Representing a Quantitative Variable with Graphs

Seeing the shape of numbers

• For a quantitative variable, we want to see how the values are distributed — clustered, spread, symmetric?
• Three standard displays reveal this: the histogram 直方图, dotplot 点图, and stem-and-leaf plot 茎叶图.
• Each shows the same data differently, but all reveal the overall shape.
• Reading these plots is where "describing a distribution" begins.

Histograms and bins

• A histogram groups values into intervals called bins 组距, then draws a bar for each bin's count.
• Unlike a bar chart, the bars touch — the scale is continuous.
• Bin choice matters: too few bins hide the shape; too many make it noisy. Aim for a number that reveals the real pattern.
• Taller bars = more data in that interval.

On a histogram with unequal class widths the bar area is the frequency

Dotplots and stem-and-leaf

• A dotplot stacks one dot per value above a number line — great for small data sets, keeps every value.
• A stem-and-leaf plot splits each number into a stem (leading digits) and leaf (last digit), so you see shape and the actual values.
• Both are best for small-to-moderate data; a histogram handles large sets.
• All three answer "where do the values pile up?"

Cumulative graphs (ogives)

• A cumulative relative frequency graph (ogive 累积频率图) plots the running total proportion up to each value.
• It rises from $0$ to $1$ (or $0\%$ to $100\%$).
• Read a percentile from it: go up to a value, read across to the proportion below it.
• Great for questions like "what score is the $75$th percentile?"

Write from bins on a histogram

• Quiz scores are numbers from 0 to 20.
• The display groups them into intervals.