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# Spread: Home on the Range - PowerPoint PPT Presentation

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Presentation Transcript
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: _______
• 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)
• 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)
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
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_.