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Categorical Variable

Variable that represents categories that place data into groups

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Quantitative Variable

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

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Distribution

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

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Frequency Table

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

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Relative Frequency Table

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

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Bar Chart

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

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Relative Frequency Bar Chart

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

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Segmented Bar Chart (Stacked Bar Chart)

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

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Pie Chart

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

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Comparative Display

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

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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"

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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

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Histogram

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

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Relative Frequency Histogram

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

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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

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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)

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Context

Identifies what is being described/compared/analyzed

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Shape

Describes the "look" of the distribution

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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)

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Uniform

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

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Symmetric

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

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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)

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Center

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

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Mean

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

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Median

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

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Spread

Describes how tightly the data is clustered around the center

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Standard Deviation

The average distance a data value is from the mean

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Quartile

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

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1st Quartile (Lower)

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

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3rd Quartile (Upper)

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

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Interquartile Range (IQR)

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

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Range

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

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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)

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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

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5-Number Summary

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

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Boxplot

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

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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

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Rescaling

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

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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

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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

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Scatterplot

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

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Association

Relationship between two quantitative variables, described by SDFOC

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Strength

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

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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

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Form

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

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Outliers

Points that fall outside of the overall pattern of a scatterplot

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Context

Identifies the two variables for which an association is being described

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Explanatory Variable

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

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Response Variable

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

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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

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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

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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

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Residual

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

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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.

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