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What else can I help you with?
Is the mean always equal to the median for a normal distribution?
Yes, in a normal distribution, the mean is always equal to the median. This is because the normal distribution is symmetric around its mean, meaning that the values are evenly distributed on both sides. As a result, the central tendency measured by both the mean and the median coincides at the same point.
What does probalility distribution mean?
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?
Is the normal distribution always being defined by the mean and standard deviation?
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.
Is mean and median always very similar?
The mean and median are not always similar; their relationship depends on the distribution of the data. In a symmetrical distribution, such as a normal distribution, the mean and median are typically very close or identical. However, in skewed distributions, the mean can be significantly affected by outliers, causing it to differ from the median, which remains more representative of the central tendency. Thus, while they can be similar in certain cases, this is not universally true.
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 do you derive mean deviation from mean for pareto distribution?
The total deviation from the mean for ANY distribution is always zero.
Is the mean always zero in a normal distribution?
No.
Is Mean is more sensitive to skewness than the median?
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.
Is in binomial distribution mean always greater then variance?
yes
Are the mean and the median always equal?
No. They are equal only if the distribution is symmetrical.
In a normal distribution you will always know that?
The mean is the same as the mode and median.
Is the mean always equal to the median for a normal distribution?
Yes, in a normal distribution, the mean is always equal to the median. This is because the normal distribution is symmetric around its mean, meaning that the values are evenly distributed on both sides. As a result, the central tendency measured by both the mean and the median coincides at the same point.
Normal distribution it is always true that mean equals median equals mode?
Yes- this can be proved from the normal distribution function.
What is the smallest measure of central tendency in a positively skewed distribution?
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.
What does probalility distribution mean?
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?
Do the mean median and mode of a collection of numbers always have to be different?
No, in a normal distribution they are the same.
Why you prefer normal distribution for other?
It is probably the most widely used distribution in statistics. In addition, a lot of information exists on this distribution.
