CHAPTER XVIII.

ON THE NATURE AND USE OF AN AVERAGE, AND ON THE DIFFERENT KINDS OF AVERAGE.

§ 1. _Preliminary rude notion of an average,_ 2. _More precise quantitative notion, yielding_ (1) _the Arithmetical Average,_ 3. (2) _the Geometrical._ 4. _In asymmetrical curves of error the arithmetic average must be distinguished from,_ 5. (3) _the Maximum Ordinate average,_ 6. (4) _and the Median._ 7. _Diagram in illustration._ 8-10. _Average departure from the average, considered under the above heads, and under that of_ 11. (5) _The (average of) Mean Square of Error,_ 12-14. _The objects of taking averages._ 15. _Mr Galton's practical method of determining the average._ 16, 17. _No distinction between the average and the mean._ 18-20. _Distinction between what is necessary and what is experimental here._ 21, 22. _Theoretical defects in the determination of the 'errors'._ 23. _Practical escape from these._

(_Note about the units in the exponential equation and integral._)