Q.3.1 - The Practice of Statistics for AP

Question

The histogram above left shows the intervals (in minutes) between eruptions of the Old Faithful geyser for all $222$ recorded eruptions during a particular month. For this population, the median is $75$ minutes. We used Fathom software to take $500$ SRSs of size $10$ from the population. The $500$ values of the sample median are displayed in the histogram above right. The mean of the $500$ sample median values is 73.5.

 Is the sample median an unbiased estimator of the population median? Justify your answer 

Step-by-Step Solution

Answer

 The sample median is an unbiased estimator of the population median. 

Step 1 Given Information

Median is $75 .$

Sample size is $500$

Mean is $73.5$

Step 2 Explanation

From the given information, it is clear that the mean of the distribution and the sample median are not equal. Thus, it cannot be said that the sample median is an unbiased estimator of the population median.