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")