Chebyshev’s theorem: At least 1-1/k2 of the data is within k standard deviations, no matter how crazy the distribution

Using Chebyshev’s theorem

Solving for k (we got k=2)

Calculating z-scores

Finding what percentile 86 is at

In the same data set, what value is at the 75th percentile?

Finding min, max, and median -- and getting ready to find Q1 and Q3

Q1 and Q3 from the data on the last slide

Boxplot of the 5-number summary we just found

More practice calculating standard deviation with a table

Finishing the calculation using the table on the last slide

Another table calculation for standard deviation with new data

Completing that calculation

So, we found that the tallest buildings in New York are more variable in height than those in Hong Kong.