1. Chapter 5 : Describing Distributions Numerically I
  Chapter 5 : Describing Distributions Numerically   I. Finding the Center: The Median   midrange_ - (highest + lowest) / 2 sensitive to outlying values median 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 data If 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, Median: _______       12, 15, 38, 25, 12, 15, 16, 22, 13, 33, 11, 25, 16, 18, 23, 18, 19, 13, 14, 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 (75th percentile)

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

5. 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 _.

6. 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

7. 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 (Terms)