Reading a Line Plot
Each dot is one measurement. Stacks show repeats, so the tallest stack is the most common value and the spread left to right is the range.
A line plot puts an X above each value every time it occurs, so the picture shows both what values there are and how often. Tall stacks are common values; gaps are values nobody had. You can read the total count by counting the X marks and the most common value by finding the tallest stack.
Eight students counted the books they read this month: . Each number gets one X on the plot. The largest value is and the smallest is , so the range is .
In the same plot, the stack above has X's, more than any other, so books is the most common amount. The stack above is empty: nobody read exactly books.
Forgetting that each X is one data point. To find "how many measured more than ", count the X marks above every value bigger than , not the number of columns.
From the book plot, how many students read more than books?
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Count the X's to the right of : three above , one above , one above . students.
In Plain Terms & More Examples
Each dot is one measurement. The tallest stack is the most common value (the mode), and the distance from smallest to largest is the range.
For the values , the value appears most, so the mode is .
The largest is and the smallest is , so the range is .
Giving the count instead of the value. In the data the mode is , the value that appears most often, not , which is how many times it appears.
For the data , find the mode and the range.
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appears three times, more than any other value: the mode is . Range: .
Reading Fraction Line Plots
Measurements are often fractions ( inch, inch, inch). The plot works the same way: each X is one measurement stacked above its value.
A plot shows X's above , above , and above . There are measurements, and the most common is .
Suppose each X in that plot is an insect's length in inches. Laid end to end, the five -inch insects measure inches. Adding fractions from a plot means adding one fraction for every X.
Reading the scale wrong. On a line marked in quarters, the first tick after is , not , and the second is . Read the label under each tick, and work out the step between ticks before counting.
In that plot, how many measurements are greater than ? What is the difference between the largest and smallest values?
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Greater than : . Largest minus smallest: .
Making a Plot
To make a line plot:
- sort the data;
- draw a number line from the smallest value to the largest, with equal steps;
- put one X above the matching value for every data point;
- give it a title and label the units.
Sorting first makes the stacks easy to count. Equal steps keep distances honest, so a gap on the plot really means "no data here". A line plot drawn this way shows the whole data set with nothing hidden: you can always count the X's back into the original list.
Shoe sizes: . Sort them: . Put two X's above , three above , two above , one above .
Plant heights in inches: . The values go up in quarters, so mark the line from to in quarter-inch steps: . Then place the X's: one at , three at , one at , one at .
Leaving out values that have no data. If nobody's plant was inches tall, the tick for still belongs on the line. Skipping it would squeeze and together and make them look like neighbours. Every step gets a tick, even an empty one.
Using the shoe-size plot above, how many students are there, and which size is the mode (most common)?
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Count the X's: students. The tallest stack is size .
Bar Graphs
A bar graph shows how many are in each category: fruits, pets, days of the week. Read each bar's height against the scale on the side. The scale can count by s, s, s or more.
A line plot needs its values on a number line, but a bar graph also works for things that are not numbers, like favourite fruits. All the bars start at and use one scale, so you can compare them at a glance: a bar twice as tall stands for twice as many.
A class voted: apples , pears , grapes , oranges . How many more chose grapes than pears? more. How many voted altogether? students.
On this graph of books read, the gridlines go . Tuesday's bar stops halfway between and , so it shows . The other bars show Monday , Wednesday and Thursday . The four days total books.
Assuming every gridline is . On the books graph the gridlines go up by , so a bar reaching the third gridline above shows , not . Read the numbers on the scale, not the number of lines.
Use the fruit votes. How many fewer students chose oranges than grapes? Which fruit got fewer than half as many votes as grapes?
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Oranges , grapes : fewer. Half of is . Only pears, with votes, got fewer than that: pears.
Why It Works
A line plot is a picture of a frequency table. Counting the marks in a stack recovers the frequency, and the marks to the right of a value count the data above it, so every question about the data can be answered by counting marks. Because the values sit on a number line, distances mean something: the plot shows the spread (largest minus smallest) at a glance, which a bar chart of categories cannot.
Do not read a proof the way you read a rule. Cover the last line, ask what the previous line forces, and only then uncover it. If a step feels like magic, that is the step to work by hand with a concrete number.