Question

How can the bin width affect the shape of a histogram?

Answer 1

Hint: We have to find the effect of bin width on the shape of a histogram. For this, first understand the concept and shape of a histogram. Then, understand the effect of inappropriate bin size on purpose of the histogram.

Complete answer:
A good histogram will show areas of higher incidence of a parameter that may help us to identify causative factors in a system. Thus, inappropriate bin size will defeat the purpose of the histogram. The extremes may help visualize the effect. ONE 'bin' only shows the population or total sample size. A 'bin' for each sample point gives us no more information, but only stretches the width of the chart.
A good bin width will usually show a recognizable normal probability distribution curve, unless the data is really multimodal. Then there could be two or more distinct 'humps' in the histogram chart.
Final solution: The bin width (and thus number of categories or ranges) affects the ability of a histogram to identify local regions of higher incidence. Too large, and you will not get enough differentiation. Too small, and the data cannot be grouped.

Note:
Purpose of the histogram:
A histogram is a quick way to get information about a sample distribution without detailed statistical graphing or analysis.
Without needing to have a good graphing program, plotting a histogram can give you a quick visualization of your data distribution. It is important to select the correct 'bin' size (groups of data) to get the best curve approximation.
This plot will show you if your data values are centered (normally distributed), skewed to one side or the other, or have more than one 'mode' - localized distribution concentrations.
They can also be rearranged as a Pareto Plot from highest frequency to lowest, allowing you to focus on the most important factors to address in problem solutions.