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lee.lenton
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Can the arithmetic mean of a data set of complex numbers be calculated?
if so, can the method be demonstrated?
if so, can the method be demonstrated?
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Exactly - that's why I wanted to see you write down the definitions, which you haven't done yet.robphy said:The median would require an ordering... but not the mean.
lee.lenton said:(snip)
the arithmetic mean would be calculated by summing the complex numbers in the data set and dividing by the sample number
(snip)
There is no min z or max z. However, the calculation of the mean does not require either. Your description of the calculation (summing and dividing by the number of entires) gives the mean.lee.lenton said:The definition is exactly as for positive real numbers i.e. the arithmetic mean lies within the minimum and maximum range of the data set and calculated as per real positive numbers .
Therefore for complex numbers this would be: min z to max z of the data set and the arithmetic mean would be calculated by summing the complex numbers in the data set and dividing by the sample number and the resultant mean value should lie within the data set's minimum and maximum values.
What I am not grasping is this: can this method be performed on a data set of complex numbers?
That's how you do the calculation all right ... but you need to write that down in math terms......for complex numbers this would be: min z to max z of the data set and the arithmetic mean would be calculated by summing the complex numbers in the data set and dividing by the sample number and the resultant mean value should lie within the data set's minimum and maximum values.
You are having trouble grasping it because you steadfastly refuse to follow the suggestions. You have to actually do the math. It is OK to start the math without knowing where you will end up - just do it.What I am not grasping is this: can this method be performed on a data set of complex numbers?
Nonsense. This is a straw man argument.lee.lenton said:I totally agree with the definition of arithmetic mean for positive real numbers, however it would not be a mean of the data set if it fell outside the minimum and maximum range of the data.
However the requirement that the arithmetic mean fall within the minimum and maximum range of the data set is what reveals the flaw with applying the concept of arithmetic mean to complex numbers.
This is utter nonsense, and with this, this thread is closed.lee.lenton said:In summary: it would appear that a mathematically valid arithmetic mean as defined for the positive real numbers, can be calculated for the complex numbers if the sample is collinear/directionally in phase, but not if the data are widely dispersed in an angular sense, not collinear/not phase.
The arithmetic mean of a set of complex numbers is the sum of all the numbers in the set, divided by the total number of numbers in the set. It is a measure of central tendency and is often used to find the average value of a set of complex numbers.
To calculate the arithmetic mean of a set of complex numbers, add all the numbers together and then divide the sum by the total number of numbers in the set. For example, if the set of complex numbers is {2 + 3i, 4 + 5i, 6 + 7i}, the arithmetic mean would be (2 + 3i + 4 + 5i + 6 + 7i) / 3 = 4 + 5i.
The arithmetic mean of complex numbers is used to find the average value of a set of numbers. It is often used in statistics and data analysis to represent the central tendency of a data set. It can also be used to compare different sets of complex numbers and determine which set has a higher or lower average value.
Yes, you can find the average of real and imaginary parts separately by calculating the arithmetic mean of the real parts and the arithmetic mean of the imaginary parts and then combining them. For example, if the set of complex numbers is {2 + 3i, 4 + 5i, 6 + 7i}, the arithmetic mean of the real parts would be (2 + 4 + 6) / 3 = 4 and the arithmetic mean of the imaginary parts would be (3 + 5 + 7) / 3 = 5. The average of the complex numbers would then be 4 + 5i.
One limitation of using the arithmetic mean for complex numbers is that it only takes into account the magnitude of the numbers and not their direction or angle. This means that two sets of complex numbers with the same arithmetic mean may have very different arrangements of points on a complex plane. Additionally, the arithmetic mean may not accurately represent the central tendency of a data set if there are extreme outliers or if the data is not normally distributed.