Histograms with hist, Density & Overlays

The problem, from first principles

ax.hist is a one-line call that hides three decisions: how the range is cut into bins, whether the bar heights are counts or a density, and, when two histograms share a plot, whether they use the same bins. Skip the last one and the comparison is meaningless: two samples drawn with different bin edges can look different purely because of where the cuts fell.

Because hist also returns the numbers it drew (the counts and the edges), the chart can be checked against np.histogram exactly. This question draws a histogram and reads its numbers back, draws a density histogram whose bars have total area 1, and overlays two samples on a shared set of bins so the comparison is fair.

From theory to code

Implement draw_histogram(data, bins), density_histogram(data, bins) and overlay_histograms(a, b, bins, labels). The signatures and docstrings are already in the editor.

Constraints

• data, a, b are 1D sequences of at least two numbers with at least two distinct values. bins is an integer number of bins.
• draw_histogram(data, bins) draws on a new Axes with ax.hist and returns (fig, ax, counts, edges) where counts and edges are the arrays returned by hist. There are bins bars.
• density_histogram(data, bins) returns (fig, ax) of a histogram whose bar heights are a density (the total area of the bars is 1) and whose y label is "density".
• overlay_histograms(a, b, bins, labels) draws both samples on one Axes using the same bin edges, computed from the combined data with np.histogram_bin_edges(np.concatenate([a, b]), bins=bins), each with alpha=0.5 and its label from labels (a pair), shows a legend, and returns (fig, ax, edges).
• Do not call plt.show().

Hints