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Does a leptokurtic distribution have a larger variance than Mesokurtic distribution?
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Would one expect more variance with a larger sample size in a chi distribution?
The larger your sample size, the less variance there will be. For instance, your information is going to be much more substantial if you took 1000 samples over 10 samples.
Can the variance of a sample be larger than the sample mean?
Yes, Mean is given by, E(X) sum of samples / no. of samples. Variance is Var.(X) = E(X^2) - [E(X)]^2. It is the 1st term which makes the variation of variance independent of mean. In other words, Variance gives a measure of how far the samples are spread out.
What happens in a normal distribution when the means are equal but the standard deviation changes?
The two distributions are symmetrical about the same point (the mean). The distribution where the sd is larger will be more flattened - with a lower peak and more spread out.
Why do you square the deviations to get the variance and then take the reverse action of taking the square root of the variance to return the variance to sigma?
because of two things- a) both positive and negative deviations mean something about the general variability of the data to the analyst, if you added them they'd cancel out, but squaring them results in positive numbers that add up. b) a few larger deviations are much more significant than the many little ones, and squaring them gives them more weight. Sigma, the square root of the variance, is a good pointer to how far away from the mean you are likely to be if you choose a datum at random. the probability of being such a number of sigmas away is easily looked up.
Why does normal distribution occur when samples get larger?
That only happens when you sample a population that is normally distributed. In that case, the question and its answer are quite circular.
Would one expect more variance with a larger sample size in a chi distribution?
The larger your sample size, the less variance there will be. For instance, your information is going to be much more substantial if you took 1000 samples over 10 samples.
When using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
Can standard deviation be larger then its variance?
No. The standard deviation is the square root of the variance.
How does the number of repetitions effect the shape of the normal distribution?
When we discuss a sample drawn from a population, the larger the sample, or the large the number of repetitions of the event, the more certain we are of the mean value. So, when the normal distribution is considered the sampling distribution of the mean, then more repetitions lead to smaller values of the variance of the distribution.
The sample variance is always smaller than the true value of the population variance is always larger than the true value of the population variance could be smaller equal to or?
yes, it can be smaller, equal or larger to the true value of the population varience.
When two dice are thrown let X be the larger of the two numbers on the two throws find the probability distribution mean and variance of X?
The probability distribution is P(X = 1) = 1/36 P(X = 2) = 3/36 P(X = 3) = 5/36 P(X = 4) = 7/36 P(X = 5) = 9/36 P(X = 6) = 11/36 P = 0 otherwise. Mean(X) = 4.4722 Variance = 1.9715
Can the variance of a sample be larger than the sample mean?
Yes, Mean is given by, E(X) sum of samples / no. of samples. Variance is Var.(X) = E(X^2) - [E(X)]^2. It is the 1st term which makes the variation of variance independent of mean. In other words, Variance gives a measure of how far the samples are spread out.
Why do you keep the larger of the two variances in the numerator while calculating f distribution variance ratio?
Off the top of my head, a perfect F-ratio would be 1.00 which is never possible. All F-ratios will be greater than one so the numerator has to be greater than denominator.
Why the normal distribution can be used as an approximation to the binomial distribution?
The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.
What are types of spatial distribution?
The types of spatial distribution include: Random distribution: where individuals are arranged without any pattern. Uniform distribution: where individuals are spaced evenly throughout an area. Clumped distribution: where individuals are found in groups or clusters within a larger area.
What is the difference between standard normal distribution table and the t distribution table?
standard normal is for a lot of data, a t distribution is more appropriate for smaller samples, extrapolating to a larger set.
What does it mean when the distribution of data is skewed to the right?
The distribution is unbalanced, because the right tail is larger than it would be if the distribution were balanced (symmetrical). Also called positive skew. See related link with diagrams that clarify this term.
