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Generally not without further reason. Extreme values are often called outliers. Eliminating unusually high values will lower the standard deviation. You may want to calculate standard deviations with and without the extreme values to identify their impact on calculations. See related link for additional discussion.
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Why is the standard deviation of a distribution of means smaller than the standard deviation of the population from which it was derived?
The reason the standard deviation of a distribution of means is smaller than the standard deviation of the population from which it was derived is actually quite logical. Keep in mind that standard deviation is the square root of variance. Variance is quite simply an expression of the variation among values in the population. Each of the means within the distribution of means is comprised of a sample of values taken randomly from the population. While it is possible for a random sample of multiple values to have come from one extreme or the other of the population distribution, it is unlikely. Generally, each sample will consist of some values on the lower end of the distribution, some from the higher end, and most from near the middle. In most cases, the values (both extremes and middle values) within each sample will balance out and average out to somewhere toward the middle of the population distribution. So the mean of each sample is likely to be close to the mean of the population and unlikely to be extreme in either direction. Because the majority of the means in a distribution of means will fall closer to the population mean than many of the individual values in the population, there is less variation among the distribution of means than among individual values in the population from which it was derived. Because there is less variation, the variance is lower, and thus, the square root of the variance - the standard deviation of the distribution of means - is less than the standard deviation of the population from which it was derived.
Why does the standard deviation weight extreme deviations more than does the arithmetic mean?
Because the standard deviation is based on the square root of the sum of the squares of the deviations, and, as a result, the sum of the squares of the deviations puts more weight in outliers than does a simple arithmetic mean.Note: I wrote this and then had second thoughts, but I'm keeping it in so that someone with more knowledge can weigh in (pun intended). I'm not certain how the arithmetic mean factors into the question. I think the questioner, and definitely this answerer, is confused.
Score that is 15 above the means be an extreme score?
It depends entirely on the variance (or standard error).
Advantage and disadvantage of range?
The advantage of range in a set of data is that it provides a simple measure of the spread or dispersion of the values. It is easy to calculate by subtracting the minimum value from the maximum value. However, the disadvantage of range is that it is heavily influenced by outliers, as it only considers the two extreme values and may not accurately represent the variability of the entire dataset. For a more robust measure of dispersion, other statistical measures such as standard deviation or interquartile range may be more appropriate.
What is a z-score used for?
The z-score is used to convert a variable with a Gaussian [Normal] distribution with mean m and standard error s to a variable with a standard normal distribution. Since the latter is tabulated, the probability of an outcome as extreme or more compared to the one observed is easily obtained.
Which of the following is least affected if an extreme high outlier is added to your data mean median or standard deviation or ALL?
The median is least affected by an extreme outlier. Mean and standard deviation ARE affected by extreme outliers.
What is a gross deviation from a standard of reasonable care?
extreme lack of attention to medical care
The project sponsored by the United Nations to eliminate extreme poverty worldwide is called the?
The project sponsored by the United Nations to eliminate extreme poverty worldwide is called the Millenium Project.
Why is the standard deviation of a distribution of means smaller than the standard deviation of the population from which it was derived?
The reason the standard deviation of a distribution of means is smaller than the standard deviation of the population from which it was derived is actually quite logical. Keep in mind that standard deviation is the square root of variance. Variance is quite simply an expression of the variation among values in the population. Each of the means within the distribution of means is comprised of a sample of values taken randomly from the population. While it is possible for a random sample of multiple values to have come from one extreme or the other of the population distribution, it is unlikely. Generally, each sample will consist of some values on the lower end of the distribution, some from the higher end, and most from near the middle. In most cases, the values (both extremes and middle values) within each sample will balance out and average out to somewhere toward the middle of the population distribution. So the mean of each sample is likely to be close to the mean of the population and unlikely to be extreme in either direction. Because the majority of the means in a distribution of means will fall closer to the population mean than many of the individual values in the population, there is less variation among the distribution of means than among individual values in the population from which it was derived. Because there is less variation, the variance is lower, and thus, the square root of the variance - the standard deviation of the distribution of means - is less than the standard deviation of the population from which it was derived.
What is the full form of xps?
In regards to Dell Computing it stands for eXtreme Performance System.
What kind of natural Selection would eliminate one extreme?
Directional selection
Advantages and disadvantages of mean deviation?
The mean deviation is a measure of dispersion that calculates the average absolute difference between each data point and the mean. One advantage of mean deviation is that it considers every data point in the calculation, providing a more balanced representation of the data spread. However, a disadvantage is that it can be sensitive to outliers, as it does not square the differences like the variance does in standard deviation, making it less robust in the presence of extreme values.
What would -2 standard deviation below the mean be?
It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.
Directional selection tends to eliminate?
Directional selection tends to eliminate individuals at one extreme of a trait spectrum, favoring those at the opposite extreme. Over time, this can lead to a shift in the average value of the trait within a population.
Why does the standard deviation weight extreme deviations more than does the arithmetic mean?
Because the standard deviation is based on the square root of the sum of the squares of the deviations, and, as a result, the sum of the squares of the deviations puts more weight in outliers than does a simple arithmetic mean.Note: I wrote this and then had second thoughts, but I'm keeping it in so that someone with more knowledge can weigh in (pun intended). I'm not certain how the arithmetic mean factors into the question. I think the questioner, and definitely this answerer, is confused.
When to use quartile deviation?
When you are looking for a simple measure of the spread of the data, but one which is protected from the effects of extreme values (outliers).
What is affected by extreme outliers?
Extreme outliers can greatly distort statistical measures such as the mean and standard deviation, making them less representative of the data. They can also impact the accuracy of predictive models by leading to overfitting. In some cases, outliers may signal data quality issues or the presence of unexpected patterns in the data that warrant further investigation.
