Saw this mention in a previous post, and it got me thinking, what are the differences?
Maybe I already know, but u der different names, English is 2nd language.
In: 1
Mean is just the average of the numbers. Median is the number that’s in the middle of the group of numbers, i.e. 50% of the numbers are greater than the median and 50% of the numbers are less than the median
Mean – All values in a range added together then the result divided by the number of values. This returns an absolute average, but does not deal with information that contains extreme outliers (e.g the mean of the numbers 1-10 is (1+2+3+4+5+6+7+8+9+10)/10=5.5)
Median – All values are lined up in sequence, the middle value in the sequence is selected. This deals with extreme outliers better, as they are ignored, but may be less effective for representing some types of data (e.g the median of the numbers 1-10 is 1 2 3 4 5 [Here] 6 7 8 9 10 = 5.5 (halfway between 5 and 6))
To compare why we might use one or the other, here’s a different dataset:
1 2 3 4 5 6 7 8 9 10000
The mean of this is 1004.5
The median is 5.5
If these numbers were peoples incomes, which do you think is more reflective of the ‘average’? 5.5 – a number which is right amongst 9/10 of the values, or 1004.5 – a number that is 100x further away from the 9th value than the 9th is from the 8th?
Let’s say I have a set of numbers 1,8,2,9,1,8,8
The average (mean) is (1+8+2+9+1+8+8)/7 = about 5.29
The median is found by arranging the numbers in order and picking the middle one. So 1,1,2,8,8,8,9 and the middle number (median) is 8
If you had an even number of numbers in the set, I believe the median is the average of the two middle-est numbers
So for 1,1,1,1,5,5,6,6 I believethe median is (1+5)/2 = 3
Take 5 numbers, like 1, 1, 3, 5, 15
If you take the mean/average, you add them up (which ist 25) and divide them by the number of numbers (which is 5) the mean is therefore 5.
If you take the median, you sort them lowest to highest and take the one in the middle, in this case 3.
Why do you need two different methods? They are good for different things. Take for example the following scenario:
Elon Musk has 225 billion dollars and moves into a city that 225 thousand people living there, all of them entirely penniless with literally not single dollar to their name. The median person is one of those penniless people and the median networth is $0. The average person has a networth of (225,000,000,000 / 255,000,000 = 1,000,000) a million dollars and is a millionaire!
Both methods tell very different stories.
Mean is what we normaly call average – add all the numbers together and divide by however many numbers there are.
Median is the actual number in the middle if you put them all in order – so half are higher and half lower.
Numbers: 1 9 3 9 1 9 1 9
Average: (1+1+1+3+9+9+9)/7 = 4.71
Median: The middlest number when ordering the sequence from lowest to highest.
Sorted: 1 1 1 3 9 9 9
so the median is 3
Suppose you have 99 people who have $1, $2, $3, $4, $5, …, $99.
– Median net worth: $50
– Mean net worth: $50
If you add Jeff Bezos to the room:
– Median net worth: Still $50
– Mean net worth: $1,000,000,000
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