Expected variance of subset of population

In summary, the conversation discusses calculating the expected variance of a randomly selected subset from a population. The speaker presents a problem where they have a set of values and are looking to find if the expected variance of a randomly selected subset is less than the variance of the entire population. They also mention two possible methods to solve this problem: a hard way involving writing sums and an easier way using the law of total variance. The speaker also asks if there is a simple proof for this solution.
  • #1
ll777
2
0
I want to calculate expected variance of a randomly selected subset of a population.

The particular problem I am trying to solve is as follows. There is a set of values X = {x1, ... , xn}. Let Y be subset of X with n-1 elements. I think that if Y is selected at random (that is, if is produced by randomly removing an element of X), the expected variance of Y is less than the variance of X. Is this right and if so is there a simply proof?
 
Physics news on Phys.org
  • #2
A hard way: write sum(Y)=sum(X)-xj etc.

An easy way: The law of total variance.
 

What is expected variance of subset of population?

The expected variance of a subset of a population is a statistical measure that estimates the variability in a subset of data from a larger population. It is calculated by taking the average of the squared differences between each data point in the subset and the mean of the subset.

How is expected variance of subset of population related to standard deviation?

The expected variance and standard deviation are closely related, as they both measure the amount of variability in a subset of data. The standard deviation is simply the square root of the expected variance, and it is often used as a more easily interpretable measure of variability.

What factors can affect the expected variance of subset of population?

There are several factors that can influence the expected variance of a subset of a population, including the size of the subset, the distribution of the data within the subset, and the presence of outliers or extreme values. Additionally, the expected variance can be affected by the method used to select the subset from the larger population.

How can expected variance of subset of population be used in data analysis?

The expected variance of a subset of a population is a useful tool in data analysis, as it allows for the comparison of variability between different subsets of data. It can also be used to identify outliers or extreme values in the data, and to determine the reliability of statistical models or predictions.

Can the expected variance of subset of population be negative?

No, the expected variance of a subset of a population cannot be negative. The expected variance is a measure of squared differences, so it will always be a positive value. If a negative value is obtained, it is likely due to an error in calculation or data entry.

Similar threads

I Desirable estimator properties...
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
465
I Linear Regression, Population, Sample
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
889
MHB Bias of functions defined on samples for population
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
2K
I Unbiasedness of estimates
    • Set Theory, Logic, Probability, Statistics
Replies
9
Views
1K
I Sampling theory and random sample
    • Set Theory, Logic, Probability, Statistics
Replies
5
Views
480
I Why does normal distribution turn into t distribution when variance is unknown?
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
I Statistical modeling and relationship between random variables
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
447
MHB Confidence interval of difference
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
660
Sample distribution and expected value.
    • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
I What is the expected value of Cov(x,y)2 in an independent X and Y scenario?
    • Set Theory, Logic, Probability, Statistics
Replies
17
Views
2K

Hot Threads

Recent Insights

Back
Top