statistics midterm

boxplot

a plot that pictures quartile data

interquartile range

Q3-Q1

quantile

the data for proportion p

• q

standard deviation

measures the average distance data have from the mean

z score

measure of interesting-ness or surprise

• used to compare data values in different populations

resistant

when a measure is not impacted much by skewness or extreme data

resistant values

• median

• Q1

• Q3

• IQR

nonresistant values

• mean

• range

• standard deviation

• r

• r squared

bivariant

data that consist of observations of two variables

• pair of variables

x variable

• independent variable

• tells about y, not exact causation

y variable

dependent variable, depends on independent

scatterplot

used to plot bivariant data on the xy plane

time series data

independent variable is time

line graph

consecutive points in time are connected by line segments

ex: scatter plot

linear

an increase in the value of one variable roughly corresponds to a proportional increase in teh value of the other variable

• has a constant slope

pearson’s correlation coefficent

magic number that measures how close data are to being perfectly linear

• r

r squared

gives the proportion of variation in the y-variable that’s explained by the linear model

• larger values of it correspond to data that is more perfectly linear

• higher it is the closer it is to linear relation ship

unrelated

a correlation of r=0 does not imply the variables are _____

ex: quadratic data=perfectly quadratic, not linear and r is basically 0, but has a relationship

residual

distance of the point from the linear regression line

line of best fit

the line that runs centrally throughout all the data

• also linear regression lines and least squares line

• most accurately represents the data

• makes the sum of squared errors small

interpolating

Xo is within the rance of x values [min, max] then we are _____ the data

• internally extending the data with a prediction

extrapolating

Xo is outside the range of x-values, [min, max], and so we are _____ the data

• we are extending the data externally

• can do it within the advisable range (5% below and above range length)

meaningful

the y-intercept, when x=0, is often not _____.

0

the sum of all residual is ____

sum of squared deviation

• measures variability of data

• totals up total deviation from the mean

continuous

if x is ____ then Prob(x=a)= 0 and Prob(x>b) = Prob(x≥b) and vice versa

continuous random variable

normal with mean and standard deviation

normal

we say x is ___ if the density function of x is ____ to mean and standard deviation for some constants a and b>0

bell curve

• symmetric

• centered at the mean

• steepest at mean-deviation and mean + deviation

• curve has most of its area btwn the mean - 3(standard deviation) and mean + 3(standard deviation)

• tapers off quickly

standardization

using z score

law of large numbers

as the number of trials grows very large, then the relative frequency of event e gets closer and closer to the probability of e

• averaging many values of X (sample) gives an estimate for mean

• can be confident that a relative frequency or average is a good estimate for a true probabity or mean mew

mean

the values of x tend to be near the ____

standard deviation

the average distance X takes from mean is the _____

probability

the study of likelihood, randomness, chance, etc

• relative frequency at which the event occurs

• equal to the proportion of instances where the event occurs when looking at a large collection of instances where it could occur

probability experiment

any situation that leads to a random result

• consists of one or more trials

• possible results are outcomes

sample space

the collection of all outcomes

event

any subcollection of outcomes

disjoint

variables have no outcomes in common

random

a rule assignment that assigns each outcome in S some real number

discrete

random variable X that only takes integer units

expected value

called the proportion mean of x

• approximates the average value of x over those trials

• does not have to be a value that x takes

continuous variable

takes on values from an interval

• measure x finitely

density function

• how to determine if a random variable is continuous

• equal to or greater than 0

• area under this curve=1

• probability: prob(a<A≤b)

• ddist

distribution function

pdist(a)=Prob(x ≤ a)

Quantive function

inverse of pdist= value of pdist(prob) is the input of in qdist and the input of pdist is the result of q dist

• qdist

• Prob(x ≤ q)