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Will the mean and median in a symmetric distribution always be equal or approximately equal and Why?
In a symmetric distribution, the mean and median will always be equal. This is because symmetry implies that the distribution is balanced around a central point, which is where both the mean (the average) and the median (the middle value) will fall. Therefore, in perfectly symmetric distributions like the normal distribution, the mean, median, and mode coincide at the center. In practice, they may be approximately equal in symmetric distributions that are not perfectly symmetrical due to rounding or sampling 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.
What does distributions free mean in statistics?
It means independent of the underlying distribution.
Is the mean of a standard normal distribution is always equal to 1?
No, the mean of a standard normal distribution is not equal to 1; it is always equal to 0. A standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. This distribution is used as a reference for other normal distributions, which can have different means and standard deviations.
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.
Will the mean and median in a symmetric distribution always be equal or approximately equal and Why?
In a symmetric distribution, the mean and median will always be equal. This is because symmetry implies that the distribution is balanced around a central point, which is where both the mean (the average) and the median (the middle value) will fall. Therefore, in perfectly symmetric distributions like the normal distribution, the mean, median, and mode coincide at the center. In practice, they may be approximately equal in symmetric distributions that are not perfectly symmetrical due to rounding or sampling variability.
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.
Is the mean of a standard normal distribution is always equal to 1?
No, the mean of a standard normal distribution is not equal to 1; it is always equal to 0. A standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. This distribution is used as a reference for other normal distributions, which can have different means and standard deviations.
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.
Why is it correct to say a normal distribution and the standard normal distribution?
A normal distribution refers to any bell-shaped distribution characterized by its mean and standard deviation, allowing for a variety of shapes depending on these parameters. The standard normal distribution, however, is a specific case of a normal distribution where the mean is 0 and the standard deviation is 1. This standardization allows for easier comparison and calculation of probabilities using z-scores, which represent the number of standard deviations a data point is from the mean. Thus, while all standard normal distributions are normal distributions, not all normal distributions are standard normal distributions.
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 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.
