RELS 309 Lecture Notes - Lecture 7: Cristiano Ronaldo, Royal Institute Of Technology, Novak Djokovic

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Chapter 3: measures of central tendency and location. The capital greek letter (sigma) is used to denote the sum of numerical values. Some properties of the summation notation: (cid:3041) (cid:3036)=(cid:2869) = (cid:1876)(cid:2869)+ (cid:1876)(cid:2870)+ + (cid:1876)(cid:3041) (cid:1876)(cid:3036) (cid:3041) (cid:3041) (cid:3041) (cid:3036)=(cid:2869) + (cid:1878)(cid:3036) (cid:3036)=(cid:2869) + (cid:1877)(cid:3036) (cid:1877)(cid:3036)+(cid:1878)(cid:3036)(cid:4667)= (cid:1876)(cid:3036) (cid:3036)=(cid:2869) (cid:3041) (cid:3041) (cid:3041) (cid:3036)=(cid:2869) (cid:1878)(cid:3036) (cid:3036)=(cid:2869) (cid:1877)(cid:3036) (cid:1877)(cid:3036) (cid:1878)(cid:3036)(cid:4667)= (cid:1876)(cid:3036) (cid:3036)=(cid:2869) (cid:3041) (cid:3041) In general, anything that does not involve the index may be taken out of the summation. (cid:3041) + (cid:1877)(cid:3036)(cid:2870) (cid:1877)(cid:3036)(cid:4667)(cid:2870) (cid:1876)(cid:3036)(cid:2870) (cid:3036)=(cid:2869) (cid:3036)=(cid:2869) (cid:3041) (cid:3041) (cid:3036)=(cid:2869) ) (cid:3036)=(cid:2869) )( (cid:1877)(cid:3036) (cid:1877)(cid:3036) ( (cid:1876)(cid:3036) Show that the above inequalities really hold using this set of observations. The arithmetic mean (usually only referred to as the mean) is the most common type of average. It is simply computed by taking the sum of the observations and dividing that sum by the number of observations. If we are dealing with data from the population,

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