AP Statistics · Unit 1 · Topic 1.5

Dotplots, Stemplots, and Histograms Study Lab

A quantitative variable is graphed on a number line so that distances between values mean something. Each display trades detail for readability. Switch among four graphs of the same data, change the histogram's bins, and read percentiles off a cumulative plot.

1. One data set, four graphs

Dotplots, stemplots, histograms, and cumulative relative frequency plots all put a quantitative variable on a number line. Change the graph and the histogram's bins to see what each display shows and hides.

Preset data sets

Graph

Controls

Bin width Wider bins smooth the shape; narrower bins show more detail and more noise.

Shift the bin start Same data, same width, different boundaries.

Y-axis

Stems

Read the plot at x = The height tells you the proportion of values at or below x.

See the raw data

Min to max

2. Key ideas

Dots

Dotplot

One dot per value above a number line, stacked when values repeat. Shows every value; best for small data sets.

Stems

Stemplot

Splits each value into a stem (leading digits) and a leaf (last digit). Keeps the actual values and shows the shape. Always include a key.

Bins

Histogram

Bars over equal-width intervals of values; bar height is the count or proportion in that bin. Bars touch because the bins cover a continuous number line.

Choices

Bin width matters

Too many bins make a jagged graph; too few hide the shape. Different reasonable choices should tell the same overall story.

Running total

Cumulative relative frequency

Plots the proportion of values at or below each x. Use it to find percentiles, the median (0.5), and quartiles (0.25 and 0.75).

Vs. categorical

Histogram vs. bar chart

A histogram's x-axis is a number scale, so the bars touch and their order is fixed. A bar chart's categories can be rearranged and are separated by gaps.

3. Choosing a display

Each graph's strengths and limits.

Display	Shows individual values?	Best for	Watch out for
Dotplot	Yes	Small data sets, seeing gaps and outliers	Gets crowded with large n
Stemplot	Yes	Small to moderate data sets, finding the median by hand	Needs a key; awkward with decimals or wide ranges
Histogram	No	Large data sets, seeing shape	Shape depends on bin width and start
Cumulative relative frequency plot	No (shows running proportions)	Percentiles, median, quartiles	Reading the y-axis as a count instead of a proportion

4. On the FRQ

How to earn the points

Label the horizontal axis with the variable and units (“Commute time, minutes”) and use an evenly spaced scale.
Give every stemplot a key with units: “4 | 7 = 47 seconds.”
When asked to estimate from a histogram, explain the reasoning: “About 12 + 9 = 21 of the 50 values are below 30, so about 42%.”
For percentile questions with a cumulative plot, show where you read the graph and state the result in context.

Common mistakes

Leaving gaps between histogram bars or drawing a histogram of categorical data.
Forgetting the stemplot key, or not putting leaves in order.
Placing a boundary value in the bin to its left instead of to its right.
Reading a cumulative relative frequency plot's height as the count at a single value.

5. Practice questions

AP-style multiple choice. Pick an answer to see the explanation.

0 / 0 correct

6. Key terms

The vocabulary for topic 1.5. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 1 terminology guide.