1. AP Statistics
Day 4
Objective: The students will be able to describe distributions with numbers and create and interpret boxplots.

2. Box Plots
Are created by finding the 5 Number Summary and Plotting those 5 points on a number line, then creating the boxplot.

3. 5 Number Summary Smallest Value (lower extreme) Lower Quartile (Q1)
Median
Upper Quartile (Q3)
Largest Value (upper extreme)

4. Median To find the median of a distribution:
Arrange all observations in order of size, from smallest to largest.
If the number of observations is odd, the median is the center observation in the ordered list.
If the number of observations is even, then the median is the mean of the two center observations in the ordered list.

5. Median
To find the median of a set of data with “n” values simply use the formula and that will
tell you where the middle term is once the pieces of data are in numerical order.

6. Interquartile Range (IQR)
Quartiles (Q1, Q3)
The quartiles are found by finding the
median of the data set on the right side of
the median and the median of the data set
on the left side of the median.
Interquartile Range (IQR)
To find the interquartile range you subtract Q1 from Q3.
IQR = Q3 – Q1

7. Mean
The equation used to find the mean of a set with “n” observations is denoted by:
Or in a more compact notation:
*The bar over the x indicates the mean of all the x-values. The symbol is pronounced “x-bar”

8. Comparing the mean and median
The mean is what we call nonresistant because it is sensitive to outliers, meaning the mean can drastically change due to one outlier.
The median is resistant to extreme observations because one or two outliers may not change the median at all.
The mean and median would be exactly the same if the distribution is exactly symmetric.

9. Comparisons Cont.
In a skewed distribution the mean would be further out along the long tail, than is the median.
Example: If the mean of a data set is 78 and the median is 67, what do we know about the shape of the distribution?

10. Modified Box Plots
A modified box plot is when there exists an outlier and it is represented by a single point and is not connected to the “box”.