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# Stats Chapter 4

### vocab

Question | Answer |
---|---|

distribution | slices up all the possible values of the variable into equal width bins and gives the number of values (or counts) falling into each bin |

histogram (relative frequency histogram) | uses adjacent bars to show the distribution of a quantitative variable; each bar represents the frequency (or relative frequency) of values falling in each bin |

gap | a region of the distribution where there are no values |

stem-and-leaf display | shows quantitative values in a way that sketches the distribution of the data |

dotplot | graphs a dot for each case against a single axis |

shape | described by: single vs. multiple modes, symmetry vs skewness, |

center | the place in the distribution of a variable that you'd point to if you wanted to attempt the impossible by summarizing the entire distribution with a single number (mean and median) |

spread | a numerical summary of how tightly the values are clustered around the center; IQR, STD DEV |

mode | a hump or local high point in the shape of the distribution of a variable; apparent location can change as scale of a histogram changes |

unimodal (bimodal) | having one (two) modes |

uniform | a distribution that is roughly flat |

symmetric | a distribution with two halves on either side of the center that look like mirror images of each other |

tails | are the parts that typically trail off on either side; distributions can be characterized as having long tails or short tails |

skewed | a distribution that is not symmetric and one tail is longer than the other (skewed LEFT if the tail is longer on the right vice versa) |

outliers | extreme values that don't appear to belong with the rest of the data; can be unusual values that need more investigation or mistakes |

median | middle value with half data above and half below; if N is even then it is the average of the two values; usually paired with the IQR |

range | max - min |

quartile | lower quartile (Q1): 1/4 data below it; upper quartile (Q3) 1/4 data above it; used with median it divides the data into 4 parts |

Interquartile Range (IQR) | difference between Q1 and Q3; Q3 - Q1 = IQR; reported along with the median |

percentile | the ith percentile is the number that falls above i% of the data |

5-number Summary | reports the minimum, Q1, median, Q3, and the maximum values |

mean | average; paired with STDDEV |

resistant | a calculated summary where outliers have a small effect |

variance | sum of squared deviations from the mean divided by the count minus 1 |

standard deviation | square root of the variance; s = sqrt((sigma(y-ybar)^2) / n-1); reported with the mean |

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