Bin Width vs Histogram
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Bin width
Graphs and displays
Bin width is the size of each equal-width interval in a histogram, and it controls how much detail or smoothing the display shows.
Bin width sets the resolution of a histogram: wide bins smooth the picture and can bury real structure, while narrow bins expose detail and can promote random noise into a fake peak. For example, 40 exam scores running from 52 to 98 fill 5 bins of width 10 (50 to 60, 60 to 70, and so on up to 100), but at width 5 those same scores fill 10 bins and one broad hump can split in two, so the shape now reads as bimodal. A rough starting point is the range divided by the number of bins you want, here , which you round to a readable 10. Because the choice can change your conclusion, check a second bin width before you commit to a description of the shape.
Histogram
Graphs and displays
A histogram displays quantitative data by grouping values into equal-width intervals and drawing a bar for the count in each interval.
A histogram divides the number line into bins of equal width and draws a bar whose height is the frequency in that bin. For example, exam scores might be binned as 60 to 70, 70 to 80, and 80 to 90, with bar heights giving how many scores land in each. Unlike a bar graph, the bars touch because the horizontal axis is a continuous number scale. The bin width you choose affects how smooth or jagged the shape looks.