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# Effets sur la médiane et la moyenne : supprimer une valeur extrême

## Transcription de la vidéo

and I played five rounds of golf and her lowest score was an 80 the firt the scores of the first four rounds and the lowest round are shown in the following dot plot and we see it right over here the lowest round she scores an 8000 scores a 90 once a 92 once and 94 once and a 96 once it was discovered that Ana broke some rules when she scored 80 so that scores cheating didn't help her so that score will be removed from the data set so they removed that 80 right over there were just left from the with the scores from the other four rounds how will the removal of the lowest round affect the mean and the median so let's actually think about the median first so the median is the middle number so over here when you had five data points the middle data point is going to be the one that has two to the left and two to the right so the median up here is going to be ninety two the median up he there is ninety two and what's the median once you remove this now you only have four data points when you're trying to find the median of an even number of numbers you look at the middle two numbers so that's a 92 and a 94 and then you take the average of them you go halfway between them to figure out the median so the median here is going to be let me do that a little bit clearer the median over here is going to be halfway between 92 and 94 which is 93 so the median the median is 93 median is 93 so removing the lowest data point in this case increase the median so the median let me write down here so the median increased by a little bit the median increases now what's going to happen to the mean what's going to happen to the mean well one way to think about it without even doing any calculations is if you remove a number that is lower than the mean lower than the existing mean and I haven't calculated what the existing mean is but if you remove that the mean is going to go up the mean is going to go up so hopefully that gives you some intuition if you removed a number that's larger than the mean your mean is your mean is going to go down because you don't have that large number anymore if you have remove a number that's lower than the mean well you take that out you don't have that that small number bringing the average down and so the mean will go up but let's verify it mathematically so let's calculate the mean over here so we're going to add 80 plus 90 plus 90 to plus 90 4 plus 96 those are our data points and that gets us 2 + 4 6 plus 6 is 12 and then we have 1 plus 8 is 9 and we essentially this is so these are 9 and you have another 9 another night another night another 9 you essentially have is this five nines right over here so this is going to be 450 450 - so that's the sum of the scores of these five rounds and then you divide it by the number of rounds you have so it'd be 450 2 divided by 5 so 450 2 divided by 5 is going to give us five goes into doesn't go into 4 it goes into 45 9 times 9 times 5 is 45 you subtract you get 0 bring down the 2 5 goes into 2 0 times 0 times 5 is 0 2 times 5 is 0 subtract you have 2 left over so you can say that the mean here the mean here is 90 and two-fifths maybe not 9 into fifths 90 and two-fifths so the mean is right around here so that's the mean of these data points right over there and if you remove it what is the mean going to be so here we're just going to take our 90 plus our 92 plus our 94 plus our 96 add them together so let's see 2 plus 4 plus 6 is 12 and then you add these together going to get 37 372 divided by 4 because I have four data points now not five four goes into three let me do this in a place where you can see it so 4 goes into 372 goes into thirty seven nine times 9 times 4 is 36 subtract you know one bring down the two goes exactly three times three times four is 12 you have no remainder so the median and the mean here are both so this is also the mean the mean here is also 93 so you see that the median the median went from 92 to 93 it increased the mean went from 90 and two-fifths to 93 so the mean increased by more than the median they both increased but the mean increased by more and it makes sense because you this number was way way below all of these over here so you can imagine if you take this out the median should increase by a good amount but let's see which of these choices are what we just described but the mean and the median will decrease nope both the mean and the median will decrease nope both the mean and the median will increase but the mean will increase by more than the median that's exactly that's exactly what happened the mean went from 90 and 2/5 or 90.4 went from ninety point four or 90 and two-fifths to 93 and then the median only increased by one so this is the right answer