9.7 Line Plots, Dot Plots, & Picture Graphs
Key Takeaways
- A line plot (dot plot) marks each data value with an X or dot above a number line, so the height of a stack is the frequency of that exact value.
- Line plots on TABE frequently use fractional scales in halves, quarters, and eighths of an inch, which turns a graph-reading item into a fraction-arithmetic item.
- A picture graph uses a symbol to stand for several units, and the key tells you the multiplier — half a symbol means half of that value.
- A scaled bar graph must be read from its axis scale, not from the number of gridlines, because each interval may represent 2, 5, 10, or more units.
Line Plots, Dot Plots, & Picture Graphs
Section 9.2 covered frequency tables, bar graphs, line graphs, and histograms. The DRC specification also assigns three displays specifically to the lower levels: picture graphs and scaled bar graphs with several categories, and line plots — including line plots "marked off in appropriate units — whole numbers, halves, or quarters" and, at Level M, in eighths of an inch.
Line Plots (Dot Plots)
A line plot, also called a dot plot, places a number line horizontally and stacks one mark for each data value directly above its position.
Number of overtime hours worked last week (14 employees)
X
X X
X X X
X X X X X X
──┼────┼────┼────┼───┼────┼──
0 1 2 3 4 5
Reading it:
| Question | Method | Answer |
|---|---|---|
| How many employees worked exactly 2 hours? | count the stack above 2 | 4 |
| How many employees in total? | count all marks | 14 |
| What is the mode? | tallest stack | 2 hours |
| What is the range? | largest minus smallest | $5 - 0 = 5$ hours |
| How many worked more than 3 hours? | stacks above 4 and 5 | $2 + 1 = 3$ |
| Total overtime hours paid? | $\sum (\text{value} \times \text{frequency})$ | $0(2)+1(1)+2(4)+3(1)+4(2)+5(1) = 26$ |
The most-missed line-plot question asks for the total of the values, not the number of data points. Two employees at 4 hours contribute 8 hours, not 2. Multiply each value by the height of its stack, then add.
Line Plots With Fractional Scales
This is the version TABE actually favors, because it tests fractions and graph reading at once.
Lengths of 12 bolts, measured to the nearest 1/8 inch
X
X X
X X X X X X
──┼────┼────┼────┼────┼────┼──
1½ 1⅝ 1¾ 1⅞ 2 2⅛
Two skills combine here:
- Read the scale. Between $1\frac{1}{2}$ and 2 there are four spaces, so each tick is $\frac{1}{8}$ inch.
- Compute with the values. "What is the difference between the longest and shortest bolt?" is $2\frac{1}{8} - 1\frac{1}{2} = 2\frac{1}{8} - 1\frac{4}{8} = \frac{5}{8}$ inch.
Worked total. "What is the combined length of all the bolts measuring 2 inches?" Two marks sit above 2, so $2 \times 2 = 4$ inches.
Worked redistribution. "If all the liquid in the beakers were redistributed equally, how much would each hold?" That question is asking for the mean: total the values, divide by the number of data points. TABE words it as redistribution rather than as "mean," and learners who do not recognize the phrasing lose the item.
Picture Graphs (Pictographs)
A picture graph uses a repeated symbol, and the key states what one symbol represents.
Books checked out (Key: 📕 = 10 books)
Monday 📕📕📕📕
Tuesday 📕📕📕📕📕📕
Wednesday 📕📕📕◗ (◗ = half symbol)
Thursday 📕📕📕📕📕
| Day | Symbols | Books |
|---|---|---|
| Monday | 4 | 40 |
| Tuesday | 6 | 60 |
| Wednesday | 3½ | 35 |
| Thursday | 5 | 50 |
The two rules:
- Always read the key first. The same picture graph means completely different things with a key of 10 versus a key of 100.
- A partial symbol is a fraction of the key value. Half a book symbol with a key of 10 is 5 books, not 1.
Typical questions: How many more books on Tuesday than Wednesday? $60 - 35 = 25$. How many books in all four days? $40 + 60 + 35 + 50 = 185$.
Scaled Bar Graphs
A scaled bar graph labels its axis in steps larger than 1. Read the scale before reading any bar.
| If the axis is labeled… | one gridline is… | a bar reaching 3 gridlines is… |
|---|---|---|
| 0, 5, 10, 15 with 1 line each | 5 | 15 |
| 0, 10, 20, 30 with 2 lines each | 5 | 15 |
| 0, 20, 40, 60 with 4 lines each | 5 | 15 |
The bars look identical; only the axis distinguishes them. TABE writes distractors by scaling the answer as if the axis stepped by 1.
Bars that end between gridlines are estimated to the nearest half interval. If gridlines are 10 apart and a bar ends midway between 30 and 40, report about 35.
Choosing the Right Display
| Display | Best when |
|---|---|
| Line plot / dot plot | small data set, want to see every individual value and its repeats |
| Picture graph | comparing a few categories for a general audience |
| Scaled bar graph | comparing categories with large counts |
| Histogram | continuous numerical data grouped into intervals (see Section 9.2) |
The distinction TABE tests most often is bar graph versus histogram: bar graphs display separated categories and their bars have gaps; histograms display continuous intervals and their bars touch.
A line plot records the daily rainfall in inches over 10 days, marked in quarter inches. Two marks sit above 1/4, three above 1/2, four above 3/4, and one above 1. What is the total rainfall over the 10 days?
A picture graph shows deliveries by week with a key stating that one truck symbol equals 25 deliveries. Week 3 shows three full symbols and one half symbol. How many deliveries occurred in week 3?