Question

Problem 4 on page 63: a) Explain the difference between the mean, median, and mode. b) In what situations might one be more useful than the others?

Answer 1

esesitive alatistical nmethodl or onein heseamive latitical methodo are a ause ofte) the approach thot con be the nesult d) mean,median and mode thase is par of measuses ofcentsal Tendency" aepination mean :-Το αγγ ive at the mean of a of Pilot studies. nuumbe, you add the numbersu and then davide the eum by the numbeos you de se dealing toith examplosuppose, sct of numbesis 3,7,2,8 10,12, 8 irst adding all numbess means sum o alt nuumbensd divide totad number of 子 5 o mean+-14286 The Tesult157-14280. . That is you γ meaf) Formula foa mean mean ion n= Toto! number of observat

median The middie value if n fe odd, The average f tho two mddlle valucs if n is even (5oth pencentiie) But FirstHy all valuos sek the ascending osders Example 0suppose set of numbens is 3.7,2,8,1o,12,8 Fisstly ascending ordes, 2,3,72,3, 10 , 12 median is 8 because n is odd na numbe ②suppose set of number is,even of obsesVation 3,7,2,4, ,9 Firstly ascending osdos 2,34,6 7, mediaun is equal to average of middlo medion 6

mode i-The mode is the tuirl ber in aset thot appeoss most frequenty. if you ase dealing with those numberss 3,1,2,9 1o,12,8 mode is equal to 3, becau se appeass twice mose thar any other suppose you have a eet of numbers inwich evesy numberr appears ust once c Then simple you then have a set of numbes that doesn't have a mode Therefote mean and median all set awr find but modo is not get some coses ikes, set of mumber n which overy numbes ppeas just once?

t) the mean,medion and mode ape oli Valid measures of cent-sad tandency but under diffesent condi Lions, some measuses of censal tendency be come mose app sopsiale to use thon others, ymeani. The mean 16 the most popular and well known meesu re of cent sal tendency ェt can be used with both discrete and continuous dat a the mean has one main disodyvantage tis parsticutoaly Susceptible to the influence of outliens these are yaluag that are unueual compar ed to the vest oF the dota set by beng especially small large in numerical value SuPpo se dtliers is avail able in data themerose in thi's situation, we woutd Vike to have a better measure ‘fcontTal tendency. As wewill Find out later, takirg the meadicn would be a better meosure of centsa tendency in this stuation.

mm e dian-the median is less affe cted by, outliexs and Skewed data. ri) modeThe modo io the most Frea uond scove in ows dataset,on a histogooum it repTesents the highest bar n a bar chos os histogram consider the mode a being the most populars option example, auppose data 2,4, 4,2, 14 That is mode=2 no、mally, the mode is used roo Categorical data whe se e wist to know which is the most commarcalegoy -00 orICo

tohen to use the mean medio and mode #05e the following summary balle to know what, the best measu γ e of contTa tendency ith pect to the diffeven type of Variable TyPeof Vasiable Bet measure of centod tendency mode median ordina Enterval Ratio (no Skewed mean) nlesval/Rotio (skewed median