AP STATS U1 Flashcards

Individuals

Objects described by a set of data, may be ppl, animal, things

Variables

Any charcteristic of an individual we measure

Data Analysis

The proccess of organizing, displaying and asking Q’s abt Data

Categorical Variable

Places an individual into one of several categories and groups

Quantitative Variable

Takes a numerical value for which it makes sense to find the average

Distribution

Tells us the values a variable takes and how often it takes those values

Inference

Drawing conclusions that go beyond the data at hand

Frequency Table

Displays the counts

Relative Frequency Table

Displays the percents

Roundoff Error

Proccess in which percents dont round exactly to 100 due to rounding of numbers

What distributions are meant for categorical variables?

Pie Chart and Bar Graph

Pie Chart 

Shows the distribution of a categorical variables as a pie 

Must include all the categories that make up a whole and emphasive each categories relation to the whole 

Bar Graph

Represents each category as a bar

Bar heights show the category of counts of percent

Bar graphs are easier to make and read then pie charts

Why can graphs be problematic?

You have to watch your scales (Area/width) and beware of photographs

Two-way table

Describes 2 categorical variables

Marginal Distributions

Appear at right and bottom margins of the two-way table

distribution of values of that variable among all individuals described in the table 

What is the downside of a marginal Distribution

They tell us nothing about the relationship between 2 variables

Conditional Distribution

Describes the values in that variable among individuals what have a specific value for another variable

Segmented Bar Graph

Problematic because difficult to compare percents of males and females in each category b/c middle segments in 2 bars start at different locations at the vertical axis

Association

Theres an association between varibles if knowing the value of one variable helps to predict the value of the other

How to describe a dot plot distribution (Shape)

Peaks, Gaps, clusters

Center

Midpoint (Signifies in a typical (scenario) wewill do (Blank))

Spread

Range

Outliers

Any data that stands out from the distribution

Roughly Symmetric

When right and left sides are approx. mirror images

Shewed to the right

Right side of graph contains more observations and is much larger then the left side

Where most of the data is low values and a couple high values skew it to the right

Skewed to the left

Left side is much longer on the left side

When there are mainly high scores and a couple low scores skew the distribution to the left

What meaurements are typically right skewed

House prices and salaries

Splitting Stemplot

0-4 are placed on 1 stem and 5-9 are placed on the next

T or F Do stemplots dont work well on large data set

True, esp where each stem shoudl hold a large number of leaves

T or F too little of too many stems doesnt make a difference in a dotplots distribution

False

When you split stems is it T or F that each stems must have an equal amount of possible leaf digits 

True

Histogram

Grouping of nearby quantitative variables (FINISH)

When Do you Use percents for comparing distributions w/ diff number of observations

In Histograms!

Mean

Add up all values and divide by n

Is mean a resistant measure of center?

NO! SENSITIVE to the influence of extreme observations

What does the mean tell us?

Tells us how large each data value would be if the total was split equally among all observations

Median

Midpoint of the Distribution, the number that such half the observations are smaller and half are larger

What do the mean and median look like in a roughly symmetric distribution?

Mean and median are close to eachother

What do the mean and median look like in a exactly symmetric distribution?

Mean and median are same

What do the mean and median look like in a skewed distribution?

Mean goes towards farther out in the long tail that the median

Range

Simplest measure of variability

Q1

Median of observations that are to the left of the median in the ordered list

Q3

Median of observations that are to the right of the median in the ordered list

IQR

Range of middle 50% of data

Q3-Q1

Are quartiles and IQR resistant measures?

Yes! B/c not affected by extreme outliers

1.5 X IQR

We consider an observation an outlier when it falls more than 1.5*IQR above the third quartile

5 Number Summary

Consists of the Small observation, Q1, Median, Q3, largest observation written from smallest to largest

Boxplot

Central box is between Q1 and Q3

Lines extend from min and max

Median is marked by a line

Outliers marked w/ an asterick

Variance

measure spread by looking at how far the observations are from their mean

Standard Deviation

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

T or F Sx measures spread of mean and should not be used when only the mean is chosen as the measure of center

F, Measures soread of mean and SHOULD be used if mean is chosen as measure of center

T or F Sx is always larger or equal to 0

T, sx=0 means theres no variability

as observations spread out, the sx does as well

Is Sx Resistant?

NO!

Whats measures of center and spread should we use for skewed distributions or distributions with strong outliers?

Median and IQR=Resistant