Consider another statistic such as the sample median Do you

Consider another statistic, such as the sample median, Do you think the sample median will be an unbiased estimator for the population median? Whaat do you think the sample distribution of the median looks like? Explain briefly what is meant by the sampleing distributionof the median, and explain how you would empirically generaate the sampling distribution.

Solution

Do you think the sample median will be an unbiased estimator for the population median?

ans: The sample median is an unbiased estimator of the population median when the population is normal. However, for a general population it is not true that the sample median is an unbiased estimator of the population median. The sample mean is a biased estimator of the population median when the population is not symmetric.

Q]What do you think the sample distribution of the median looks like?

ans: (Quite a vague question but to give you an answer )Just as the population models can be described with parameters, so can the sampling distribution. It can be represented by normal distribution if we have infinite samples.

Explain briefly what is meant by the sampleing distributionof the median, and .

ans: Every statistic has a sampling distribution. Normally we calculate different statistics for mean but consider another case for example, suppose that instead of the mean, medians were computed for each sample. The infinite number of medians would be called the sampling distribution of the median.

explain how you would empirically generaate the sampling distribution

ans: Liked I have mentioned, Just as the population models can be described with parameters, so can the sampling distribution. The expected value (analogous to the mean) of a sampling distribution will be represented here by the symbol $ \\mu$ . the expected value of the sampling distribution of the median is represented by the $\\mu_{M_{d}}$ which can be thought as the mean of a distribution of medians.the standard deviation of the sampling distribution of the median is called the standard error of the median and is symbolized by $\\sigma_{M_{d}}$. So, if we have large number of samples, we can easily sample from Normal distribtution from any techniques using these parameters.