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1Quan Variable
Basic Stats
| Question | Answer |
|---|---|
| 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
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