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**Additional Measures of Center and Spread**

Math Alliance Fall 2011

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Measures of Center Mode Most frequent value Mean Fair share or balance point Median If odd number of values then middle number If even number of values then mean of middle two numbers

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Five Number Summary Minimum: lowest value 1st Quartile: median of the lower half Median: middle number 3rd Quartile: median of the upper half Maximum: highest value

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Box Plot Graph of the five number summary

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**Interpretation of Box Plots**

The five number summary divides a data distribution into 4 parts. About what percent of the data values in each of the following intervals? • before the median • after the median • in the box (between the 1st and 3rd quartiles) • before the upper quartile • after the upper quartile • before the lower quartile • after the lower quartile • between median and upper quartile • between the median and the lower quartile

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**Definition of outliers**

Steps to determine if there are outliers: Find the Interquartile range (IQR) IQR = Q3 – Q1 Multiply: 1.5 * IQR Add: Q *IQR Any value greater than Q3+ 1.5*IQR is an outlier Subtract Q1 – 1.5*IQR Any value less than Q1-1.5*IQR is an outlier

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Definition of Outlier Any value more than 1.5 IQRs above Q3 or below Q1. Or Any value more than 1.5 “boxes” above Q3 or below Q1 Example: Natural Peanut Butter Quality Ratings: Find the 5 number summary Make a box plot Determine if there are any outliers

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**Comparing two or more Groups**

Side by side box plots Calories for all beef hot dogs: Calories for all poultry hot dogs:

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**Comparing two groups Each each type of hot dog**

Find the 5 number summary Construct a box plot of each using the same scale for both. Place the beef hot dog box plot above the poultry hot dog box plot. What type of hot dog has the fewer number of calories? Use the box plots and the percent to explain your answer.

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1 Distribution Summaries Measures of central tendency Mean Median Mode Measures of spread Range Standard Deviation Interquartile Range (IQR)

1 Distribution Summaries Measures of central tendency Mean Median Mode Measures of spread Range Standard Deviation Interquartile Range (IQR)

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