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
There’s 5 people. Their ages are 5, 6, 7, 8, and 55.
Their average/mean age is (5+6+7+8+55)/5 = 16.2.Their median age is the value if you list all the ages of each person in order and then pick the value in the middle. So, 5, 6, 7, 8, 55. Since there are 5 values, you pick the third one in the list, which is 7.
If you were to, at a glance, just look at the average, you’d think half the people are below 16 and half are older than 16. But that 55 year old really skews things. So you look at the median. To see that the REAL middle point is 7.
In a normal distribution the median and the average are more or less the same. But when there is a big difference between the two, you can see that there’s something strongly skewing the distribution. In terms of income, if the mean income is $122K, but the median income is only $35K, that indicates a small number of VERY high earners are skewing the distribution; so a lot of income inequality. Some could make the argument that those ultra high earners therefore make “too much”.
In our case, with the above ages, that 55 year old skewing the average so much signals to us that there’s something “off” about the 55 year being in that set.
If you have a bunch of numbers, the median is the point where half of the numbers are higher, and half are lower.
Average is what you get if you add all the numbers and divide by how numbers you added.
Example: you ask 7 people how many boxes of cereal they have in the cabinet at home and their answers are 0, 1, 1, 2, 3, 4, 5. The median is 2 because half the people had fewer and half had more. The average is (0 + 1 + 1 + 2 + 3 + 4 + 6) / 7 = 2.43.
There’s 5 people. Their ages are 5, 6, 7, 8, and 55.
Their average/mean age is (5+6+7+8+55)/5 = 16.2.Their median age is the value if you list all the ages of each person in order and then pick the value in the middle. So, 5, 6, 7, 8, 55. Since there are 5 values, you pick the third one in the list, which is 7.
If you were to, at a glance, just look at the average, you’d think half the people are below 16 and half are older than 16. But that 55 year old really skews things. So you look at the median. To see that the REAL middle point is 7.
In a normal distribution the median and the average are more or less the same. But when there is a big difference between the two, you can see that there’s something strongly skewing the distribution. In terms of income, if the mean income is $122K, but the median income is only $35K, that indicates a small number of VERY high earners are skewing the distribution; so a lot of income inequality. Some could make the argument that those ultra high earners therefore make “too much”.
In our case, with the above ages, that 55 year old skewing the average so much signals to us that there’s something “off” about the 55 year being in that set.
There are different types of averages. Usually when we say “average” we’re talking about the mean – specifically the arithmetic mean. This is the one where you add up all the numbers and divide by the number of numbers. Say someone had 5 kids, aged 3,4,4,4,10. Then 3+4+4+4+10=25. 25÷5=5, so the mean age is 5.
Another type of average is the median. For this, you line them all up in order (like we have above) and the median is just the middle one. Since there are 5 kids, the 3rd is the middle one. The 3rd is 4 years old, so the median age is 4.
The mean takes in all values, but this also means it can be skewed by outliers. Say the kid was 20 rather than 10. Suddenly the mean is 7, but the median stays the same.
There are some other versions too. The mode is the most common value, again 4 in this example. There’s also the geometric mean where you multiply the numbers together, then take the n-th root. So 3×4×4×4×10=1920. 5th root of 1920 is about 4.5. It’s a rarer one, but has some applications in physics.
Anyway, tldr, the *mean* average uses all the data. The median tells you about the middle.
There are different types of averages. Usually when we say “average” we’re talking about the mean – specifically the arithmetic mean. This is the one where you add up all the numbers and divide by the number of numbers. Say someone had 5 kids, aged 3,4,4,4,10. Then 3+4+4+4+10=25. 25÷5=5, so the mean age is 5.
Another type of average is the median. For this, you line them all up in order (like we have above) and the median is just the middle one. Since there are 5 kids, the 3rd is the middle one. The 3rd is 4 years old, so the median age is 4.
The mean takes in all values, but this also means it can be skewed by outliers. Say the kid was 20 rather than 10. Suddenly the mean is 7, but the median stays the same.
There are some other versions too. The mode is the most common value, again 4 in this example. There’s also the geometric mean where you multiply the numbers together, then take the n-th root. So 3×4×4×4×10=1920. 5th root of 1920 is about 4.5. It’s a rarer one, but has some applications in physics.
Anyway, tldr, the *mean* average uses all the data. The median tells you about the middle.
There are different types of averages. Usually when we say “average” we’re talking about the mean – specifically the arithmetic mean. This is the one where you add up all the numbers and divide by the number of numbers. Say someone had 5 kids, aged 3,4,4,4,10. Then 3+4+4+4+10=25. 25÷5=5, so the mean age is 5.
Another type of average is the median. For this, you line them all up in order (like we have above) and the median is just the middle one. Since there are 5 kids, the 3rd is the middle one. The 3rd is 4 years old, so the median age is 4.
The mean takes in all values, but this also means it can be skewed by outliers. Say the kid was 20 rather than 10. Suddenly the mean is 7, but the median stays the same.
There are some other versions too. The mode is the most common value, again 4 in this example. There’s also the geometric mean where you multiply the numbers together, then take the n-th root. So 3×4×4×4×10=1920. 5th root of 1920 is about 4.5. It’s a rarer one, but has some applications in physics.
Anyway, tldr, the *mean* average uses all the data. The median tells you about the middle.
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.
There’s 5 people. Their ages are 5, 6, 7, 8, and 55.
Their average/mean age is (5+6+7+8+55)/5 = 16.2.Their median age is the value if you list all the ages of each person in order and then pick the value in the middle. So, 5, 6, 7, 8, 55. Since there are 5 values, you pick the third one in the list, which is 7.
If you were to, at a glance, just look at the average, you’d think half the people are below 16 and half are older than 16. But that 55 year old really skews things. So you look at the median. To see that the REAL middle point is 7.
In a normal distribution the median and the average are more or less the same. But when there is a big difference between the two, you can see that there’s something strongly skewing the distribution. In terms of income, if the mean income is $122K, but the median income is only $35K, that indicates a small number of VERY high earners are skewing the distribution; so a lot of income inequality. Some could make the argument that those ultra high earners therefore make “too much”.
In our case, with the above ages, that 55 year old skewing the average so much signals to us that there’s something “off” about the 55 year being in that set.
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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