A bar chart's bar height shows frequency. A histogram's bar area shows frequency — because class widths can be unequal, and area is the only way to avoid a wide class looking artificially huge. This means the $y$-axis is never labelled "Frequency"; it's always Frequency Density:

Bars always touch (continuous data has no gaps between classes), and they can never be reordered, since the $x$-axis is a genuine numerical scale.

This is rounded, not genuinely gapped, data — the real boundary between $10$–$19$ and $20$–$29$ is the midpoint, $19.5$. The fastest reliable method: subtract the lower limits of two consecutive classes.

For each class: find the class width, then $FD=\dfrac{F}{CW}$, then draw a bar of that width and height. The bars must touch and the $y$-axis must be labelled Frequency Density.

Worked example: Class $40\le d<60$ with frequency $12$: $CW=20$, so $FD=\dfrac{12}{20}=0.6$.

Rearrange the same relationship: $F=FD\times CW$ — read the bar's height (FD) and width (CW) straight off the axes.

Worked example: a bar spans $60$ to $70$ with height $0.8$: $F=0.8\times10=8$.

Use one bar whose true frequency you're told, convert it to the frequency density it must represent, then divide by its measured height (e.g. in squares) to find what one square is worth. Apply that conversion factor to read every other bar.

Use linear interpolation — assume the data is spread evenly across each class.

where $L$ is the lower boundary of the class containing the median, $F$ is the cumulative frequency before that class, $f$ is that class's own frequency, and $w$ is its width. (For $Q_1$ use position $\frac n4$; for $Q_3$ use $\frac{3n}4$, with the matching class's $L,F,f,w$.)

Worked exam-style question: Weights (kg): $4\le w<8$ ($F{=}4$), $8\le w<10$ ($F{=}16$), $10\le w<12$ ($F{=}19$), $12\le w<15$ ($F{=}12$), $15\le w<30$ ($F{=}9$). Total $n=60$. Estimate the median.

1. Median position: $\dfrac{60}{2}=30$th value.
2. Cumulative frequencies: $4,\ 20,\ 39,\ 51,\ 60$. The 30th value falls inside the $10\le w<12$ class (since CF passes 30 between 20 and 39).
3. $L=10$, $F=20$ (CF before), $f=19$, $w=2$.

• Treating frequency density as if it were frequency, especially when reading bar heights directly.
• Getting the class width wrong for "gapped" rounded data.
• Using the class midpoint instead of proper interpolation for the median/quartiles.
• Comparing two histograms with different class widths or scales as if they were directly comparable.