Final answer:
The problem with using a too-large bin size in a histogram is that it reduces data resolution, potentially hiding valuable details of the data distribution such as peaks and gaps.
Step-by-step explanation:
The problem with having too big a bin size in a histogram is that it can greatly reduce the resolution of the data, making it difficult to see the finer details of the distribution. Large bins may combine too much data into single bars, potentially masking interesting patterns such as peaks and gaps, which are necessary quantitative measures in understanding distribution characteristics.
Consider the example where student-athletes play different numbers of sports. If we choose bin sizes that are too large, we might end up with a single bar covering all students, thus losing the distribution information across different numbers of sports played. A reasonable calculation of bin size, consistent with the number of data points and the range of values, helps in creating an informative histogram.
Each bin should capture a range of data values that is narrow enough to show the distribution but wide enough to ensure that the histogram isn't overly complex with too many bars. Therefore, consistency and careful consideration of the range and number of bins is important when calculating bin size for an accurate representation of the dataset.