Question

Design your own measure of central tendency that is:
a) unaffected by extreme scores
b)Inappropriate for use on nominal or ordinal data
demonstrate that your measure meets these requirements and contrast it with the commonly used measures of central tendency

Answer 1

mean is effected by extremes

ex: 2.1,3.1,2.8,2.7,1.9,2.5.2.6 be some observations

mean=some of observations/total no. of observations=2.53(rounded to 2 decimals)

suppose that if 2.7 is replaced by an extreme value 35 then mean =7.14

hence mean is very much affected by extreme values

median is not affected by extreme values

ascending order of values:1.9,2.1,2.5,2.6,2.7,2.8,3.1

here median =2.6

let 2.7 be replaced by 35

ascending order of values:1.9,2.1,2.5,2.6,2.8,3.1,35

here median is 2.6

but the median is appropriate for nominal and ordinal data

weighted arithmetic

if the extreme values are given very less weight then the weighted average will not be affected by extreme values

ex 2.1,3.1,2.8,2.7,1.9,2.5.2.6 with weights 10,20,15,30,25,17,22 respectively

let 2.7 be replaced by 35 and its weight be 1

weighted mean is inappropriate for use on nominal and ordinal data

we can also go ahead with Interquartile mean

Interquartile mean :a truncated mean based on data within the interquartile range