This question has already been submitted and answered:
https://www.mathhomeworkanswers.org/283559/sample-sample-and-probability-distribution
10 samples can be drawn.
We need to decide which statistic from each sample best represents the sample. The median seems to be an ideal statistic, because there is less variation of the median and some of the samples share the same median as the population. From the answer already given, there are 3 different values for the median: 6, 12 and 18, 12 also being the median of the population.
| MEDIAN |
PROBABILITY |
| 6 (frequency: 3 samples) |
0.3 or 30% |
| 12 (frequency: 4 samples) |
0.4 or 40% |
| 18 (frequency: 3 samples) |
0.3 or 30% |
If the mean had been chosen instead of the median, we would have had 10 different values, all but one being expressed as a mixed number (containing a fraction), so the next task might be to tabulate the means in ranges to construct a histogram. For example, the range 23/3 (7.67) to 50/3 (16.67) could be divided into 4: 7.67-9.92, 9.92-12.17, 12.17-14.42, 14.42-16.67. So if we did this, the probability distribution changes: 2 samples fit into each of the first quarter and the last quarter, 3 samples fit into each of the second and third quarter.
| RANGE OF MEAN |
PROBABILITY |
| 7.67-9.92 (freq: 2 samples) |
0.2 or 20% |
| 9.92-12.17 (freq: 3 samples) |
0.3 or 30% |
| 12.17-14.42 (freq: 3 samples) |
0.3 or 30% |
| 14.42-16.67 (freq: 2 samples) |
0.2 or 20% |