Discover Mathematics P6: Term 1, Unit 6, Lessons 1–2
GoalMake and read a dot plot and describe its shape with the words peak, cluster, gap, symmetric and skewed.
New words
dot plot · a number line with one dot above the number for each data valuecluster · values that are close togethergap · an empty space where there are no datapeak · the tallest stack of dots, the most common valueskewed · a shape with a long tail on one side
Explanation
A dot plot shows numerical data on a number line. For every data value we put one dot above its number, and when a value repeats the dots stack up. So the number of dots equals the number of data values. Then we look at the shape. The peak is the tallest stack. A cluster is a group of dots close together. A gap is an empty space between dots. If the left and right sides look like mirror pictures, the shape is symmetric. If most dots are on one side and a long tail stretches to the other side, the shape is skewed. The tail pointing right is skewed right; the tail pointing left is skewed left.
★Remember
One dot = one value. Look for the peak, clusters, gaps and whether the shape is symmetric or skewed.
Worked examples
Twenty pupils were asked how many brothers and sisters they have. The peak is at 2 (7 pupils). Most pupils form a cluster from 0 to 3 (3 + 6 + 7 + 3 = 19 pupils). There is a gap at 4, and one pupil has 5.
Shoe sizes of 15 pupils: 2 pupils wear 35, 3 wear 36, 5 wear 37, 3 wear 38 and 2 wear 39. The left and right sides match around the peak at 37, so the shape is symmetric. Check: 2 + 3 + 5 + 3 + 2 = 15.
The walking times from before (5, 10, 15, 20, 25 minutes) give 5, 8, 4, 2 and 1 pupils. Most dots are on the left and the tail stretches to the right, so the shape is skewed right. It tells us that most pupils live close to school and only a few live far away.
Class activity
Dot plot with seeds. Ask ten people at home or in the street how many glasses of water they drink in a day. On a long strip of paper write the numbers, then put one dried bean above the number for each answer. Describe the shape: where is the peak, is there a gap?
Practice
1
The dot plot shows how many books 16 pupils carry in their bags. Which number of books is the peak? Where is the gap? How many pupils carry more than 5 books?
The peak is 3 books (6 pupils). The gap is at 5 and 6. The pupils with more than 5 books are those at 7: 2 pupils.
2
Is this dot plot symmetric? How many data values does it show?
Yes, it is symmetric around 3. It shows 2 + 4 + 6 + 4 + 2 = 18 values.
3
A dot plot has 14 dots. What does this tell you about the data?
There are 14 data values, because each dot stands for one value.
4
Most dots of a dot plot are at the left end and a long tail goes to the right. Is it skewed left or skewed right?
Skewed right, because the tail points to the right.
5
Make a dot plot of the data 2, 3, 3, 4, 4, 4, 5, 5, 7. Describe the peak and any gap.
Dots: 2 has 1, 3 has 2, 4 has 3, 5 has 2, 6 has 0, 7 has 1. The peak is at 4. There is a gap at 6.
