*Central value of a normal distribution curve for a set of data 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)*

*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)*

*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 spead of data - High Certainty**Uncertainty can be expressed in SD, SE and CI if the data is normally distributed**Rate can be expressed = (Rate ±SD), (Rate ±SE), (Rate ±CI)*

*.........................................................................................................................................................*

*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.*

*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**Conc increase - Rate increase**Significant different between rates at different concentration*

*Data collected by student 2*

*Uncertainty in Rate is High*

*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**No significant diff bet rate at higher conc**Significant diff bet rate at lower conc*

*Data from both student shown below*

*Uncertainty/Error bar/SD will determine**Small SD - High Certainty - Error bar don't overlap - Significant diff bet rates at diff Conc**Small SD - Highly Certain about relationship bet Rate and Conc (Conc up - Rate up)**High SD - High Uncertainty - Error bar overlap - No significant diff bet rates at diff Conc**High SD - High Uncertainty about relationship bet Rate and Conc (Conc up - Rate constant)*

*...........................................................................................................................................................*

*Notes on using statistical t test - Testing of significant difference between two means*

**IB Biology statistical analysis, t test, significant difference, hypothesis testing and standard deviation**

*.............................................................................................................................*

*Good video using Excel for graphing/ error bar plotting*

*All notes for the above post is summarised in powerpoint below.*

*Thanks to all picture and video contributors use for the above post*
The book was written for people who have little to no experience with R, statistical software, and programming. fengshui

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