1. GRAPHICAL DESCRIPTIVE STATISTICS FOR QUANTITATIVE DATA

2. Graphical Techniques Quantitative Data HistogramsHistograms –Consider measurement classesBoundaries of measurement classes –Choose values that are easy to read/understand –Number of classes will “fall out” “break points”Where to place data occurring at “break points” –Excel –Excel – in the lower interval Outliers?Inclusion of Outliers? – unrepresentative data far above or far below most of the rest of the data –Seek reason for outliers Relative Frequency (Percentage) HistogramsRelative Frequency (Percentage) Histograms Cumulative Relative Frequency OgivesCumulative Relative Frequency Ogives

3. Frequency Distributions Take a Survey of Incomes of 200 High School Graduates 2 Years After Graduation Results: $31,500, $26,900, …., $26,100 Create Class Intervals So Data Can Convey Information –Not too many –Not too few –Include All Data (?) --- Outliers –Intervals of Equal Size

4. Results Income Frequency Rel. Freq. $15,000-$20,000 9 9/200 =.045 $20,000-$25,00034 34/200 =.170 $25,000-$30,00091 91/200 =.455 $30,000-$35,00061 61/200 =.305 $35,000-$40,000 5 5/200 =.025

5. Histogram

6. RELATIVE FREQUENCY HISTOGRAM Same shape as histogram – different scale on y-axis

7. EXCEL DATA ANALYSIS Go to Tools Menu –Select Data Analysis What If Data Analysis Isn’t There? –Go to Tools Menu Select Add-Ins Check Analysis Tool Pak Check Analysis Tool Pak-VBA Click OK

8. EXCEL Histograms Basic Approach: –Put Data in a Column –Create Bins (Measurement Classes) Tools –Go To Tools Data Analysis Select Data Analysis Histogram Select Histogram Chart Output Check Chart Output

9. Data put into a column

10. CREATE BINS 2. lower bound of the first measurement class First entry should be less than lowest value – actually the lower bound of the first measurement class – this allows us to begin the histogram at a value >0. 3. upper bound of the first measurement class Enter the upper bound of the first measurement class 4. Highlight the first two entries and drag down to the upper bound of the last measurement class+ 1. Enter label for X-Axis

11. TOOLS/DATA ANALYSIS/HISTOGRAM Go to Tools Select Data Analysis Select Histogram

12. Histogram Dialogue Box 1. 1.Enter cells containing data including label 2. 2.Enter cells containing bins including label 3. Check Labels 5. 5.Enter where you want the output 4. Check Chart Output

13. Resizing Grab Lower Corner and drag to resize

14. Result of Resizing Click and Delete Click and RenameClick in Grey Area and Delete Change Numbers to Midpoint Values Delete first entry (15000) and last entry (More) To close gap width: Right mouse click on a bar Format Data Series Select Format Data Series Options Select Options Gap Width Set Gap Width = 0

15. Resulting Histogram

16. Relative Frequency Proportion of Data in a Particular Class Divide Frequencies by 200 gives these results:

17. Relative Frequency Histogram Change the numbers on the y-axis to percentages Can manipulate Excel Histogram –Numbers on Y-axis appear in column B –Somewhere create a cell with the formula =B2/200 (Say in cell B12) –Drag down until all relative frequencies are shown –Highlight this new set of numbers and press COPY –Then PASTE SPECIAL (Values) these numbers back into cell B2 –Erase numbers in cells B12 and below –Change Name in cell B1 and on Y-Axis to Relative Frequency

18. Creating Relative Frequencies 3. Put cursor in cell B2 1. Enter =B2/200 Drag to B18 Then highlight B12:B18 2. Select Copy 4. 4.Go to Edit Select Paste Special 5. Select Values

19. Creating Relative Frequencies 6. Change to Relative Frequency 7. Highlight and delete

20. Cumulative Relative Frequencies Give the proportion of values that are less than the upper boundary point of the class Cumulative frequency for first class is the relative frequency For subsequent classes cumulative frequency = relative frequency + cumulative frequency of previous class

21. Cumulative Relative Frequencies The same as the relative frequency.670 =.455 +.215

22. Ogives Line graph of cumulative relative frequencies –Begin with y-value = 0 at $15,000 and draw line to.045 at $20,000 –Draw line from.045 at $20,000 to.215 at $25,000 –Draw line from.215 at $25,000 to.670 at $30,000 –Draw line from.670 at $30,000 to.975 at $35,000 –Draw line from.975 at $35,000 to 1 at $40,000 –Draw line flat at 1 (to infinity)

23. Result

24. Using Ogives to Approximate Prob (Income < $27,500) 27500 0.44

25. EXCEL Ogives Check both

26. 2. Delete Legend 4. Change Names 1. Resize 6. Delete More 3. Delete Background 5. Right Mouse Click On any bar --Delete

27. RESULT

28. Review Frequency Distributions Frequency Histograms Relative Frequency Distributions Relative Frequency Histograms Cumulative Relative Frequencies Cumulative Relative Frequency Ogives