Ch.1 Stats Vocab

categorical variable

assigns labels that place each individual into a particular group, called a category

• can not take the average

• distribution description is one-one

quantitative variable

takes number values that are counts or measurements

• can take measurements

• distribution description is SOCS

two-way table

table of counts that summarizes data on the relationship between two categorical variables for some group of individuals

• try to include the total counts of the rows and columns

marginal relative frequency

gives the percent/proportion of individuals that have a specific value for one categorical variable

• only describes ONE of the variables in the two-way table

• row or column total/total total

joint relative frequency

gives the percent or proportion of individuals that have a specific value for one categorical variable and a specific value for ANOTHER categorical variable

• answers information about BOTH variables in the two-way table

• AND!

• one box/total total

conditional relative frequency

gives the proportion of individuals that have a specific value for one categorical variable among individuals who share the same value of another categorical variable

• proportion of individuals of a certain category within one overarching variable

• one box/row or column total

side-by-side bar graph

displays the distribution of a categorical variable for each value of another categorical variable

• groups based on values of the categorical variables and placed side by side

• several bars in one category

segemented/ribbon bar graph

displays the distribution of a categorical variable as segments of a rectangle, with the area of each segment proportional to the percent of individuals in the corresponding category

• one rectangle divided up per category

• separate bars

mosaic plot

a modified segmented bar graph in which the width of each rectangle is proportional to the number of individuals in the corresponding category

• one rectangle divided up per category

• CONNECTED

• width of the rectangle is as large as the population of the category

categorical graphs

side-by-side bar graphs

mosaic plots

segmented/ribbon bar graphs

pie charts

association

when knowing the value of one variable can help predict the value of the other

• DOES NOT MEAN CAUSATION

no association

when knowing the value of one variable does NOT help predict the value of the other

dotplot

shows each data value as a dot above its location on a number line

full points for graph

• title

• correct graph

• labeled axis

• if necessary: subheadings and key

stemplot

shows each data value separated into two parts

1. stem, all digits minus the final digits (ex: 10s or 100s)

2. lead, the final digit (ex: 1s or 0.1s)

• kind of like a dot plot on its side + grouped into 10s or 5s

splitting stems

stemplot when the data is very clustered

back-to-back stemplot

combining two distributions of the same quantitative variable

• requires two keys and subheadings

describe the distrbution

SOCS in CONTEXT

• use variable name, not just units

• write in complete sentences

• start with capital and end with period

• NO bullets

shape

• unimodal/bimodal/etc

• skewed left/skewed right/symmetric

  • use QUALIFERS

  • skew towards the TAIL

outlier

• can do approximate, but if possible do EXACT

High-End Outlier

Q3 + 1.5 x IQR

Low-End Outlier

Q1 - 1.5 x IQR

unimodal

one peak

bimodal

two distinct clusters

uniform

frequency about the same for all values

mean

the average of all the individual data values

• better for more symmetric data

• NOT resistant

resistant

is not sensitve to extreme values

median

midpoint of a distribution

• resistant

symmetric

data forms a basic “U”

• mean = median (approximately)

skewed left

tail end is at the left

• mean < median

skewed right

tail end is at the right

• mean > median

range

distance between minimum and maximum values

• NOT resistant measure of variability

standard deviation

the typical distance of the values in a distribution from the mean

• NOT resistant

quartiles

groups of the distribution divided into fours

first quartile (Q1)

median of the data values LEFT or LESS THAN the median

third quartile (Q3)

median of the data values RIGHT or GREATER THAN the median

interquartile range (IQR)

distance between first and third quartiles

• Q3 - Q1

• more resistant

mode

the data value that occurs the most

histogram

uses intervals of values as a bar

• bin width = size of interval

• heights = frequency/relative frequency

  • use relative frequency when comparing distributions of different total counts

• good for large data sets

• do not know individual values

how many bins

1. count data points

2. square root the number of data points

3. round up

quantitative graphs

• dotplots

• histograms

• stemplots