1. Basic Descriptive Statistics Dr. Yeh

2. Why? Descriptive statistics do just that: Describe Data! Descriptive statistics do just that: Describe Data! What we’ll cover in this slidecast What we’ll cover in this slidecast –Mean (average) –Median –Mode –Range

3. Mean Fancy Formula µ =  X/N

4. Mean Fancy Formula µ =  X/N What this means: add up all your data, then divide by the number of data points What this means: add up all your data, then divide by the number of data points

5. Mean Sample data: 98cm76cm82cm54cm90cm

6. Mean 98cm76cm82cm54cm90cm How to calculate: 98+76+82+54+90 = 400cm

7. Mean Sample data: 98cm76cm82cm54cm90cm How to calculate: 98+76+82+54+90 = 400cm 400cm/5 = 80cm

8. Mean Sample data: 98cm76cm82cm54cm90cm How to calculate: 98+76+82+54+90 = 400cm 400cm/5 = 80cm

9. Median The median is the middle data point in a set The median is the middle data point in a set To determine the median, sort the data from smallest to largest and find the middle data point To determine the median, sort the data from smallest to largest and find the middle data point

10. Median Sample data: 98cm76cm82cm54cm90cm

11. Median 98cm76cm82cm54cm90cm Rearranged Data: 54cm76cm82cm90cm98cm

12. Median Sample data: 98cm76cm82cm54cm90cm Rearranged Data: 54cm76cm82cm90cm98cm

13. Median If there is an even number of data, there will be two middle points. If there is an even number of data, there will be two middle points. To find the median, take the average of those two data. To find the median, take the average of those two data.

14. Median Sample Data: 4ml8ml12ml2ml

15. Median 4ml8ml12ml2ml Rearranged Data: 2ml4ml8ml12ml

16. Median Sample Data: 4ml8ml12ml2ml Rearranged Data: 2ml4ml8ml12ml 4 + 8 = 12ml 12/2 = 6ml

17. Mode The mode is the most frequently occurring data point. The mode is the most frequently occurring data point. To find the mode, arrange the data from smallest to largest, and then determine which amount occurs most often. To find the mode, arrange the data from smallest to largest, and then determine which amount occurs most often.

18. Mode Sample Data: 20g23g 30g30g 22g27g 25g20g 23g24g 23g25g 20g23g

19. Mode Sample Data: 20g23g 30g30g 22g27g 25g20g 23g24g 23g25g 20g23g Rearranged Data: 20g 20g 20g 22g 23g 23g 23g 23g 24g 25g 25g 27g 30g 30g

20. Range The range is the distance between the smallest and largest data point. The range is the distance between the smallest and largest data point. To calculate, determine the smallest data point and the largest data point, then subtract the smallest from the largest. To calculate, determine the smallest data point and the largest data point, then subtract the smallest from the largest.

21. Range Sample data: 98cm76cm82cm54cm90cm Rearranged Data: 54cm76cm82cm90cm98cm

22. Range Sample data: 98cm76cm82cm54cm90cm Rearranged Data: 54cm76cm82cm90cm98cm 98cm – 54cm = 44cm

23. Recap Mean, Median, Mode, and Range “describe” the data. Mean, Median, Mode, and Range “describe” the data.

24. Acknowledgements American Chemical Society. (2006). Chemistry in the community: ChemCom (5 th ed). New York: W.H. Freeman