1. Quantitative Data Continued
Histograms

2. Histograms Used with numerical data Bars touch on histograms
For comparative histograms – use two separate graphs with the same scale on the horizontal axis

3. Histograms
Histogram is used when quantitative variables are too many for a stemplot or dotplot.
Divide the range of the data into groups of equal width
Count the number of individuals in each group
Draw the histogram, title, label axis
There is no horizontal space between bars unless a group is empty

8. Calculator Instructions
STAT choose 1 Edit – Type values into L1
Set Up Histogram – 2nd Y (Stat Plot) Enter 1 Plot 1 ON Type “histogram” X List: L1 Freq: 1
Quick Graph ZOOM Choose 9 Trace to look at class intervals
Set Window to match intervals
Graph - Trace

9. Histograms The following are ages in months of 15 AP Stat students

10. Histogram (Xmin at 189)

11. Things to look for Center Shape Spread Outliers
Cautions: Pancake and skyscraper effect

12. Histogram Example 2
States differ widely with respect to the percentage of college students who are enrolled in public institutions. The U.S. Department of Education provided the accompanying data on this percentage for the 50 U.S. states for fall Create a histogram to display this data and then give a brief description of the distribution. (use a minimum of 40, and maximum of 100 with class widths of 10) Percentage of College Students Enrolled in Public Institutions

13. Histogram Example
Complete the frequency table below and construct the corresponding histogram.
Class
Count
25 to < 34
34 to < 43
43 to < 52
52 to < 61
61 to < 70
70 to < 79
Describe the shape: roughly symmetric, roughly skewed left, roughly skewed right, or no discernible shape.
Describe the spread of the distribution. …………………………
What is the center of the distribution? (Hint: look at the original data set) ……………
Do there appear to be any obvious outliers? If so, name them …………………………………
What is the width of each class in the histogram? …………
Could this data set be represented by a pie graph? Why or why not?

14. Boxplots

15. Why use boxplots? ease of construction convenient handling of outliers
construction is not subjective (like histograms)
Used with medium or large size data sets (n > 10)
useful for comparative displays

16. How to construct find five-number summary Min Q1 Med Q3 Max
draw box from Q1 to Q3
draw median as center line in the box
extend whiskers to min & max

17. ALWAYS use modified boxplots in this class!!!
display outliers
fences mark off mild & extreme outliers
whiskers extend to largest (smallest) data value inside the fence
ALWAYS use modified boxplots in this class!!!

18. Creating a Box Plot on your Calculator

19. Create a modified boxplot. Describe the distribution.
A report from the U.S. Department of Justice gave the following percent increase in federal prison populations in 20 northeastern & mid-western states in 1999.
Create a modified boxplot. Describe the distribution.
Use the calculator to create a modified boxplot.

20. Symmetrical boxplots
Approximately symmetrical boxplot
Skewed boxplot

21. Evidence suggests that a high indoor radon concentration might be linked to the development of childhood cancers. The data that follows is the radon concentration in two different samples of houses. The first sample consisted of houses in which a child was diagnosed with cancer. Houses in the second sample had no recorded cases of childhood cancer.

22. Cancer
No Cancer
Create parallel boxplots. Compare the distributions.

23. Creating a Box Plot
Cancer
No Cancer
Radon

24. Cancer
No Cancer
100
200
Radon
The median radon concentration for the no cancer group is lower than the median for the cancer group. The range of the cancer group is larger than the range for the no cancer group. Both distributions are skewed right. The cancer group has outliers at 39, 45, 57, and The no cancer group has outliers at 55 and 85.

25. Knowing about the DATA Which terms best represent the data?
The mean and median best illustrate skewed data
While variance and standard deviation represent symmetrical data
Spread – how far away from the mean does the data stretch
To calculate variances – we need to square the differences between the mean and each data value.
Variance (s2) - a measure of how far a set of numbers is spread out.
A variance of zero indicates that all the values are identical
A small variance indicates a small spread, while a large variance means the numbers are spread out
Standard Deviation (s) - shows how much variation or dispersion from the average exists