No, not always. It depends on the type of data you collect. If it is quantitative data, you will be able to calculate a mean. If it is qualitative data, a mean can't be calculated but you can describe the data in terms of a mode.
In parametric statistical analysis we always have some probability distributions such as Normal, Binomial, Poisson uniform etc.In statistics we always work with data. So Probability distribution means "from which distribution the data are?
Yes, the normal distribution is uniquely defined by its mean and standard deviation. The mean determines the center of the distribution, while the standard deviation indicates the spread or dispersion of the data. Together, these two parameters specify the shape and location of the normal distribution curve.
The variance is always positive. The variance is not directly related to the sign (nor magnitude) of the mean.
100%
The importance is that the sum of a large number of independent random variables is always approximately normally distributed as long as each random variable has the same distribution and that distribution has a finite mean and variance. The point is that it DOES NOT matter what the particular distribution is. So whatever distribution you start with, you always end up with normal.
The total deviation from the mean for ANY distribution is always zero.
No.
If the distribution is positively skewed , then the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency (If it is a uni-modal distribution). If the distribution is negatively skewed then mean will always be the lowest estimate of central tendency and the mode will be the highest estimate of central tendency. In both positive and negative skewed distribution the median will always be between the mean and the mode. If a distribution is less symmetrical and more skewed, you are better of using the median over the mean.
yes
No. They are equal only if the distribution is symmetrical.
The mean is the same as the mode and median.
Yes- this can be proved from the normal distribution function.
If the distribution is positively skewed distribution, the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency. This is true if we assume the distribution has a single mode.
In parametric statistical analysis we always have some probability distributions such as Normal, Binomial, Poisson uniform etc.In statistics we always work with data. So Probability distribution means "from which distribution the data are?
No, in a normal distribution they are the same.
It is probably the most widely used distribution in statistics. In addition, a lot of information exists on this distribution.
A shortage can be temporary or long-term, but scarcity always exists.