The document discusses error analysis, standard deviation, and t-tests in the context of evaluating data sets with different distributions. It explains how to calculate mean, median, and mode, highlighting the appropriate use of measures of central tendency based on data clustering and outliers. Additionally, it emphasizes the implications of standard deviation on the certainty of the relationship between concentration and reaction rate, illustrated through examples from two students' experiments.

1. Video Tutorial Error analysis, Standard
deviation, error uncertainty and t test for
significant difference.
Prepared by
Lawrence Kok
http://lawrencekok.blogspot.com

2. Central value of normal distribution curve can be recorded as
• Mean
• Mode
• Median
Consider the following set of data collected
5, 6, 6, 6, 6, 7, 9
Average can be in the form of Mean, Mode or Median
• Mean = ( 5 + 6 + 6 + 6 + 6 + 7 + 9 ) /7 = 6.42
• Median = 6 ( middle number )
• Mode = 6 ( most common )
Conclusion = Can use mean, median or mode if data cluster together
(normal distribution)

3. Consider the following set of data collected
1, 7, 8, 8, 8, 9, 9
Average can be in the form of Mean, Mode or Median
• Mean = ( 1 + 7+ 8 + 8 +8 +9 +9 )/7 = 7.14
• Median = 8
• Mode = 8
Conclusion = 1 is an outlier, mean is not appropriate (not normal
distribution)

4. Uncertainty or standard deviation measures the spread/variability of
values from the mean
Uncertainty can the the form of
• standard deviation (SD)
• standard error (SE)
• confidence interval (CI)
• uncertainty error
High SD - High spread of data - High Uncertainty
Low SD - Small spread of data - High Certainty
Uncertainty expressed in SD, SE and CI if the data is normally distributed
Rate can be expressed = (Rate SD), (Rate SE), (Rate CI)

5. IA by two students on effect of Conc on Rate of reaction.
How concentration of hydrochloric acid affect the rate of reaction?
Data collected by student 1
Uncertainty in Rate expressed as SD, SE and CI is small.

6. Rate SD against Conc was plotted below
• Error bar/ SD do not overlap
• High certainty a line passes through error bar
• Small SD - More precise and highly certain a linear relationship bet Rate
and Conc
• Concentration increase - Rate increase
Significant different between rates at different concentration

7. Data collected by student 2
Uncertainty in Rate is High

8. Rate SD against Conc was plotted below
• Error bar as SD overlap
• High Uncertainty how the line pass through error bar
• High SD - Less certain on the relationship between Conc and Rate
• As Conc increase rate may be constant
Significant difference between Rate at lower conc
No significant difference between Rate at higher conc

9. Data from both student shown below
Uncertainty/Error bar/SD will determine
• Small SD - High Certainty - Error bar don't overlap –
Significant difference between rates at different Conc
• Small SD - Highly Certain about relationship between Rate and Conc
(Conc up - Rate up)
• High SD - High Uncertainty - Error bar overlap –
• No significant difference between rates at different Conc
• High SD - High Uncertainty about relationship bet Rate and Conc
(Conc up - Rate may be constant, increase or decrease)

10. Good video using Excel for graphing/ error bar plotting
Click here to view video from Youtube.
T test for significant difference between two means
Click here to view on slideshare.

11. Acknowledgements
Thanks to source of pictures and video used in this presentation
Thanks to Stephen Taylor for the video graphing using Excel
Thanks to Creative Commons for excellent contribution on licenses
http://creativecommons.org/licenses/
Prepared by Lawrence Kok
Check out more video tutorials from my site and hope you enjoy this tutorial
http://lawrencekok.blogspot.com