Transcript ch 5

Center
• Midrange: taking the average of the maximum &
the minimum values. Sensitive to outliers.
• Median: the value that divides the data into 2
equal areas. More variation, less effective.
• Mean: sum of all the data values divided by the
count. The point at which the histogram would
balance. Outliers & skewness “pull” the mean in
that direction.
Spread
• Range: the difference between the
maximum and minimum values
• Interquartile range: when you divide the
data into quartiles, the difference between
the first and third quartiles. (Q3 - Q1) Q1
= 25%ile; Q3 = 75%ile
• 5 Number Summary: reports the median,
quartiles, maximum and minimum values.
Used to construct a boxplot.
• Constructing a boxplot:
– 1) mark Q1, Q3 & median to create your box.
– 2) Erect “fences” at 1.5 and 3 IQR’s below Q1
and above Q3 (OUTLIERS!)
– 3) Add whiskers to extreme values within
fences
– 4) Mark any outliers with special symbols
County Size of New Jersey
• Interpretation of boxplots
– Median centered in box…middle half is
symmetric
• If not, skewed to the other side
– Whiskers same length…symmetric
• If not, skewed to side with longer whisker
Histogram
Aaron vs.
Bonds
Barry Bonds
Hank Aaron
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Comparative B & W
• Deviation: how far each value is from the
mean.
• Variance: adding the squared deviations
and finding their average.
s 
2
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 y y
n 1
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s
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 y y
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n 1
• Standard Deviation…
s
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 y y
n 1
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Counting Chips
• Rules for center/shape/spread:
– Skewed Data: report median & IQR
– Symmetric Data: Report mean and standard
deviation
– If outliers, report mean and standard deviation
with and without the outliers.
MC ???