Basic Stats
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| useful graph | boxplot or histogram
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| useful numbers | location: mean and median
spread: standard deviation and IQR
5-number summary: min, max, IQR and median
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| formula for mean | x ̅=1/N ∑_((i=1))^N▒xi
preferable for approximately normal data
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| formula for median | M=midn or midx1+midx2/2
less affected by outliers therefore used for outlier ridden data
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| formula for standard deviation | s=√(1/(N-1) ∑_(i=1)^N▒〖(xi-x)〗^2 )
preferable for approximately normal data
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| formula for IQR | Q3 - Q1= IQR
less affected by outliers therefore used for outlier ridden data
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| numerically define an outlier | more than 1.5 x IQR lower than Q1
more than 1.5 x IQR higher than Q3
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| define linear transformation | transformation of a variable from x to xnew
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| examples of linear transformation use | change of units
use of normal assumption therefore to find 'z' scores
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| formula for linear transformation | xnew=a+bx
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| formula for new mean once linear transformation has occurred | xbar new=a+bxbar
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| formula for new median once linear transformation has occurred | Mnew=a+bM
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| formula for new standard deviation once linear transformation has occurred | snew=bs
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| formula for new IQR once linear transformation has occurred | 1QRnew=bIQR
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| 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
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| total area under the density curve equals? | 1
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| 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
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| normal quantile plot | if in a straight line, or close to it, then normal and assumption is reasonable
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| 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
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| symbol for the mean of a density curve | μ
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| symbol for the standard deviation of a density curve | σ
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| normal distribution shorthand | X = random variable
N = normal distribution
first number in brackets = mean
second number in brackets = standard deviation
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| standard normal variable | Z
corresponds to the area under the curve of the corresponding region
will always be to the left
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| 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
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| reverse standard normal distribution table | P(Z<c)
c = right of Z
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| X is | N(μ,σ)
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| standardising transformation | Z= (X-μ)/σ
used when distribution is N(0,1)(is normal but needs proportions changed)
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| useful test | 1-sample test for μ when σ is unknown
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| useful inference | Cl for μ
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Nymphette
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