# Is this weighted mean and standard deviation correct?

• I
• JorgeM
In summary, the conversation discusses the value of the constant "alpha" and its representation in the equation for weights. The speaker is looking for information on the best formula to use for analyzing their data on stock prices. They mention a footnote that may provide more information, but it is not accessible at the moment. The expert advises that the weights should reflect the relative importance of the items in the data.
JorgeM
TL;DR Summary
I have to analize an small set of data(1000 points). But anyways I am not really sure if it is correct to use this one because this one refers to use an specific expression that I could not find anywhere.
The expression I have found is this one.
https://ibb.co/kqG24L3
I have been looking for information because I could not to realize what is the value that "alpha" has to have.

If any of you do know what this alpha value is supposed to represent or if you have seen it before I would be really grateful if you could help me.
Thanks
JorgeM

In your image, where it gives the equation for the weights ##w_i##, it also says that ##\alpha## is a constant, and there is a footnote (14). Possibly the footnote explains what the constant is, but the image doesn't show that part of the text.

JorgeM
The formulas (ignoring alpha) are general. The Definition of the weights in terms of alpha apprears to specific to the situation being discussed. What you need for the weights is determined by the nature of the data you have.

JorgeM and FactChecker
Yes, actually the footnote reffers to a GNU statistics library which instructions are not still available.
Can you please recommend me some bibliography to find out which is the best option (formula) that I may use to analize my data (The data is about stocks' prices)

I can't answer your question, since I don't what data you have. The weights should reflect relative importance of the items. That is for you to work out.

JorgeM

## 1. What is a weighted mean and standard deviation?

A weighted mean and standard deviation are statistical measures used to calculate the average and variability of a set of data. The weighted mean takes into account the importance or weight of each data point, while the standard deviation measures how much the data deviates from the mean.

## 2. How is a weighted mean and standard deviation calculated?

To calculate the weighted mean, you multiply each data point by its corresponding weight, add all the products, and then divide by the sum of the weights. To calculate the weighted standard deviation, you first calculate the weighted mean, then find the difference between each data point and the weighted mean, square these differences, multiply them by their corresponding weights, add all the products, and then divide by the sum of the weights.

## 3. When should a weighted mean and standard deviation be used?

A weighted mean and standard deviation should be used when the data set contains outliers or when certain data points are more important than others. For example, in a survey where some responses are more representative of the population than others, a weighted mean and standard deviation would provide a more accurate representation of the data.

## 4. How do you interpret a weighted mean and standard deviation?

The weighted mean represents the average value of the data set, taking into account the importance of each data point. The weighted standard deviation measures the variability of the data, with a higher standard deviation indicating a larger spread of data points from the mean. A lower standard deviation indicates a more consistent data set.

## 5. Can a weighted mean and standard deviation be incorrect?

Yes, a weighted mean and standard deviation can be incorrect if the data or weights used are incorrect or if the calculation is done incorrectly. It is important to double-check the data and calculations to ensure accuracy. Additionally, a weighted mean and standard deviation may not be appropriate for certain types of data, such as categorical data or data with extreme outliers.

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