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All courses Math I · S-ID.1 50 of 59
Represent one-variable data with dot plots, histograms, and box plots.

Create a dot plot from a small data set

Problem
Construct the dot plot for data 2,2,3,5,5,5,6 using axis ticks 2 through 6 by 1. Give the axis ticks, count at each tick, total dots, and maximum stack.
Source statistical display: Which record correctly specifies the dot plot for data {2,2,3,5,5,5,6} using axis ticks 2 through 6 by 1? No requested counts, analysis, or box-plot conclusion is annotated. Open full size
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Hint

List every tick in order, tally every datum once, then sum the frequencies back to n.

One dot represents one observation. A complete non-drawing specification includes zero-count ticks so spacing and gaps are preserved.

Solution walkthrough

01

Write every required axis tick

\[\text{axis}=2,3,4,5,6\]

The prompt fixes ticks from 2 through 6 by 1, so tick 4 must remain even though its frequency is zero.

02

Tally each data value

\[2:2;~3:1;~4:0;~5:3;~6:1\]

In 2,2,3,5,5,5,6, 2 occurs twice, 3 once, 4 never, 5 three times, and 6 once.

03

Check the total number of dots

\[2+1+0+3+1=7\]

The frequencies sum to the seven observations in the source data, so every value is counted exactly once.

04

Find the tallest stack

\[\text{maximum}~\text{frequency}=3~\text{at}~\text{value}~5\]

The stack over 5 has three dots, more than the stack over any other tick.

05

Report the complete dot-plot record

\[\text{axis}~=~2,3,4,5,6;~\text{counts}~=~{2:2,3:1,4:0,5:3,6:1};~\text{total}~\text{dots}~=~7;~\text{maximum}~\text{stack}~=~3~\text{dots}~\text{at}~5\]

This non-drawing specification preserves the axis, every frequency including the gap, the total, and the maximum stack.

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Another way

  1. Mark off each datum from the raw list as it is added to a five-row frequency table, then convert each frequency to a vertical dot stack.

!

Common mistake

Do not omit tick 4. A zero-count tick preserves the equal spacing and makes the gap in the distribution explicit.

Worked statistical display: axis = 2,3,4,5,6; counts = {2:2,3:1,4:0,5:3,6:1}; total dots = 7; maximum stack = 3 dots at 5
axis = 2,3,4,5,6; counts = {2:2,3:1,4:0,5:3,6:1}; total dots = 7; maximum stack = 3 dots at 5