1. 5-Number Summaries, Outliers, and Boxplots
Section 2.3 Day 2
5-Number Summaries, Outliers, and Boxplots

2. 5-Number Summary AKA 5-point summary
If you include the minimum and maximum values of the data set along with the median and quartiles, you get the 5-number summary.
AKA 5-point summary

3. 5-Number Summary

4. Find 5-number summary.

5. Find 5-number summary….don’t forget key!
3I2 represents 32 mph

6. Find 5-number summary….n=18
3I2 represents 32 mph

7. 5-Number Summary
Graphical display of a 5-number summary is a boxplot or box-and-whiskers plot

8. How do we construct a boxplot?

9. 1. Plot the 5 points

10. 1. Plot the 5 points
2. Draw box from Q1 to Q3

11. 1. Plot the 5 points
2. Draw box from Q1 to Q3
3. Draw vertical line at median

12. 1. Plot the 5 points
2. Draw box from Q1 to Q3
3. Draw vertical line at median
4. Extend whiskers to min and max values

13. 1. Plot the 5 points
2. Draw box from Q1 to Q3
3. Draw vertical line at median
4. Extend whiskers to min and max values
5. Label graph (context)

14. Outliers
What are outliers?

15. Outliers
Recall outliers in a set of data are any values that differ significantly from the other values.

16. For this data, are there any outliers?

17. Formula for Outliers
A value is an outlier if it lies more than 1.5 times the IQR from the nearest quartile.

18. Formula for Outliers
A value is an outlier if it lies more than 1.5 times the IQR from the nearest quartile.
Thus, a value is an outlier if it is
< Q1 – 1.5(IQR) or
> Q (IQR)

19. For this data, are there any outliers?

20. IQR = Q3 – Q1 = 42 – 30 = 12
Lower end:Q1 – 1.5(IQR) = 30 – 1.5(12) = 12
Upper end:Q (IQR) = (12) = 60

21. Modified Boxplot
Modified boxplot is like a basic boxplot except the whiskers only go as far as the largest and smallest nonoutliers (sometimes called adjacent values).
Any outliers appear as individual dots or other symbols.

22. Modified Boxplot
Modified boxplot is like a basic boxplot except the whiskers only go as far as the largest and smallest nonoutliers (sometimes called adjacent values).
Any outliers appear as individual dots or other symbols.

23. Boxplots Useful when plotting a single quantitative variable and
you want to compare shapes, centers, and spreads of two or more distributions
you don’t need to see individual values, even approximately
you don’t need to see more than the
5-number summary but would like outliers to be clearly indicated

24. Graphing Calculator You can use graphing calculator to find
5-number summary and draw boxplot.
Use data from Display 2.46 on page 61

25. Graphing Calculator You can use graphing calculator to find
5-number summary and draw boxplot.
Use data from Display 2.46 on page 61
Press “STAT”
Select 1:Edit
Enter the data elements in list
Note: no need to reorder data first

26. Graphing Calculator is Your Friend!
Your calculator will compute the summary statistics for a set of data.
After entering data in list:
Press “STAT”
Arrow right to “CALC”
Select “1: 1-Var Stats”
1-Var Stats L1
Enter

27. 1-Var Stats
Display 2.46 on page 61

28. 1-Var Stats

29. Draw Boxplot 2nd STAT PLOT 1: Plot 1 …on
Type: select modified boxplot symbol
Xlist: L1
Freq: 1
Mark:
Graph

30. Draw Boxplot If you can not see the boxplot, press “Zoom”
Select 9: ZoomStat

31. Standard Deviation
Differences from the mean, x – x, are called deviations.

32. ∑(x – x ) = 0 Standard Deviation
Differences from the mean, x – x, are called deviations.
Mean is balance point of distribution so the set of deviations from the mean will always sum to zero.
∑(x – x ) = 0

33. Standard Deviation
Formula for standard deviation, s, is:

34. Standard Deviation Formula for standard deviation, s, is:
Dividing by n - 1 gives a slightly larger value than dividing by n. This is useful because otherwise the standard deviation of the sample would tend to be smaller than the standard deviation of the population the sample came from.

35. Computing Standard Deviation

36. Computing Standard Deviation
Use 1-Var Stats.
Symbol for standard deviation is sx

37. Summary from Frequency Table

38. Summary from Frequency Table
Page 68

39. Summary from Frequency Table
Enter “values” in List 1
Enter “frequency” in List 2
“STAT”, “CALC”, “1: 1-Var Stats”
1-Var Stats L1, L2
Enter

40. Important Note
When homework says to use the formulas to compute something, you may use your calculator

41. Questions?