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When two distributions have the same mean but different distribution and variability?
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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 does distributions free mean in statistics?
It means independent of the underlying distribution.
What do mode meadian and mean mean in maths?
A variable is a measure that can take different values. How often it can take these different values defines its distribution. Mode, median and mean are three common measures of central tendency of distributions.
When should you use relative frequency such as percentages in comparing two distributions?
When comparing the spread or variability rather than the location or mean. For example, men's heights and women's heights. You "know" that, on average, men will be taller but you may want to see if the variability within the two sets is the same or different.
How do you derive the mean deviation about the mean of the pareto type 1 distributions?
Easy. The mean deviation about the mean, for any distribution, MUST be 0.
How many standard normal distributions are there?
Only one. A normal, or Gaussian distribution is completely defined by its mean and variance. The standard normal has mean = 0 and variance = 1. There is no other parameter, so no other source of variability.
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.
The mean of a symmetrical distribution is 40What is its median?
for symmetrical distributions your mean equals the median. that is one of the properties of the symmetrical distribution.
What does distributions free mean in statistics?
It means independent of the underlying distribution.
Normal distribution is symmetric with single peak.Does this mean that all distibutions are normal?
No, not all distributions are symmetrical, and not all distributions have a single peak.
What do mode meadian and mean mean in maths?
A variable is a measure that can take different values. How often it can take these different values defines its distribution. Mode, median and mean are three common measures of central tendency of distributions.
What does variability mean in math?
Variability is an indicationof how widely spread or closely clustered the data valuesnare. Range, minimum and maximum values, and clusters in the distribution give some indication of variability.
When should you use relative frequency such as percentages in comparing two distributions?
When comparing the spread or variability rather than the location or mean. For example, men's heights and women's heights. You "know" that, on average, men will be taller but you may want to see if the variability within the two sets is the same or different.
How do you derive the mean deviation about the mean of the pareto type 1 distributions?
Easy. The mean deviation about the mean, for any distribution, MUST be 0.
What does it mean normal distribution?
The Normal distribution is a probability distribution of the exponential family. It is a symmetric distribution which is defined by just two parameters: its mean and variance (or standard deviation. It is one of the most commonly occurring distributions for continuous variables. Also, under suitable conditions, other distributions can be approximated by the Normal. Unfortunately, these approximations are often used even if the required conditions are not met!
What is the mean of frequency distribution?
It is a mathematically calculated summary statistic. With discrete distributions it is the arithmetic mean whereas with a continuous distribution it is the value of the random variable (RV) such that it divides the area under the probability distribution curve in half.
What does the coefficient of the variation tell you?
The coefficient of variation (CV) is a measure of relative variability, indicating the degree of dispersion of a distribution relative to its mean. A high CV value suggests greater variability, while a low CV value suggests more consistency. It is useful for comparing the variability of different datasets with differing units of measurement.
