Unit 1A Stats Vocabulary

categorical frequency distibutions

a summary of data that shows the number of observations (frequencies) in each category or qualitative group.

histograms

the most common graph of distributions with one quantitative variable; displays data by using vertical bars of various heights to represent the frequency of the classes

datum

a piece of information about an item or individual (singular form of data)

relative frequency graps

used when the proportion of data values that fall into a given class is more important than the actual number of data values that fall into that class.

overall pattern

a distribution that can be described by observing its center, spread, and shape

deviation

the difference between a value in a frequency distribution and a fixed number (as the mean)

center

the value or description of the middle of the data

spread

the extent of the data from the smallest to largest value

shape

the approximate design of a distribution as either symmetric or skewed

symmetric

the right and left sides of a distribution of a graph are approximately mirror images of each other

skewed to the right

the upper half of the observations extends much farther out than the left half

skewed to the left

the lower half of the observations extends much farther out than the right half

outliers

any graph of data is an individual observation that falls outside the overall pattern of the graph; calculated as a value that is more than 1.5*IQR below Q1 or above Q3

raw data

data collected in original form

frequency table

the number of observational units in each category of a categorical variable

individuals

objects described by a set of data (i.e. people, animals, things)

variables

any characteristic that may change from one observational unit to another

exploratory data analysis

statistical tools and ideas that can help examine data to describe their main features

categorical variables

aka qualitative variable, takes on values that are category names or group labels

quantitative variable

takes numerical values for which it makes sense to do arithmetic operations like adding and averaging

distribution

tells us what values the variable takes and how often it takes these values (the pattern of variation of a variable)

Dotplots

another name for a line plot, which is used to graph a distribution of data

stemplots

an additional method of graphic a distribution of quantitative data (for small data sets) using a “stem” and a “leaf”

descriptive statistics

the collection organization, summarization, and presentation of data

inferential statistics

generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions

population

consist of all items or individuals of interest

sample

a subset of the populations from which data are obtained

discrete variables

variables that take on a countable number of values that may be finitee of countably infinite, as with whole numbers

continuous variables

variables that take on an infinite number of possible values within a given interval, and can take on variables that are measurable but not countable

relative frequency table

shows the proportion of obervational units in each category of a categorical variable

mean

an arithmetic average

median

the middle of a set of data when arranged in order from least to greatest

quartiles

segments of the data in groups of 25% intervals

five number summary

a useful numerical description of a distribution of data contained the set (min, q1, M, q3, max)

boxplot

the graph of the distributions of numbers contained in the five-number summary

modified boxplot

a boxplot that plots outliers as isolated points

variance (s²)

the mean of the squares of the deviations of the observations from their means

standard deviations (s)

measures spread by looking at how far the observations are from the mean

range

the difference from the largest and smallest observations (full spread of data)

nonresistant

variables, such as the mean, that are sensitive to the influence of extreme observation

resistant

variables, like the median, that are non-changing in response to a change of extreme observations

interquartile range

the difference between Q3 and Q1, which is 50% of the data distribution

degrees of freedom

the number of free choices left after a sample statistics such as mean is calculated

variability

a numeric summary of a distribution reporting its center and spread

statistics

a numerical attribute or summary of the variable of interest for a sample

parameter

a numerical attribute or summary of the variable of interest for a population