Standard deviation and mean - combining the two

In summary, the conversation discusses the concept of combining standard deviation and mean in order to make decisions using data. The participants explore different methods, such as multiplying the standard deviation and mean, and combining percentages from different cases. They also consider the legality and effectiveness of these methods.
  • #1
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Standard deviation and mean - "combining" the two

Lets say one was to have a range of data, with the mean and standard deviations for the different subsets of data. The "best" subset is that with the lowest mean, however how do I include the standard deviation when making my decision. For example, the place with lowest infant mortality has the "best" figures for infant mortality, however how could one include the standard deviation into this, in order to predict where the lowest infant mortality will be next year - assuming that there is no trend over the period of the years (ie. it is NOT slowly decreasing in any place - it is equally likely to be above or below the mean next year).

I hope I have explained this well enough, I am open to suggestions. I was thinking of multiplying the standard deviation and mean, but thought that there must be a better statistical method to do this.
 
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  • #2


I'm trying to do the same thing with combining SD and Mean. But here's my situation...

For a given signal A, there are two cases were signal A is observed. In case 1 an original mean value and an associated SD are reported for that signal. After a change to the system, Case 2 has it's own mean value as well as SD. I can also manipulate these new Case 2 values to come up with a % change from Case 1 value and % change from Case 2 SD. I want to combine these two percentages into one to give an overall percentage benefit to the change in the system that separates Case 1 and Case 2. Here's what I've done...

% Overall Benefit = [(Case 1 Value)*(% change from Case 1 to Case 2 value) + (Case 1 SD)*(% change from Case 1 to Case 2 SD)] / [(Case 1 Value)+(Case 1 SD)]

I'm not sure if this is legal, but if it is (and my numbers seem to make sense), then this is a great way to view these two parameters as one value.

Let me know!
 

1. What is the purpose of combining standard deviation and mean?

The combination of standard deviation and mean is used to describe the spread of data around the average value. Standard deviation measures how much the data values deviate from the mean, while the mean represents the central tendency of the data set.

2. How is standard deviation and mean calculated?

To calculate the standard deviation, take the square root of the sum of the squared differences between each data point and the mean, divided by the total number of data points. The mean is calculated by summing all the data points and dividing by the total number of data points.

3. What does a high standard deviation and mean indicate?

A high standard deviation and mean indicate that the data is spread out, with data points deviating significantly from the average. This suggests that there is a large variation in the data points and the mean may not be a good representation of the data set.

4. Can standard deviation and mean be used to compare data sets?

Yes, standard deviation and mean can be used to compare data sets. The data set with a lower standard deviation and mean is more tightly clustered around the average, indicating less variation and a more reliable representation of the data.

5. How does the sample size affect the standard deviation and mean?

The sample size has an impact on the standard deviation and mean. As the sample size increases, the standard deviation decreases, and the mean becomes a more accurate representation of the data. This is because a larger sample size reduces the effect of outliers and random fluctuations in the data.

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