Defining SD from a set of errors

Ultimately, this will give you a comparable error for the entire set of data. In summary, it is possible to calculate a standard deviation for a data set consisting of independent samples. This can be done using the formula σ = √((1/n)∑(Xi-Ti)^2), where n is the number of samples and Xi and Ti are the observed and true values respectively. Visualizing the data using a histogram can also provide further insight and a comparable error for the entire set of data.
  • #1
mikeph
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Hi, I never took stats so maybe this doesn't make sense or is really simple, either way any help is appreciated.

I have a series of data, say Xi (i=1,...1000) and a series of true values of that data, say Ti. Each true value is different and independent. Is it possible to get some kind of standard deviation for the whole data set? For example if I plot (Ti-Xi), can I use a histogram to find some value which means something along the lines of standard deviation, even though the samples are all independent? I want to get a comparable error for the entire set of data.
 
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  • #2
Yes, it is possible to get a standard deviation for the whole data set. You can calculate the standard deviation using the formula σ = √((1/n)∑(Xi-Ti)2), where n is the number of samples and Xi and Ti are the observed and true values respectively. Additionally, you can plot a histogram to visualize the spread of the values and gain further insight into the data.
 

1. What is Standard Deviation (SD)?

Standard Deviation is a statistical measure of how much the data values deviate or vary from the mean. It provides information about the spread or dispersion of the data set.

2. How is SD calculated?

SD is calculated by finding the square root of the sum of squared differences between each data point and the mean, divided by the total number of data points in the set.

3. Why is SD important in defining a set of errors?

SD helps in quantifying the amount of variation or errors present in a data set. It gives a better understanding of the data and helps in identifying any outliers or extreme values that may affect the accuracy of the results.

4. How does SD differ from Mean Absolute Deviation (MAD)?

SD takes into account the magnitude of each data point, as it involves squaring and taking the square root of the differences. On the other hand, MAD only considers the absolute differences between each data point and the mean, making it less sensitive to extreme values.

5. Can SD be used to compare data sets with different units?

No, SD is not suitable for comparing data sets with different units as it is affected by the scale of the data. It is better to use Coefficient of Variation (CV), which is calculated by dividing SD by the mean, to compare data sets with different units.

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