D. Data · Data and ProbabilityFinding the Mode
D1.4About 35 minutes
Learning goals- I can find the mode of a set of data: the answer that happens most often.
- I can find the mode in a table, pictograph, concrete graph, line plot, and bar graph.
- I can tell when a set of data has two modes or no mode.
- I can explain what the mode tells us about the data.
Words to know
mode
The answer that appears most often in a set of data. It is the most common answer.
frequency
How many times an answer appears in the data.
two modes
When two answers are tied for appearing most often, both are modes.
no mode
When every answer appears the same number of times, there is no mode.
Let's get started!
Your class is planning a pizza lunch. Most people want cheese pizza, a few want pepperoni, and only 2 want veggie. Which kind should you order the most of?
The answer chosen most often has a special math name: the mode!
What is the mode?
The mode is the answer that shows up most often in a set of data.
Here are the favourite colours of 9 kids:
blue, red, blue, green, blue, red, yellow, blue, green
- blue: 4 times
- red: 2 times
- green: 2 times
- yellow: 1 time
Blue appears most often. So the mode is blue.
Mode sounds like most
A trick to remember: mode and most both start with mo. The mode is the most common answer.
Finding the mode in graphs
Each kind of graph shows the mode in its own way:
- Table or tally chart: the biggest number, or the most tallies.
- Concrete graph or pictograph: the longest row (or tallest column) of objects or pictures.
- Bar graph: the tallest (or longest) bar.
- Line plot: the number with the tallest stack of Xs.
🍎🍎🍎🍌🍌🍌🍌🍌🍌🍇🍇🍇🍇
A concrete graph of favourite fruits. The banana row is the longest, so the mode is banana.Worked exampleMode in a line plot
Ms. Kaur's class asked, "How many pets live in your home?" Look at the line plot. What is the mode?
- Look for the tallest stack of Xs.
- Above 0 there are 4 Xs. Above 1 there are 7 Xs. Above 2 there are 3. Above 3 and 4 there is 1 each.
- The tallest stack is above 1.
The mode is 1 pet. Having 1 pet is the most common answer in this class.
Line plot of the number of pets. Source: survey of Ms. Kaur's class.Careful!
The mode on a line plot is the number with the most Xs. It is not the biggest number on the line, and it is not how many Xs there are. In the pet line plot, the mode is 1 (not 4, and not 7).
Just for funWhy was the number 2 so popular in the survey?
It was the mode: more people picked it than any other number! 🎉
Two modes or no mode
Sometimes two answers are tied for most often. Then the data has two modes.
Sometimes every answer appears the same number of times. Then there is no mode, because no answer is more common than the others.
Worked exampleTwo modes in a bar graph
Look at the bar graph Favourite Snow Activity. What is the mode?
- Find the tallest bars.
- Skating 6, Sledding 9, Building a snowman 9, Skiing 4.
- Two bars are tied for tallest at 9.
There are two modes: sledding and building a snowman.
Worked exampleNo mode
Ella tossed a counter onto a mat with 3 colours, 6 times. She landed on red, blue, yellow, blue, red, yellow. What is the mode?
- Count each: red 2, blue 2, yellow 2.
- Every answer appears the same number of times. No answer appears most often.
What does the mode tell us?
The mode tells us the most common or most popular answer.
- If the mode of favourite fruit is banana, then more children chose banana than any other fruit.
- It helps us make decisions: buy more bananas for the class snack!
The mode does not tell us that everyone likes bananas. Some children chose other fruits.
| Snack | Number of children |
|---|
| Crackers | 5 |
| Cheese | 8 |
| Grapes | 5 |
| Carrots | 3 |
Hands-on activityMode hunt at home
- Grab a handful of something with different colours: crayons, LEGO bricks, buttons or fruit snacks.
- Sort them by colour into rows, like a concrete graph.
- Which colour has the longest row? That is the mode!
- Is there a tie? Then you have two modes.
- Now try: look at the first 10 cars that drive by and tally their colours. Find the mode. (In many places, white, black or grey are common, but your street might be different!)
Math talk: "What does the mode tell us about these crayons?"
Your turn
1What is the mode of this data? cat, dog, dog, fish, dog, cat
Dog. Dog appears 3 times, cat 2 times, fish 1 time.
2Use the snack table above. What is the mode?
Cheese, with 8. It is the biggest number.
3Use the pet line plot. How many children have 0 pets?
4What is the mode of these numbers? 3, 5, 5, 2, 3, 5
5. It appears 3 times. 3 appears 2 times and 2 appears 1 time.
5What is the mode? red, blue, red, blue, green
There are two modes: red and blue. Each appears 2 times.
6What is the mode? 1, 2, 3, 4
No mode. Every number appears just once.
7The mode of favourite season in a class is summer. What does that tell you?
Summer was chosen by more children than any other season. It does not mean everyone chose summer.
More practice: warm-up
1What is the mode? ⭐⭐⭐ ❤️❤️ 🔵
Star (⭐). It appears the most, 3 times.
2What is the mode? 4, 4, 4, 1, 2
3In a bar graph, how do you find the mode?
Look for the tallest (or longest) bar.
4In a line plot, how do you find the mode?
Look for the number with the tallest stack of Xs.
The answer that appears most often in the data.
More practice: on your own
1Tally table: skating: one bundle and 1 more; hockey: one bundle and 3 more; skiing: 4 lines. What is the mode?
Skating 6, hockey 8, skiing 4. The mode is hockey, with 8.
2Lunch boxes: 5 blue, 5 red, 3 green, 2 yellow. What is the mode?
Two modes: blue and red. They are tied with 5 each, and 5 is the most.
3Liam says the mode of the pet line plot is 4, because 4 is the biggest number. Is he right?
No. The mode is the number with the most Xs. That is 1 (7 Xs). Only 1 child has 4 pets.
4A pictograph: 🍁 = 1 child. Fall: 🍁🍁🍁🍁🍁. Winter: 🍁🍁🍁. Spring: 🍁🍁🍁🍁🍁🍁. Summer: 🍁🍁🍁🍁. What is the mode?
Spring, with 6 pictures (the longest row).
5Number of siblings for 8 kids: 1, 0, 2, 1, 1, 3, 0, 1. What is the mode?
Count: 0 appears 2 times, 1 appears 4 times, 2 once, 3 once. The mode is 1.
Challenge
1Change ONE answer in this data so that it has no mode: red, red, blue, green. (Hint: there are 4 answers.)
Change one red to a new colour, like yellow: red, yellow, blue, green. Now every colour appears once, so there is no mode. (Other answers that make every colour appear once are also correct.)
2Hot lunch votes: pizza 7, pasta 5, soup 6. Two more kids vote, and now there are two modes. What did they vote for?
There are two ways. Both voted pasta: pizza 7, pasta 7, soup 6, so the modes are pizza and pasta. Or one voted soup and one voted pasta: pizza 7, soup 7, pasta 6, so the modes are pizza and soup. (If anyone voted pizza, pizza would have 8 and be the only mode.)
3The mode of favourite fruit in a class is apple, with 7 votes. There are 20 children. Can you say most of the class likes apples best?
No. 7 is the most votes for one fruit, but 20 − 7 = 13 children chose other fruits. So more children did not choose apple. The mode is just the most common single answer.
Quiz
2. What is the mode? 2, 6, 6, 3, 6, 2
3. In a bar graph, the mode is shown by...
4. What is the mode? blue, green, red, yellow
5. What is the mode? hat, mitt, hat, scarf, mitt
6. A line plot has 2 Xs above 0, 5 Xs above 1, 3 Xs above 2. What is the mode?
7. The mode of favourite drink is milk. What does that tell you?
What your child is learning: to identify the mode (the most frequent answer) of data shown in tables, concrete graphs, pictographs, line plots and bar graphs, to recognize data with two modes or no mode, and to explain what the mode tells us (Ontario expectation D1.4).
Common difficulties:
- On a line plot, giving the biggest number on the line, or the number of Xs, instead of the number with the most Xs.
- Missing a tie. Encourage your child to check all the categories before deciding.
- Thinking the mode means "everyone" or "more than half". The mode is only the single most common answer.
At home: look for modes everywhere: the most common colour of car on your street, the most common number rolled on a die in 10 rolls, the snack chosen most often this week. Ask, "Is there a tie? What does this tell us?"