# Weighted average with uneven errors

• freeman2
In summary, the conversation discusses the difficulty of averaging two values with asymmetric errors. The speaker suggests using a regular weighted average for values with symmetric errors, but is unsure of how to handle values with asymmetric errors. They also mention the possibility of normalizing the data, but are unsure of the validity of this approach. The expert concludes that without more information, it is difficult to recommend a safe way to combine the two estimates due to the asymmetry and different skewness of the samples.

#### freeman2

Cant seem to find information on this anywhere...

If I want to average two values with errors, say

x1 = 10 +/- 2
x2 = 12 +/- 4

I would do a regular weighted average that would reflect the fact that x1 is a more precise measurement.

But what if my errors are asymmetric? So if I had

x1 = 10 +2/-1
x2 = 12 +3/-4

How would I take the average of those values? My first thought was to somehow "normalize" x1 and x2 such that they have symmetric errors, but I am not sure whether that is valid or how I would do that. Anyone have any ideas? thanks...

freeman2 said:
Cant seem to find information on this anywhere...

If I want to average two values with errors, say

x1 = 10 +/- 2
x2 = 12 +/- 4

I would do a regular weighted average that would reflect the fact that x1 is a more precise measurement.

But what if my errors are asymmetric? So if I had

x1 = 10 +2/-1
x2 = 12 +3/-4

How would I take the average of those values? My first thought was to somehow "normalize" x1 and x2 such that they have symmetric errors, but I am not sure whether that is valid or how I would do that. Anyone have any ideas? thanks...

What are these values? Assuming they are random sample means from the same population, it's usual to express the uncertainty of the estimate in terms of confidence intervals (CI)which in turn are based on the standard error of the sample mean.

If so, the asymmetry of these intervals suggest the original data was transformed for analysis because the data was not normally distributed. Moreover the CIs should not be this different. Because of this and the lack of other information, I can't recommend any "safe" way to combine the two estimates.

EDIT: To make matters worse, the asymmetry indicates the two samples are skewed in different directions!

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## 1. What is weighted average with uneven errors?

Weighted average with uneven errors is a statistical method used to calculate an average value while taking into account the uncertainty or error associated with each data point. It is commonly used in situations where the data points have varying degrees of accuracy or precision.

## 2. Why is weighted average with uneven errors used?

Weighted average with uneven errors is used to give more weight to data points that are more accurate or precise, while reducing the impact of outliers or data points with higher error. This allows for a more accurate representation of the overall average value.

## 3. How is weighted average with uneven errors calculated?

The weighted average with uneven errors is calculated by multiplying each data point by its corresponding weight, which is determined by the level of uncertainty or error associated with that data point. The resulting products are then added together and divided by the sum of the weights.

## 4. What types of data can be analyzed using weighted average with uneven errors?

Weighted average with uneven errors can be used for any type of numerical data, including continuous and discrete variables. It is commonly used in fields such as economics, finance, and science to analyze data sets with varying degrees of accuracy or reliability.

## 5. How is the accuracy of the weighted average with uneven errors determined?

The accuracy of the weighted average with uneven errors is determined by the uncertainty or error associated with each data point. Generally, data points with lower error will have a higher weight and therefore a greater impact on the overall average value, resulting in a more accurate calculation.