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Advantages and disadvantages of median in statistics?
The median is advantageous because it is not influenced by extreme values, making it a robust measure of central tendency for skewed data sets. It is also easy to interpret and calculate. However, the median may not accurately represent the true center of a dataset if the data is heavily skewed or if there are outliers present. Additionally, the median may not be as efficient as the mean for certain statistical calculations due to its lack of sensitivity to all data points.
How is frequency distribution useful to us?
I suspect you are referring to a sample frequency distribution.Providing that the sample size is sufficiently large there are various kinds of information that can be gleaned from one:the approximate range of values in the populationthe location of the population as measured by the value that appears most often in the frequency distribution-known as its modethe likely shape of the population's distribution, in particular whether it is symmetric or skewedobviously how values of the population variable are distributedwhether there are any curious peaks or valleys, even when the sample size is largethe amount of variation around the central value
What central tendency should be used when the item being studied is constantly fluctuating for example daily temperature?
That depends entirely upon what is varying. For instance - in your example of daily temperature - average would be meaningless and be of little use, but daily maximum and daily minimum would be useful. To use the average of anything that is fluctuating is not easy as you have to define a sample rate and be sure that it is meaningful.
Why do we study dispersion?
It is not enough to know only the mean or some other measure of the central tendency: it is useful to know the dispersion. If, in a test, the average score is 50 and you score 52 you have clearly scored better than average but how much better? If the scores range from 0 to 100, you are pretty close to average whereas if they range from 48 to 52 you are amongst the top of the class!
What is the mean of the sampling distribution of the sample mean?
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
