Question

a dataset has sample proportions with a minimum of 0.20 and a maximum of 0.30 which bin width would allow for seeing the variabillity of the data in sampling distribution

Answer 1

To visualize the variability of sample proportions within a specified range (in your case, from 0.20 to 0.30), an appropriate bin width is crucial for effectively analyzing the data in a histogram or a similar plot.

A good starting point for choosing a bin width is to consider the range of the data and the desired level of detail in your visualization. Here are a few steps to determine an appropriate bin width:

1. **Determine the range of the data**: In your case, the range is from 0.20 to 0.30, which gives you a range of 0.30 - 0.20 = 0.10.

2. **Select the number of bins**: A common rule of thumb for histograms is to use between 5 to 20 bins, depending on the dataset size and the level of detail you wish to achieve.

3. **Calculate bin width**:
- If you want to create 5 bins, the bin width would be:
\[
\text{Bin width} = \frac{\text{Range}}{\text{Number of bins}} = \frac{0.10}{5} = 0.02
\]
- If you opt for 10 bins:
\[
\text{Bin width} = \frac{0.10}{10} = 0.01
\]
- For 15 bins:
\[
\text{Bin width} = \frac{0.10}{15} \approx 0.0067
\]
- For 20 bins:
\[
\text{Bin width} = \frac{0.10}{20} = 0.005
\]

4. **Consider practicality and clarity**: While you can calculate very small bin widths (like 0.005 or 0.0067), consider the practicality of displaying and interpreting such fine divisions. A bin width of **0.01 or 0.02** might provide a good balance between detail and readability.

In summary, a bin width of **0.01 or 0.02** would generally allow for seeing the variability of the data within the specified range of sample proportions (0.20 to 0.30). Adjust based on your specific dataset and the overall visualization goals.