Dot Plots
A dot plot shows numerical data as dots stacked above a number line, one dot for each value. In NSW Year 7 maths it is one of the first displays that shows every value at a glance (NESA outcomes MA4‑DAT‑C‑01 and MA4‑DAT‑C‑02).
You will read frequencies and count the values, draw a dot plot from a list, find the mode, spot clusters, gaps and outliers, describe the shape as symmetrical or skewed, and compare two dot plots on the same scale. Recording how many minutes late the school bus is each day is a typical use. This subtopic is part of Year 7 Analysing Data.
Theory
A dot plot shows numerical data as dots above a number line. Each dot is one data value, and equal values stack up. The tallest stack is the mode. This Year 7 maths page shows how to read and draw dot plots, and how to describe clusters, gaps, outliers and shape.
Reading. The number of dots in a stack is the frequency of that value. The number of data values is the total number of dots.
Drawing. Draw an even scale from the smallest value to the largest, with a label and units. Tally each value, put one dot above it for each time it appears, then check the number of dots matches the number of values.
Mode. The mode is the most common value: the tallest stack. Data with two tallest stacks has two modes (bimodal).
Features. A cluster is a group of values close together. A gap is a part of the scale with no dots. An outlier is a value far away from the rest; look for a reason, such as a recording mistake.
Shape. Find the peak, then the tail (where the stacks thin out). Symmetrical: both sides match. Positively skewed: the tail goes to the right. Negatively skewed: the tail goes to the left.
Comparing two dot plots. Draw both on the same scale and compare where the peaks and clusters sit, how spread out they are, and any outliers.
Words for describing a dot plot:
| Word | Meaning |
|---|---|
| frequency | how many dots above a value |
| mode | the value with the tallest stack |
| cluster | values close together |
| gap | part of the scale with no dots |
| outlier | a value far from the rest |
| positively skewed | tail to the right |
| negatively skewed | tail to the left |
How to draw a dot plot
- Find the smallest and largest values and draw an even scale.
- Tally each value.
- Stack one dot per value, evenly spaced.
- Check the number of dots, and add a title and label.
(i) What was the range of marks?
(ii) What was the mode?
(iii) How many students scored above \(6\)?
| \(10 - 3\) | \(=\) | \(7\) |
| \(5 + 3 + 1 + 1\) | \(=\) | \(10\) |
(i) \(7\) (highest \(10\), lowest \(3\))
(ii) \(7\) (\(5\) students)
(iii) \(10\) students
(i) How many students are there?
(ii) What is the mode?
(iii) How many bought lunch more than \(2\) times?
| \(3 + 5 + 6 + 4 + 1 + 1\) | \(=\) | \(20\) |
| \(4 + 1 + 1\) | \(=\) | \(6\) |
(i) \(20\)
(ii) \(2\)
(iii) \(6\) (more than \(2\) means \(3\), \(4\) or \(5\))
Tally: \(0\) once, \(1\) twice, \(2\) once, \(3\) five times, \(4\) twice, \(5\) once. Check: \(1 + 2 + 1 + 5 + 2 + 1 = 12\).
The tallest stack is above \(3\): the mode is \(3\) trips.
(i) Describe the cluster and the gap.
(ii) Which time is an outlier?
(iii) How many took at most \(5\) minutes?
| \(2 + 4\) | \(=\) | \(6\) |
(i) Cluster from \(4\) to \(7\) min; gap from \(8\) to \(13\) min.
(ii) \(14\) min (that student may have started late).
(iii) \(6\) students (\(4\) or \(5\) minutes)
(i) How many students scored \(9\)?
(ii) Describe the shape of the data.
| \(1 + 1 + 2 + 3 + 5 + 6 + 3\) | \(=\) | \(21\) |
| \(25 - 21\) | \(=\) | \(4\) |
(i) \(4\)
(ii) The peak is at \(8\) and the tail goes to the left: negatively skewed.
Common pitfalls
Frequently asked questions
What does each dot on a dot plot show?
One data value. Equal values stack on top of each other.
How do you find the mode from a dot plot?
Find the tallest stack of dots. Its value is the mode.
What is an outlier?
A value far away from the rest of the data.
What does positively skewed mean?
Most values are low and the tail stretches to the right.
How do you count the number of values?
Count every dot on the plot.