1. 5 Number Summary, Boxplots, Outliers, and Resistance

2. Mean
Bill Gates makes $500 million a year. He’s in a room with 9 teachers, 4 of whom make $40k, 3 make $45k, and 2 make $55k a year. What is the mean salary of everyone in the room? What would be the mean salary if Gates wasn’t included?
Mean With Gates:
$50,040,500
Mean Without Gates:
$45,000

3. Resistance
The mean is a non-resistant measurement, which means that extreme values will pull it towards that end of the data.
The median is a resistant measurement.
Extreme values have no affect on it.
Note- If the mean and median are the same then the dist. is roughly symmetric. Mean smaller-skewed left, mean larger-skewed right

4. 5 Number Summary/Boxplot

5. Example: Ages of actresses at the time they first won the Oscar50 44 35 80 26 28 41 21 61 38 49 33 74 30 31 42 37 34 60 24 27 39 25

6. Box Plot We need 5 numbers, called the 5 number summary:
1. minimum value
2. Q1 (median of 1st half)
3. median
4. Q3 (median of 2nd half)
5. maximum value

7. Calculate the 5 number summary for actresses data
Min = 21
Q1 = 30
Med = 34
Q3 = 41
Max = 80
Construct a boxplot for the 5 number summary

8. Distribution Shape Based Upon Boxplot
1. If the median is near the center of the box and each of the horizontal lines are approximately equal length, then the distribution is roughly symmetric.
2. If the median is left of the center of the box and/or the right line is substantially longer than the left line, the distribution is right skewed.
3. If the median is right of the center of the box and/or the left line is substantially longer than the right line, the distribution is left skewed

9. Symmetric

10. Skewed Right

11. Skewed Left

12. In a set of numbers, a number that is much LARGER or much SMALLER than the rest of the numbers is called an Outlier.

13. Criteria for Outliers
Remember that an outlier is a data value that lies very far away from the majority of all the other data values in the data set. The following is criteria to identify outliers in a data set.
The inter-quartile range (IQR) is the value of Q3 – Q1
x is an outlier if of one the following inequalities is true:
1. x > Q x IQR
x < Q x IQR
Does our data have any outliers?

14. Box plot with outliers (Modified Boxplot)
When we select the 1st box plot on the TI, it allows us to see outliers. Select the mark that is visible for you.

16. Trace and go to the right twice.
The 50 is the last data value that is not an outlier.

17. Homework
1.26, 29, 31-34,36-39