Stats Vocab Ch 1

Categorical Variable

Categorical Variable

Variable that represents categories that place data into groups

Quantitative Variable

Variable for which the numbers act as numerical values with known units

Distribution

The possible values of a variable and the frequency that each value occurs

Frequency Table

lists the categories for a categorical variable and displays the counts for each category

Relative Frequency Table

lists the categories for a categorical variable and displays the proportion/percentage for each category

Bar Chart

Display where bars represent the count of each category for a categorical variable

Relative Frequency Bar Chart

Display where bars represent the proportion/percentage of each category for a categorical variable

Segmented Bar Chart (Stacked Bar Chart)

Display where one bar represents a "whole" that is proportionally divided by each category for a categorical variable

Pie Chart

Display where one circle represents a "whole" that is proportionally divided by each category for a categorical variable

Comparative Display

Display (of any type) that is used to directly compare two or more distributions at once

Stem & Leaf Plot

Display that shows both the distribution and the individual data values for a quantitative variable as shared with "stems" with individual "leaves"

Dot Plot

Display where a dot is graphed on a single axis for each data value, stacking repeated values, this showing the distribution of a quantitative variable

Histogram

Display where bars represent the count of values falling into intervals ("bins") for a quantitative variable, showing its distribution

Relative Frequency Histogram

Display where vars represent the proportion/percentage of values falling into intervals ("bins") for a quantitative variable, showing its distribution

Cumulative Relative Frequency Plot

Display where a line shows the percentage of observations that are less than or equal to particular values for a quantitative variable

Percentile

The nth percentile is the value that falls above n% of the data (for example, the 90th percentile is above 90% of the data, demarking the top 10% of the data)

Context

Identifies what is being described/compared/analyzed

Shape

Describes the "look" of the distribution

Mode(s)

The most commonly occurring value(s) in a distribution, seen as hump(s) in displays. Can be unimodal (one mode), bimodal (two modes), or multimodal (three or more)

Uniform

A distribution that is roughly flat in shape, meaning there is no consequential mode

Symmetric

A distribution whose left & right halves form the center are approximately the same

Skewed

A Distribution that is not symmetric and has a longer tail on one side. Skewness is where the tail is (tail on left = skewed left, tail on right = skewed right)

Center

A value that attempts to summarize the entire distribution with s single number

Mean

The arithmetic average of a distribution. Sum of all the data values divided by the number of data values.

Median

The middle value of a distribution, where half the data is above and half of the data is below this value (50th percentile)

Spread

Describes how tightly the data is clustered around the center

Standard Deviation

The average distance a data value is from the mean

Quartile

One of three values (Q1, median, Q3) that divide a data set into four equal parts

1st Quartile (Lower)

The median of the lower half of the distribution (25th percentile), known as Q1

3rd Quartile (Upper)

The median of the upper half of the distribution (75th percentile), known as Q3

Interquartile Range (IQR)

The difference between the first and third quartiles, which is the middle 50% of the data

Range

The difference between the maximum and minimum values in a data set

Outlier

A data value that falls outside of the overall pattern of the rest of the data, specifically beyond 1.5IQR from either Q1 or Q3 (these form your fences)

Resistant

A calculated summary statistic is resistant if outliers have little to no effect on it...for example, medians/IQR's are resistant while means/standard deviations/ranges are not

5-Number Summary

Reports the minimum, Q1, median, Q3, and maximum of a distribution

Boxplot

Display that shows the 5-Number Summary as a central box, whiskers, and outliers, effectively dividing the data into quartiles

Shifting

Adding or subtracting a constant to every data value, which adds or subtracts that same constant to all measures of position and leaves measures of spread unchanged

Rescaling

Multiplying or dividing every data value by a constant, which multiplies or divides all measures of position and spread by that same constant

Standardized Values

Values for which the units have been systematically eliminated, allowing for comparison, even if the original variables had different scales and/or units

z-Score

Standardized value that identifies how many standard deviations a value is from the mean; z-scores don't change a distribution's shape, but force the mean to 0 and standard deviation to 1

Scatterplot

Display that shows the relationship between two quantitative variables measured for the same subjects on an x-y coordinate plane

Association

Relationship between two quantitative variables, described by SDFOC

Strength

Describes how well/closely the data follows the identified pattern of a scatterplot

Direction

A positive direction means that one variable increases as the other increases...a negative direction means that one variable decreases as the other increases

Form

Describes the overall shape of a scatterplot; we focus on linear vs. non-linear

Outliers

Points that fall outside of the overall pattern of a scatterplot

Context

Identifies the two variables for which an association is being described

Explanatory Variable

The variable that is thought to explain or predict the response variable (x-axis)

Response Variable

The variable that is thought to be explained/predicted by the explanatory variable (y-axis)

Correlation Coefficient (r)

The number that describes both the direction and strength of the linear association between two quantitative variables, from -1 to 1, where -1 is perfectly negative linear and 1 perfectly positive linear

Linear Model via Least Squares Regression Line of Best Fit

A linear equation that is used to simplify and represent an association, found via the line that minimizes the sum of the squared residuals

Predicted Value (ŷ)

The predicted y-value found for each x-value by substituting that x into the linear model producing the points (x, ŷ)...a "hat" in Statistics means that a value is predicted

Residual

The difference between an observed data value and the predicted value from the model...Residual = observed - predicted = y - ŷ

Coefficient of Determination (R^2)

The square of the correlation coefficient, which gives the percentage of the variability of y that is accounted for by the least squares regression on x, from 0% to 100%. Provides an overall measure of how strong the regression is in linearly relating y to x.