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When the variance calculated from a distribution of phenotypes is zero it means that?
When the variance calculated from a distribution of phenotypes is zero, it means that all individuals in the population exhibit the same phenotype, indicating no variation among them. This uniformity can result from genetic homogeneity, environmental factors, or a lack of diversity in the population. In such cases, any measurements taken will yield identical values, reflecting complete consistency in the trait being assessed.
What else can I help you with?
Can the variance of a normally distributed random variable be negative?
No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.
When distribution has zero variance?
When a distribution has zero variance, it means that all the values in the dataset are identical; there is no variability or spread among the data points. Essentially, every observation is equal to the mean, resulting in a distribution that is a single point. This condition indicates complete certainty and no risk, as there is no deviation from the mean. In practical terms, a zero variance suggests that the dataset lacks diversity or fluctuation in its values.
How do you calculate distribution of sample means?
The sample mean is distributed with the same mean as the popualtion mean. If the popolation variance is s2 then the sample mean has a variance is s2/n. As n increases, the distribution of the sample mean gets closer to a Gaussian - ie Normal - distribution. This is the basis of the Central Limit Theorem which is important for hypothesis testing.
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.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
What word means the average of the squared deviation scores from a distribution mean?
Variance
Can the variance of a normally distributed random variable be negative?
No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.
In a population that is not undergoing natural selection for a certain trait what does the phenotype distribution look like?
The distribution will center towards hetrotrophs and thus dominant phenotypes. The distribution approaches all dominant phenotypes
What phenotype distribution pattern is common with polygenic inheritance?
A continuous variation of phenotypes is common with polygenic inheritance, often resulting in a bell-shaped curve known as a normal distribution. This means that individuals will exhibit a range of phenotypes with no clear-cut categories.
When distribution has zero variance?
When a distribution has zero variance, it means that all the values in the dataset are identical; there is no variability or spread among the data points. Essentially, every observation is equal to the mean, resulting in a distribution that is a single point. This condition indicates complete certainty and no risk, as there is no deviation from the mean. In practical terms, a zero variance suggests that the dataset lacks diversity or fluctuation in its values.
How do you calculate distribution of sample means?
The sample mean is distributed with the same mean as the popualtion mean. If the popolation variance is s2 then the sample mean has a variance is s2/n. As n increases, the distribution of the sample mean gets closer to a Gaussian - ie Normal - distribution. This is the basis of the Central Limit Theorem which is important for hypothesis testing.
(b)For a set of numbers 1,4,7. Find population mean and Variance. Draw up frequency distributions of means of all possible samples of size 3 when sampling is carried out with replacement. Find mean and variance of distribution?
lowest
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.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
What are adverse variances?
Adverse variances means unfavourable variance which is actual expenses are more than budgted variance.
An analysis of variance differs from a t test for independent means in that an analysis of variance?
Analysis of Variance (ANOVA) compares 3 or more means. The t-test would only compare 2 means.
What does homogeneity of variance mean?
It means that the variance remains the same across the range of values of the variable.
