1. Additional Measures of Center and Spread
Math Alliance
Fall 2011

2. 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

3. 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

4. Box Plot
Graph of the five number summary

5. 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

6. 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

7. 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

8. Comparing two or more Groups
Side by side box plots
Calories for all beef hot dogs:
Calories for all poultry hot dogs:

9. 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.