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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