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# Impact on median & mean: increasing an outlier

AP.STATS:
UNC‑1 (EU)
,
UNC‑1.K (LO)
,
UNC‑1.K.2 (EK)
CCSS.Math:

## Video transcript

let's think about what happens to the median and mean of a set of numbers when I change one of the numbers and so let's look at this example a group of four friends likes to Bowl together and each friend keeps track of his all-time highest score in a single game their high scores are all between 180 and 220 except for Adam whose high score is 250 Adam then bowls a great game and has a new high score of 290 I will increasing Adams high score affect the mean and median now like always pause this video and see if you can figure this out yourself alright so let's just think about what they're saying we have four friends and they're each going to have they each keep track of their all-time high score so we're going to four data points an all-time high score for each of the friends so let's see this is the lowest score of the friends is the second lowest second highest and this is the highest scoring of the friends so let's see their high scores are all between 100 and 220 except for Adam whose high score is 250 so before Adam bowls this the super awesome game the score is looks something like this the lowest score is 180 Adam scores 250 250 and if you take Adam out of the picture the high scores of 220 and we actually don't know what this score right over there is now after Adam bowls a great new game it has a new high score of 290 what does the data set look like well this guy's high score hasn't changed this guy's high score hasn't changed this guy's high score hasn't changed but now Adams has a new high score instead of 250 it is now it is now 290 so my question is well the first question is does this change the median well remember the median is the middle number and if we're if we're looking at four numbers here the median is going to be the average of the middle two numbers so we're going to take the average or whatever this whatever this question mark is in 220 that's going to be that's going to be the median now over here after ad has scored a new high score how would we calculate the median well we still have four numbers in the middle two are still the same two middle numbers whatever this whatever this friend's highest score was it hasn't changed and so we're going to have the same median it's going to be 220 plus question mark divided by 2 it's going to be halfway between question mark and 220 so our median won't change so median median no change median no change so let's think about the mean now well the mean you average all you take the sum of all these numbers and then you divide by four and then you take the sum of all these numbers and divide by four so which sum is going to be higher well these first three numbers are the same but in the second list you have a higher number 290 290 250 so if you take this these four and divide by four you're going to have a larger value than if you take these four and divide by four because their sum is going to be larger and so the mean is going to go up the mean will increase the mean will increase so median no change and mean increase all right so this says both increase no that's not right the median will increase no median doesn't change the mean will increase yep and the median will stay the same yep that's exactly that's exactly what we're talking about and if you want to make it a little bit more tangible and you can replace question mark with some number you could replace it maybe this question mark is 200 and if you if you try it out with 200 just to make things tangible you're going to see that that is indeed going to be the case the median would be halfway between these two numbers and I just arbitrarily pick 200 it could be any number someplace someplace between 180 and 220 but you see for this example it's very tangibly that the median does not change but the mean increases because we increase the sum we increase the sum by 40 because we've increased this last number and only the last number by 40