Density Curve 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.
Density curve
Graphs and displays
A density curve is a smooth curve that models a distribution, never dipping below the axis, with total area underneath exactly equal to 1.
A density curve is the idealized version of a histogram: you stop reading heights as counts and start reading area as proportion. The total area under the curve is exactly , and the area above any interval is the proportion of the data, or the probability, falling in that interval. For example, a uniform density curve spread over 0 to 4 has constant height because , so the area from 1 to 3 is and exactly half the values lie there. Every normal distribution problem you solve is an area-under-a-density-curve problem.
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.