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# 1Quan Variable

### Basic Stats

useful graph boxplot or histogram
useful numbers location: mean and median spread: standard deviation and IQR 5-number summary: min, max, IQR and median
formula for mean x ̅=1/N ∑_((i=1))^N▒xi preferable for approximately normal data
formula for median M=midn or midx1+midx2/2 less affected by outliers therefore used for outlier ridden data
formula for standard deviation s=√(1/(N-1) ∑_(i=1)^N▒〖(xi-x)〗^2 ) preferable for approximately normal data
formula for IQR Q3 - Q1= IQR less affected by outliers therefore used for outlier ridden data
numerically define an outlier more than 1.5 x IQR lower than Q1 more than 1.5 x IQR higher than Q3
define linear transformation transformation of a variable from x to xnew
examples of linear transformation use change of units use of normal assumption therefore to find 'z' scores
formula for linear transformation xnew=a+bx
formula for new mean once linear transformation has occurred xbar new=a+bxbar
formula for new median once linear transformation has occurred Mnew=a+bM
formula for new standard deviation once linear transformation has occurred snew=bs
formula for new IQR once linear transformation has occurred 1QRnew=bIQR
density curves area under the curve in any range of values is the proportion of all observations that fall within that range for a quantitative variable = like a smoothed out histogram describes probabilistic behaviour
total area under the density curve equals? 1
normality assumption normal curve can be used if a histogram looks like a normal curve termed 'reasonable' must start at 0 and end at 0
normal quantile plot if in a straight line, or close to it, then normal and assumption is reasonable
68-95-99.7% rule 68% of results will be within 1 standard deviation of the mean 95% of results will be within 2 standard deviations of the mean 99.7% of data will be within 3 standard deviations of the mean
symbol for the mean of a density curve μ
symbol for the standard deviation of a density curve σ
normal distribution shorthand X = random variable N = normal distribution first number in brackets = mean second number in brackets = standard deviation
standard normal variable Z corresponds to the area under the curve of the corresponding region will always be to the left
standard normal distribution table to find P: Z found along x and y axis to find Z: P found in table ordered from smallest to largest
reverse standard normal distribution table P(Z<c) c = right of Z
X is N(μ,σ)
standardising transformation Z= (X-μ)/σ used when distribution is N(0,1)(is normal but needs proportions changed)
useful test 1-sample test for μ when σ is unknown
useful inference Cl for μ
Created by: Nymphette