A dot plot is a graph that shows each data value as a dot above its place on a number line. Dots for repeated values stack up in a column, so the tallest stack shows the mode, and you can see the center, spread, gaps and outliers of the data at a glance.
In Spanish
diagrama de puntos
Also called
dot diagram, line plot (in Common Core), dot chart
One dot per data value. Stacks show how often each value occurs, so the shape of the data, its peak at 1 and its gap at 4 jump out.
Formal definition and notation
A dot plot displays a numerical data set by drawing a number line that covers the data and placing one dot (or X) above the line for each observation, stacking dots for equal values at equal spacing. It shows the distribution of the data: its center, its spread and its overall shape, including clusters, gaps, peaks and unusual values. It suits small to medium data sets where each value can be shown individually.
Symbol
Read it as
Meaning
●
dot
one data value (one person, one day, one trial)
×
X
some books draw an X instead of a dot; it means the same thing
Key facts
Count the dots to get the number of data values, n.
The tallest stack is the mode. The middle dot, counting from either end, is the median.
Space the number line evenly and include values with no dots, so gaps show up.
Dot plots show every value, so you can rebuild the data list from the plot.
Common Core calls this kind of graph a line plot in grades 2 to 5 and a dot plot from grade 6 on.
In Common Core, a line plot (grades 2 to 5) and a dot plot (grade 6 on) are the same kind of graph: marks above a number line. Outside school, “line plot” sometimes means a line graph, which connects points over time.
A histogram groups values into intervals and draws bars, so single values are lost. A dot plot shows every value.
Quick check: 3 questions
Question 1 of 3
A dot plot has 2 dots over 3, 5 dots over 4 and 1 dot over 6. How many data values are there?
Show answer and explanation
Answer: D. Count every dot: 2 + 5 + 1 = 8. 3 counts stacks, 13 adds the values 3 + 4 + 6, and 5 is only the tallest stack.
Question 2 of 3
In a dot plot, what does the tallest stack show?
Show answer and explanation
Answer: B. The tallest stack is over the value that occurs most often, which is the mode. The median is the middle dot, the mean is the balance point, and the range is the distance between the end dots.
Question 3 of 3
A dot plot shows 1 dot at 1, 3 dots at 2, 3 dots at 3 and 2 dots at 4. What is the median?
Show answer and explanation
Answer: A. There are 9 dots, so the median is the 5th from the left. Dot 1 is at 1, dots 2 to 4 are at 2, and dot 5 is at 3. 2.5 is the middle of the axis, 2 is a mode, and 4 is the maximum.
Dot Plot: frequently asked questions
What is the difference between a dot plot and a line plot?
In US school math they are the same picture: marks stacked above a number line, one mark per value. Common Core uses the name line plot in grades 2 to 5 and dot plot from grade 6 on. Be careful: some people use “line plot” to mean a line graph, which is a different display.
How do you find the mean from a dot plot?
Multiply each value on the number line by the number of dots above it, add those products, and divide by the total number of dots. For 2 dots at 10, 4 at 15, 3 at 20 and 1 at 25, the mean is 20 + 60 + 60 + 2510 = 16.5.
Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6ModeThe mode is the value that appears most often in a data set. To find it, count how many times each value occurs and pick the most frequent one. A data set can have one mode, more than one mode, or no mode at all when every value appears only once. The mode works for categories, too.Statistics · Grade 5, Grade 6, Grade 7OutlierAn outlier is a data value that is far away from most of the other values in a set. In 4, 5, 6, 7, 50, the value 50 is an outlier. A common test flags any value more than 1.5 times the interquartile range below the first quartile or above the third. Outliers pull the mean strongly.Statistics · Grade 6, Grade 7, Grade 8DataData are facts or values collected to answer a question, such as survey answers, measurements or counts. Numerical data are numbers you measure or count, like heights; categorical data are labels or groups, like favorite colors. Data are organized in tables and shown in graphs so patterns are easy to see.Statistics · Grade 2, Grade 3, Grade 6NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2MedianThe median is the middle value when data are listed in order. If there is an even number of values, the median is the average of the two middle values. Half the data lie at or below the median and half at or above it, and outliers barely move it.Statistics · Grade 5, Grade 6, Grade 7Line PlotA line plot shows data values along a number line, often with marks above each value. Each X or dot stands for one data value, and repeated values stack in a column, so the tallest stack is the mode. Line plots make it easy to see clusters, gaps, outliers and the spread of a small data set.Statistics · Grade 3, Grade 4, Grade 5HistogramA histogram uses bars to show how numerical data are grouped into intervals. The data are split into equal-width intervals, called bins, and each bar’s height is the count of values in that interval. The bars touch, because the intervals are continuous, which is what distinguishes a histogram from a bar graph.Statistics · Grade 6, Grade 7, Grade 8Box PlotA box plot displays a data set through five numbers: minimum, first quartile, median, third quartile, and maximum. The box holds the middle half of the data, a line inside it marks the median, and whiskers reach out to the smallest and largest values. It makes spread easy to compare between sets.Statistics · Grade 6, Grade 7, Grade 8SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2HeightHeight is how tall something is: the distance from its bottom to its top, measured straight up and down. In geometry, the height of a shape is the perpendicular distance from a base to the opposite vertex or side, so it always meets the base at a right angle. Area and volume formulas use it.Measurement · Grade 2, Grade 5, Grade 6Scatter PlotA scatter plot displays paired numerical data as points on a coordinate plane, one point for each pair. It helps show whether two quantities have a pattern or relationship: points rising from left to right show a positive association, points falling show a negative association, and a shapeless cloud shows no association.Statistics · Grade 8, Algebra 1Mean Absolute DeviationThe mean absolute deviation (MAD) is the average distance between each data value and the mean. Find the mean, find how far each value is from it, then average those distances. A small MAD means the data cluster close to the mean; a large MAD means they are spread out.Statistics · Grade 6, Grade 7Bar GraphA bar graph uses bars to compare amounts in different categories. The taller or longer the bar, the larger the value it represents. Each bar stands for one category, such as a favorite sport, and its length is read against a number scale. Bars can be vertical or horizontal, with gaps between them.Statistics · Grade 3, Grade 4, Grade 5