Q.3.3 - The Practice of Statistics for AP

Question

3. Describe the shape of the

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 $73.5$.

Sampling distribution. Explain what this means in terms of overestimating or underestimating the population median 

Step-by-Step Solution

Answer

 The distribution is unimodal and skewed to the left. 

Step 1: Given Information

Median is $75 .$

Sample size is $20 .$

Mean is $73.5$

Step 2: Explanation

The figure is

From the figures given above, it is clear that most of the data points are lying on the left side of the graph and it has one peak. Thus, it could be said that the distribution is unimodal and skewed to the left.