How to get the typical value or typical data from the dataset

[Pengtaofu]

TL;DR Summary

get the typical data from database

I make a theoretical calculation and then compare the calculation result and the median of the corresonding measured dateset. The difference between them is very slight, so I state that the theoretical model is right and good. However one expert has suspended whether the median is typical value. Could anyone help to explain how to get the typical value in the experiment dataset.
Measures of central tendancy, e.g. median, mean and mode, have been introduced in a lot of statistical books, however these books seldom include the defination of the typical value or introduce the method to get the typical value in dataset. It could be found that median, mean and mode of the dataset is the typical value in some web(http://www.physics.csbsju.edu/stats/descriptive2.html). I don't know whether the typical value is one common expression or scietifical term. Could anyone help how to get the typical value or choose the typical data from the known dateset. Thank you very much.

 

[phyzguy]

I don't think there is an agreed upon definition of the "typical value". In your dataset, how different are the mean, mode, and median? Another thing you could look at is the χ^2 value. This will depend on the difference between the theoretical model and the measured value, but also on the error in the measured value. How does the difference between the theoretical and measured values compare to the statistical error in the measured value?

 

[Stephen Tashi]

I don't know whether the typical value is one common expression or scietifical term.

"Typical value" is not a scientific term (in English).

Could anyone help how to get the typical value or choose the typical data from the known dateset. Thank you very much.

Applying statistics is a subjective matter, often influenced by traditions. Look at published articles in your field of study and see what methods have been accepted by the editors of journals.

It is possible to formulate the problem of choosing the "most typical" value as a specific mathematical problem. This can be done in various ways. The procedure requires a sophisticated understanding of mathematical statistics. It also requires many specific assumptions. Which assumptions should be made? - that is also a subjective decision.

 

[zinq]

"Measures of central tendency, e.g. median, mean and mode"

No, that is not what a "measure of central tendency" means. Central tendency is detected by e.g. the standard deviation σ: the larger σ is, the less central tendency the distribution has.

"one expert has suspended whether the median is typical value."

Huh? This is not the normal use of the word "suspended". It's not clear what this means.

Mean, and median are both measures of "middle" of a distribution. But there are a number of possible means that could be used. Usually it's the arithmetic mean. If all data is positive, it is sometimes more useful to use the geometric mean (the nth root of the product of the n data values).

The mode is the data value that is the most common. Or in the case of a distribution, it's the value with the largest probability. (Or for a continuous distribution, the value with the largest probability density.) But depending on the distribution, it need not be at all "typical".

 

[Pengtaofu]

"Measures of central tendency, e.g. median, mean and mode"

No, that is not what a "measure of central tendency" means. Central tendency is detected by e.g. the standard deviation σ: the larger σ is, the less central tendency the distribution has.

"one expert has suspended whether the median is typical value."

Huh? This is not the normal use of the word "suspended". It's not clear what this means.

Mean, and median are both measures of "middle" of a distribution. But there are a number of possible means that could be used. Usually it's the arithmetic mean. If all data is positive, it is sometimes more useful to use the geometric mean (the nth root of the product of the n data values).

The mode is the data value that is the most common. Or in the case of a distribution, it's the value with the largest probability. (Or for a continuous distribution, the value with the largest probability density.) But depending on the distribution, it need not be at all "typical".

Thank you for explanation and remind of the word "suspended". I acknownledge that use of "suspended" is not right. It should be replaced by ask, i.e. "one expert has asked whether the median is typical value."

 

[Pengtaofu]

"Typical value" is not a scientific term (in English).Applying statistics is a subjective matter, often influenced by traditions. Look at published articles in your field of study and see what methods have been accepted by the editors of journals.

It is possible to formulate the problem of choosing the "most typical" value as a specific mathematical problem. This can be done in various ways. The procedure requires a sophisticated understanding of mathematical statistics. It also requires many specific assumptions. Which assumptions should be made? - that is also a subjective decision.

Thank you for explanation. When I studied the statistics course at uinivesity many years ago, I thought statistics is one subject of scietific. However, I have recently realized the there are a lot of subjective factors to affect the results in statistics.

 

[Pengtaofu]

I don't think there is an agreed upon definition of the "typical value".

Thank you very much for your explanation. Do you known whether the "typical data" isn't also agreed upon definition in statistics.

In your dataset, how different are the mean, mode, and median? Another thing you could look at is the χ^2 value. This will depend on the difference between the theoretical model and the measured value, but also on the error in the measured value. How does the difference between the theoretical and measured values compare to the statistical error in the measured value?

I have checked that the mean and median approximate in the dataset. But it is found that the some theoretical results has been out of the range [median - std, median + std]. I think the mesured values have been affected by other factors and I need to make more explanation in physics mechanism.