Stats Ch. 2
Degrees of freedom
(n - 1) ^From the variance formula
Formula to find the mean of a set of observations
Add their values and divide by the number of observations x̄ = (x1 + x2 + ... + xn)/n
Resistant measure (definition)
Aspect of a distribution that would be relatively unaffected by changes in the numerical value of small proportion of the total number of observations, no matter how large these changes are
Box plots
Based on the 5 number summary. Useful for comparing several distributions
The 1.5 x IQR Rule for Outliers
Call an observation a suspected outlier if it falls more than 1.5 x IQR above Q3 or below Q1 Q1 - (1.5 x IQR) = Result ^ Must be between results to not be a suspected outlier v Q3 - (1.5 x IQR) = Result
The first quartile
Has 1/4th of the observations below it
The third quartile
Has 3/4th of the observations below it
The five number summary
Has the median, the 1st quartile, the 3rd quartile, largest observation, lowest observation
Interquartile Range IQR Formula
IQR = Q3 - Q1
When is the mean and median exactly the same?
When the distribution is symmetric
Formula to find LOCATION of the median ("med-dle")
M = (n+1)/2
Good description for symmetric distributions without outliers
Mean and standard deviation
These are not resistant measure
Mean and standard deviation
Good description for skewed distributions or distributions with strong outliers
Median and quartiles
These are resistant measure
Median and quartiles
A numerical summary of a distribution shoulder report at least it's...
center and its spread or variability
How to find Median, Mean, Q1, Q3, Minimum, and Maximum, Standard Deviation, and Variance on Calculator
Stat --> Edit --> Enter variables in list --> Calc --> 1-Var Stats FOR VARIANCE, JUST SQUARE THE STANDARD DEVIATION
Standard deviation measures what about the mean?
The spread... And should be used only when the mean is chosen as the measure of center
Standard deviation
The square root of the variance s
Standard deviation is always 0 or greater than 0
s = 0 only when there is no spread. This only happens when all observations HAVE THE SAME VALUE!!! Otherwise, s > 0
Standard deviation... Regarding the units of measure
s has the same units of measurement as the original observations. For example, if you measure weight in kilograms, both the mean x̄ and standard deviation s are also in kilograms. This is one reason to prefer s to the variance s^2, which would be kilograms^2.
Variance Formula
The variance s2 of a set of observations is an average of the squares of the deviations of the observations from their mean s^2 = (x1 - x̄)^2 + (x2 - x̄)^2 + ... + (xn + x̄)^2 / (n - 1)
Mean
The arithmetic average of the observations
Interquartile Range IQR
The distance between the first and the third quartiles. This is mainly used as a basis for a rule of thumb for identifying outliers
Median
The midpoint of the values (The "Med-dle")
