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Spread: Home on the Range

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Spread: Home on the Range

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  1. Chapter 5 : Describing Distributions Numerically I. Finding the Center: The Medianmidrange_ - (highest + lowest) / 2 sensitive to outlying valuesmedian the middle value that divides the histogram into 2 equal areas (include units)After you find it ask yourself how well it actually summaries the dataIf odd number of values ; if n is even there is 2 middles so Find the median of the values:12, 15, 38, 25, 12, 15, 16, 22, 13, 33, 11, 25, 16, 18, 23, 18, 19, 13, 14 Median: _______12, 15, 38, 25, 12, 15, 16, 22, 13, 33, 11, 25, 16, 18, 23, 18, 19, 13, 14, 16 Median: _______

  2. Spread: Home on the Range • The more the data vary, the less the median alone can tell us. So, you should always report a measure of spread. • Range: max – min (single number, not an interval, also sensitive to outliers) • Spread: The Interquartile Range • Concentrate on the middle . (ignore extremes) • Quartiles – divides data into 4 equal parts Lower Quartile (Q1) Median (Q2) Upper Quartile (Q3) • Interquartile Range(IQR): Upper Quartile – Lower Quartile • Textbook includes median in each half, graphing calculator does not) • Lower Quartile 25th percentile); Upper Quartile (75thpercentile)

  3. 5 Number Summary • Reports a distributions median, quartiles, and extremes (min, Q1, median, Q3, max) • Making Boxplots • Box plot– displays the 5 number summary as a central box with whiskers that extend to the non-outlying data values • Particularly effective for comparing distributions. • Fences - used to identify outliers • (help with construction, but never include in your boxplot) • If a data value falls outside one of the fences, we do not connect it with whiskers • Lower Fence: Q1 – 1.5IQR • Upper Fence: Q3+ 1.5IQR

  4. Mean or Median? • Mean cuts the data into 2 halves not taking into account their size • Median takes their size into account (the point at which the histogram would balance) • Left Skewed → mean to the left of the median • Right Skewed → mean to the right of the median • If data is skewed better to use themedian_.

  5. What about the Spread? The Standard Deviation • IQR is good but ignores individual data • Standard deviation– takes into account how far each value is from the mean • Only appropriate for symmetric data • Deviation– distance a value is from the mean • Could average them but the + and – would cancel each other out, so we square them • Standard Deviation_ – the average (almost) of the deviations

  6. Shape, Center, and Spread • So… • Skewed →IQR & MEDIAN • Symmetric → MEAN & STANDARD DEVIATION • Outliers → median / IQR_ OR Mean / standard deviation without outliers • Read page 87 (What Can Go Wrong) and 88- 89 (Terms)

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