.g., Standard Deviation, Range, IQR), there is no change.

Effect of multiplying/dividing by a constant on center and spread

Both measures of center (e.g., Mean, Median) and measures of spread (e.g., Standard Deviation, Range, IQR) are multiplied or divided by that same constant value.

Statistic

A measurement used to describe a sample (e.g., sample mean $\bar{x}$, sample standard deviation $S_x$).

Parameter

A measurement used to describe a population (e.g., population mean $\mu$, population standard deviation $\sigma$).

Empirical Rule

Gives the approximate percentage of observations within 1 standard deviation ($68\%$), 2 standard deviations ($95\%$), and 3 standard deviations ($99.7\%$) of the mean when the histogram is well approximated by a normal curve.

Standard Deviation Interpretation Template

"The (context) typically varies by (SD value) from the mean of (mean value)"

Percentiles

Tells what proportion of values are at or below a given value.