JAWS
PROBLEM
I wonder if the median lengths of male sharks tend to be longer than the median lengths of female sharks back in the population. From my own observations, the males of most species tend to be larger or longer than the female [your example here] so I expect this to occur with sharks too.
pLAN
I will take my sample from NZGrapher. The sample size is 1155 female and 1355 male sharks. NZGrapher will generate a dot plot and a box and whisker graph with 5 number summaries so I can analyse and make a conclusion about which gender of shark is longer.
dATA
ANALYSIS
Comparing medians I can see from my graph that the median length for male sharks (123 cm) is longer than the median length for female sharks (116 cm). Based on this sample I would also expect similar results back in the shark population.
Comparing distributions I can see that the middle 50% (IQR), for male sharks ( 104 cm - 139 cm) is longer than the middle 50% for female sharks (101 cm - 133 cm). This means that there is more variation in the middle 50% for the male sample. I would also expect similar distributions of shark lengths back in the shark population. There is almost complete overlap of the two boxes for male and female sharks which shows that almost 50% of the sharks when comparing their length are similar. The curve for female shark lengths from the dot plot is bell shaped and there is a possible outlier at 230 cm. This is longer than the possible outlier for the male of 211 cm. The male dot plot is slightly left skewed. I would also expect these characteristics to appear back in the shark population.
Comparing distributions I can see that the middle 50% (IQR), for male sharks ( 104 cm - 139 cm) is longer than the middle 50% for female sharks (101 cm - 133 cm). This means that there is more variation in the middle 50% for the male sample. I would also expect similar distributions of shark lengths back in the shark population. There is almost complete overlap of the two boxes for male and female sharks which shows that almost 50% of the sharks when comparing their length are similar. The curve for female shark lengths from the dot plot is bell shaped and there is a possible outlier at 230 cm. This is longer than the possible outlier for the male of 211 cm. The male dot plot is slightly left skewed. I would also expect these characteristics to appear back in the shark population.
Making the call - which is bigger, longer or heavier
when the boxes are closely aligned
using the measurements from the box plots
CONCLUSION
The graph shows that although the median lengths for male sharks tends to be longer than for the female sharks in the sample, I still cannot determine which fish sex length is greater by comparison back in the population. This is because the median for female shark length is inside the box for males and the median for male shark length is inside the box for female sharks. Alternatively, the distance between the medians compared to the overall visible spread is less than one third.
If I were to take another sample I would expect to get similar results with the box plots and 5 number summaries. Taking a larger sample might help to produce a more accurate reflection of what the shark lengths looks like back in the population. However, this sample of 1000 for each sex would already be considered acceptable.
On the process of the sampling we do not know anything about how the data was obtained or the nature of the sharks themselves. Were they all from the same area or ocean? What age were they? Were they even the same species? More research would be required into the data collection method.
If I were to take another sample I would expect to get similar results with the box plots and 5 number summaries. Taking a larger sample might help to produce a more accurate reflection of what the shark lengths looks like back in the population. However, this sample of 1000 for each sex would already be considered acceptable.
On the process of the sampling we do not know anything about how the data was obtained or the nature of the sharks themselves. Were they all from the same area or ocean? What age were they? Were they even the same species? More research would be required into the data collection method.