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Mode
There is no meaningful average wen data are categorical (qualitative). Also, the arithmetic mean is not a good measure of central tendency when the data distribution is skewed.
This would be the average. When the numbers are all over the place, it is difficult to use them to come to conclusions.
mode
As n increases, the distribution becomes more normal per the central limit theorem.
Mode
Yes. Central tendency is the way data clusters around a value. Even if the distribution of the value is skewed, the median would be the best indicator of central tendency because of the way the data is clustered.
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.
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.
The mean may be a good measure but not if the data distribution is very skewed.
There is no meaningful average wen data are categorical (qualitative). Also, the arithmetic mean is not a good measure of central tendency when the data distribution is skewed.
This would be the average. When the numbers are all over the place, it is difficult to use them to come to conclusions.
One of the characteristics of mean when measuring central tendency is that when there are positively skewed distributions, the mean is always greater than the median. Another characteristic is that when there are negatively skewed distributions, the mean is always less than the median.
mode
i) Since Mean<Median the distribution is negatively skewed ii) Since Mean>Median the distribution is positively skewed iii) Median>Mode the distribution is positively skewed iv) Median<Mode the distribution is negatively skewed
Stability means that there will be less variation between random samples drawn on the same population. With categorical data, you may not have a choice, the mode is the only measure of central tendency that will be meaningful. With measureable, numerical data, the mean may be the only meaningful measure of central tendency, even though the median may show less variation. Some data may be assumed to have a skewed distribution, such as the price of homes, or incomes. The more stable and meaningful value for skewed distributions is the median, as a few high numbers can have a large impact on the estimate. See related links. You can find more information on central tendency by doing a search on the internet.