I was looking up the average networth of 30 year olds in the United States and it said: “The average net worth is $122,000 and the median net worth is $35,112” my brain is too smooth please help.
In: 8
Median – If you lined up every person in order of their net worth, take the guy in the very middle and use his net worth. No math involved really. You just pick the guy in the middle and that’s it.
Average (mean) – If you added up everyone’s net worth together and divided it out equally so everyone had the same amount, how much would each person have? There’s math involved with this one. Adding it up and dividing.
So what does it mean when the median is far lower than the average? Well, it means that there are a few people with loads of cash, and most people are very poor in comparison to the rich. The median will ignore the billions of dollars that the richest have as part of their net worth because they aren’t the middle guy. But the average will redistribute their wealth among everyone and that money will show up in the average! That’s why it’s so much higher.
Average is, well, the average. You take all values, add them up, and divide them by how many you have. Average TENDS TO BE more dependent on the values themselves rather than the number of values.
Median is the middle. 50% of people make less, 50% of people make more. The median TENDS TO BE more dependent on the number of values rather than the values themselves.
Let’s do an example. Say a class of 11 students had a test and the scores were
2, 3, 10, 13, 16, 22, 23, 33, 40, 66, and 100
The median is 22 because that’s the middle value. Half the students did better, half the students did worse.
The average, however, is actually (rounded) 29.
Now let’s take 2 scenarios.
The first is that there are actually 13 kids in the class, not 11. 2 kids were just sick and had to take the test later. They both scored 29. The average remains unchanged, but the median now becomes 23. Since we added 2 new data points, the median went up by 1 student but also because the scores were equal to the average, the average remains unchanged.
Scenario 2 is back to 11 students, but this time the teacher realized they forgot to grade the extra credit question that adds 20 points to the test. The only person who got the extra credit was the student prodigy who got the perfect score, replacing the 100 with a 120. The median remains unchanged as no new scores were added but the average increases to 32.
What you discovered is the “Wage Gap”. Half of Americans make less-than 32K, but people above the median tend to make significantly more than 32K, enough to make the average 4x the median. The problem becomes more apparent when you realize that there’s still a signifigant number of people above the median that still make around the median. People who tend to make a lot of money REALLY make a LOT of money.
Average is, well, the average. You take all values, add them up, and divide them by how many you have. Average TENDS TO BE more dependent on the values themselves rather than the number of values.
Median is the middle. 50% of people make less, 50% of people make more. The median TENDS TO BE more dependent on the number of values rather than the values themselves.
Let’s do an example. Say a class of 11 students had a test and the scores were
2, 3, 10, 13, 16, 22, 23, 33, 40, 66, and 100
The median is 22 because that’s the middle value. Half the students did better, half the students did worse.
The average, however, is actually (rounded) 29.
Now let’s take 2 scenarios.
The first is that there are actually 13 kids in the class, not 11. 2 kids were just sick and had to take the test later. They both scored 29. The average remains unchanged, but the median now becomes 23. Since we added 2 new data points, the median went up by 1 student but also because the scores were equal to the average, the average remains unchanged.
Scenario 2 is back to 11 students, but this time the teacher realized they forgot to grade the extra credit question that adds 20 points to the test. The only person who got the extra credit was the student prodigy who got the perfect score, replacing the 100 with a 120. The median remains unchanged as no new scores were added but the average increases to 32.
What you discovered is the “Wage Gap”. Half of Americans make less-than 32K, but people above the median tend to make significantly more than 32K, enough to make the average 4x the median. The problem becomes more apparent when you realize that there’s still a signifigant number of people above the median that still make around the median. People who tend to make a lot of money REALLY make a LOT of money.
Average is, well, the average. You take all values, add them up, and divide them by how many you have. Average TENDS TO BE more dependent on the values themselves rather than the number of values.
Median is the middle. 50% of people make less, 50% of people make more. The median TENDS TO BE more dependent on the number of values rather than the values themselves.
Let’s do an example. Say a class of 11 students had a test and the scores were
2, 3, 10, 13, 16, 22, 23, 33, 40, 66, and 100
The median is 22 because that’s the middle value. Half the students did better, half the students did worse.
The average, however, is actually (rounded) 29.
Now let’s take 2 scenarios.
The first is that there are actually 13 kids in the class, not 11. 2 kids were just sick and had to take the test later. They both scored 29. The average remains unchanged, but the median now becomes 23. Since we added 2 new data points, the median went up by 1 student but also because the scores were equal to the average, the average remains unchanged.
Scenario 2 is back to 11 students, but this time the teacher realized they forgot to grade the extra credit question that adds 20 points to the test. The only person who got the extra credit was the student prodigy who got the perfect score, replacing the 100 with a 120. The median remains unchanged as no new scores were added but the average increases to 32.
What you discovered is the “Wage Gap”. Half of Americans make less-than 32K, but people above the median tend to make significantly more than 32K, enough to make the average 4x the median. The problem becomes more apparent when you realize that there’s still a signifigant number of people above the median that still make around the median. People who tend to make a lot of money REALLY make a LOT of money.
Maybe a simple example will help. For {1,2,3}, ‘2’ is both the median and average. But the median will stay the same even if the ‘3’ is increased quite a lot. For example {1,2,1000} still has a median of 2, but the average is much higher.
As others have probably pointed out, for the median, half of the values are below and half are higher. This is not always true for the average.
It’s also possible to show that the median is the point ‘x’ which minimizes the total distances from x to values in the set. But the mean minimizes the sum of the squared distances.
The average can be influenced by a few large (or small) values. If you were applying for a sales job, it might be more interesting to know the median salaries of salesmen, since the average could be grossly inflated by even one super-salesman.
Maybe a simple example will help. For {1,2,3}, ‘2’ is both the median and average. But the median will stay the same even if the ‘3’ is increased quite a lot. For example {1,2,1000} still has a median of 2, but the average is much higher.
As others have probably pointed out, for the median, half of the values are below and half are higher. This is not always true for the average.
It’s also possible to show that the median is the point ‘x’ which minimizes the total distances from x to values in the set. But the mean minimizes the sum of the squared distances.
The average can be influenced by a few large (or small) values. If you were applying for a sales job, it might be more interesting to know the median salaries of salesmen, since the average could be grossly inflated by even one super-salesman.
Maybe a simple example will help. For {1,2,3}, ‘2’ is both the median and average. But the median will stay the same even if the ‘3’ is increased quite a lot. For example {1,2,1000} still has a median of 2, but the average is much higher.
As others have probably pointed out, for the median, half of the values are below and half are higher. This is not always true for the average.
It’s also possible to show that the median is the point ‘x’ which minimizes the total distances from x to values in the set. But the mean minimizes the sum of the squared distances.
The average can be influenced by a few large (or small) values. If you were applying for a sales job, it might be more interesting to know the median salaries of salesmen, since the average could be grossly inflated by even one super-salesman.
When there’s a big gap between Median and Average, it means there are extremes pulling up the average.
Lets pretend the numbers reflect the net worth of 9 30 year-olds in a room.
The median is $35K meaning that person number 5 (the middle or median) has that much net worth. Half the people in the room have more than him, half have more. He is in the exact middle.
But lets say one of the 9 people had a huge net worth, we’re talking like $M. The average net worth in the room could theoretically be over $100k. (the math to keep things simple: everyone else has $35K except the last person has $1M. The total net worth in the room is $1.28M. Divide that by 9 and you get an average net worth of $142K)
TLDR: Averages can be misleading due to outliers. Sometimes median tells a better story of what the “average person” in a group is actually getting.
When there’s a big gap between Median and Average, it means there are extremes pulling up the average.
Lets pretend the numbers reflect the net worth of 9 30 year-olds in a room.
The median is $35K meaning that person number 5 (the middle or median) has that much net worth. Half the people in the room have more than him, half have more. He is in the exact middle.
But lets say one of the 9 people had a huge net worth, we’re talking like $M. The average net worth in the room could theoretically be over $100k. (the math to keep things simple: everyone else has $35K except the last person has $1M. The total net worth in the room is $1.28M. Divide that by 9 and you get an average net worth of $142K)
TLDR: Averages can be misleading due to outliers. Sometimes median tells a better story of what the “average person” in a group is actually getting.
When there’s a big gap between Median and Average, it means there are extremes pulling up the average.
Lets pretend the numbers reflect the net worth of 9 30 year-olds in a room.
The median is $35K meaning that person number 5 (the middle or median) has that much net worth. Half the people in the room have more than him, half have more. He is in the exact middle.
But lets say one of the 9 people had a huge net worth, we’re talking like $M. The average net worth in the room could theoretically be over $100k. (the math to keep things simple: everyone else has $35K except the last person has $1M. The total net worth in the room is $1.28M. Divide that by 9 and you get an average net worth of $142K)
TLDR: Averages can be misleading due to outliers. Sometimes median tells a better story of what the “average person” in a group is actually getting.
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