Question bank — 2D plots — line, scatter, bar, histogram, contour, imshow

False. A line plot draws straight segments between consecutive points; smoothness is an illusion from using many close points. With 5 points a sine looks jagged.

Nearly identical visually, but the APIs differ: plt.plot(x, y, "o") (marker-only) draws every point in one shared style and color, while plt.scatter(x, y, s=..., c=...) lets each point carry its own size and color — extra data dimensions plot cannot express per point.

False. A bar chart draws one bar per category you supply; a histogram counts samples into value-ranges (bins) and throws the individual values away, keeping only frequency $c_j$.

False. It makes the total area equal 1 (heights become $c_j/(nh)$, where $n$ is sample count and $h$ is bin width). Heights sum to 1 only in the special case $h=1$.

False. imshow treats rows as y and columns as x, so Z[i, j] = Z[row, col] = Z[y, x] — the opposite of the usual (x, y) reading order.

False. A contour at level $c$ is the set $\{(x,y):f(x,y)=c\}$; for a saddle or an edge-cropped surface it can be an open curve that runs off the plot without closing.

False in intent. plt.plot draws on a hidden current axes; with multiple subplots you can't reliably say which axes gets it. The explicit ax. API always targets a known axes.

False. Close contours mean a steep slope — you cross many height levels over a small horizontal distance, exactly like tightly packed elevation lines on a map.

The error is passing 1D coordinates directly for a surface. You must first build 2D grids with np.meshgrid (which broadcasts the two axes into a full coordinate table — see NumPy meshgrid and broadcasting); Z must be 2D shaped (len(ys), len(xs)).

imshow defaults to origin="upper" (row 0 at the top, image convention). For a math matrix with y increasing upward, pass ==origin="lower"==.

Too many bins for the sample count — most bins get $c_j\in \{0,1\}$, so shape drowns in noise. Use roughly $B\approx \sqrt{n}\approx 17$ here.

width=1.0 fills the entire unit spacing between integer positions. Use width < 1 (e.g. 0.6) so categories read as visually separate blocks.

Color is meaningless without a key. Add fig.colorbar(...) so the reader can map color back to value — and pick a perceptually uniform map (see Colormaps and perceptual uniformity (viridis)).

Missing plt.show(). Notebooks auto-render, but a plain script needs the explicit call to open the figure window.

plot connects points in the order given, not sorted order. Sort by x first, or use scatter if order is genuinely meaningless.

So the summed bar area equals 1. Bar $j$ has area $\text{height}\times h=\frac{c_j}{nh}\cdot h$. Summing: ${\sum }_j\frac{c_j}{nh}\cdot h=\frac{1}{n}{\sum }_j{c}_j=\frac{n}{n}=1$, using the identity ${\sum }_j{c}_j=n$ (every sample lands in exactly one bin). This matches a probability density — see Probability density functions and normalization.

A surface needs a value of $z$ at every $(x,y)$ combination — a 2D table. meshgrid expands the two 1D axes into two 2D coordinate grids so you can evaluate $Z=f(X,Y)$ over the whole plane at once.

Dual coding is a cognitive-science idea: a viewer absorbs information faster when it arrives through two channels at once (here, position and color) rather than one. Position already spends both axes; mapping color to a third variable adds a third dimension onto a flat 2D canvas without a 3D plot.

Transparency lets overlapping points stack visually darker, revealing where many points pile up — information you'd lose with fully opaque dots that just paint over each other.

The Figure is the whole canvas; an Axes is one coordinate system inside it. Caring keeps you in control when a figure holds several subplots — each is its own ax.

Without it, axes are labeled by pixel/array indices (0..N). extent remaps those indices to real world coordinates so ticks read as actual x, y values.

Nothing visible by default — a line needs two points to draw a segment. You'd have to add a marker (marker="o") to see the lone point.

All counts collapse into a single bin ($c_j=n$ for one bin, $0$ for the rest), giving one tall bar. The range $[\min ,\max ]$ has zero width, so Matplotlib pads it slightly to draw anything at all.

Almost nothing. When the data's min == max, Matplotlib's auto-locator finds no interval to place levels in, so requested levels that don't lie strictly between distinct min and max are dropped — the flat plane is one single level with no boundary to trace, so no curves appear.

That cell is drawn in the colormap's "bad" color, which by default is transparent — so exact appearance depends on the colormap. For reproducibility set it explicitly: cmap = plt.get_cmap("inferno").copy(); cmap.set_bad(color="grey"), so masked/NaN data always shows the same way.

With $n=1$, one bin gets that sample ($c_j=1$); its height becomes $\frac{1}{1\cdot h}=1/h$ so area is still 1. The "distribution estimate" is meaningless at $n=1$, but the normalization identity ${\sum }_j{c}_j=n$ still forces area 1.

No curve is drawn for that level — the set $\{(x,y):f=10\}$ is empty, so it's silently skipped.