Which of the following best describes the effect of increasing the bin size in a histogram?

• A. The histogram will have fewer, wider bars, potentially obscuring details in the data distribution.
• B. The total area under the histogram will increase.
• C. The mean of the data will change.
• D. The histogram will have more, narrower bars, making the distribution appear more detailed.

Answer: (A)

Verified step by step guidance

1. Understand what a histogram represents: it is a graphical representation of the distribution of numerical data, where the data is divided into intervals called bins, and the frequency of data points within each bin is shown by the height of the bars.
2. Recognize that the bin size determines the width of each bar in the histogram. Increasing the bin size means each bin covers a larger range of data values.
3. When the bin size increases, the number of bins decreases because the entire data range is divided into fewer, wider intervals.
4. Fewer, wider bins cause the histogram bars to be broader, which can smooth out or obscure finer details in the data distribution, such as small peaks or gaps.
5. Note that the total area under the histogram remains constant (equal to the total number of data points or probability 1 if normalized), and the mean of the data does not change because the histogram is just a visual summary, not a transformation of the data itself.