Categorical data sorts things into groups, such as eye color. Quantitative data measures an amount, such as height. If averaging the values would be meaningless, the data is categorical. Categorical data suits bar charts; quantitative data suits dot plots, histograms and box plots.
Step 1: Picture It
Start with something you already know.
Bins in a closet, marks on a tape
- A closet has three bins: hats, scarves and gloves.
- The bins can stand in any order on the shelf.
- Nothing belongs between the hat bin and the scarf bin.
- A measuring tape is different: 152 cm comes after 151 cm and before 153 cm.
- Every mark has its place in order, and further along always means more.
Categorical data is the bins: separate groups in no fixed order, so a bar chart keeps a gap between its bars.
Quantitative data is the tape: amounts in order, where a bigger mark means more, so histogram bars touch.
Where the picture falls short: a count such as pets lands only on whole marks, yet it is still on the tape; and the count in a bin is a number, but the data is still which bin each thing went in.
Step 2: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Five friends list two things. Pets at home: 1, 2, 2, 2 and 3, which average 2. Locker numbers: 104, 215, 230, 318 and 333, which average 240. Which average tells you something about the friends?
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Numbers can still be categorical
Jersey numbers are digits, yet the average jersey number tells you nothing. Postcodes, phone numbers, ID codes: labels that look numeric. Ask whether the average would mean anything.
Sorting a list
Shoe size: quantitative, an amount. Favorite subject: categorical. Number of siblings: quantitative, a count. Bus route number: categorical, a label. Temperature: quantitative.
The gap matters
Bar chart bars stand apart because the categories are separate: nothing lies between "blue" and "green". Histogram bars touch because the numbers run continuously: 165 cm sits between 160 and 170.
What to look for
Describe shape, center and spread, and mention any outlier. Shape: symmetric, skewed, or with two peaks. Centre: where the middle sits. Spread: how far the values reach. Those four together describe a distribution.
Reading a histogram
Bars at 150–155: 2, 155–160: 6, 160–165: 12, 165–170: 11, 170–175: 7, 175–180: 2. Roughly symmetric, centered near 165 cm, spread from 150 to 180, no outliers. Four facts, one sentence.
Why the choice matters
The wrong display hides the story. A bar chart of heights loses the shape; a histogram of eye colors invents an order the colors never had. The graph should match what the data can say.
Step 3: Try It Yourself
Tap and try it out.
Classify each and name a display: favorite subject, minutes of homework, bus route number, number of pets
- Answerfavorite subject: an average subject is meaningless, categoricala bar chart, bars apart
Step 0 of 3
Apple
Banana
Cherry
Cherry has the most. It has 5 more than Banana.
Step 4: In Real Life
A school report
Favorite subjects are categories: a bar chart. Test scores are numbers: a histogram. A newspaper that puts categories on a histogram is misleading its readers before saying a word.
Step 5: Watch an Example
One step at a time.
Watch Leo Graph a Trip to School
Leo asked 30 students two things: how they get to school (walk, bus, car or bike) and how many minutes the trip takes. He wants one graph for each answer.
- Step 1
The averaging test comes first. An "average way to school" halfway between bus and bike means nothing, so the way to school is categorical. An average trip of 12 minutes does mean something, so trip time is quantitative.
Watch Ana Sort a Cafe’s Receipts
A cafe kept three things from each of 40 receipts: the table number (1 to 12), the bill in dollars, and the first drink ordered. Ana wants a fitting graph for each one.
- Step 1
The same test settles every column: would an average of these values mean anything? The type decides the graph, so the type comes first each time.
Step 6: Your Turn
Practice makes it stick.
The Bake Sale
Problem 1 of 15
A bake sale grouped its 20 sales by price in a histogram: $0–$2: 6 sales, $2–$4: 8 sales, $4–$6: 4 sales, $6–$8: 2 sales. Each bar runs from its first price up to, but not including, its second. How many sales were for $4 or more?
sales
The Fun Run
Problem 2 of 15
A histogram shows 25 runners’ finishing times: 20–25 minutes: 2 runners, 25–30: 6, 30–35: 9, 35–40: 6, 40–45: 2. Which sentence describes the distribution?
Name the Data, Pick the Graph
Ask whether an average would mean anything. The type decides the graph.
Problem 3 of 15
The number of text messages each student sent yesterday. Which kind of data is it?
Problem 4 of 15
Each student’s favorite kind of music. Which kind of data is it?
Problem 5 of 15
The number printed on each raffle ticket sold at a fair. Which kind of data is it?
Problem 6 of 15
A survey records the kind of pet each student owns: dog, cat, fish or none. Which graph fits?
Problem 7 of 15
A histogram of reading time has these bars: 0–10 minutes: 4 students, 10–20 minutes: 9, 20–30 minutes: 5, 30–40 minutes: 2. How many students does the histogram show?
students
Whose Step?
Each page has one line that slipped. Find it, then put it right.
Problem 8 of 15
A help line logged the area code of each of 50 callers. Dev chose a graph for them. One line is a slip. Which?
Dev’s working: 50 callers’ area codes, and a graph for them
- 1area codes such as 212, 312 and 415
- 2they are numbers, so the data is quantitative
- 3quantitative data gets a histogram
- Answera histogram of area codes, bars touching
Problem 9 of 15
Which graph fits the 50 callers’ area codes?
Problem 10 of 15
A histogram shows 20 students’ homework time: 0–15 minutes: 3, 15–30: 7, 30–45: 9, 45–60: 1. Each bar runs from its first number up to, but not including, its second. Maya worked out how many spent less than 30 minutes. One line is a slip. Which?
Maya’s working: how many spent less than 30 minutes?
- 1bars: 0–15: 3, 15–30: 7, 30–45: 9, 45–60: 1
- 2less than 30 minutes: the bars 0–15, 15–30 and 30–45
- 33 + 7 + 9 = 19
- Answer19 students spent less than 30 minutes
Problem 11 of 15
From the same histogram, how many students spent less than 30 minutes on homework?
students
Pick the Move
Which move settles it? No full working is needed here.
Problem 12 of 15
A new column of survey answers arrives, and you need a graph for it. Which question settles what kind of data it is?
Problem 13 of 15
Noor recorded the shoe size of each of 25 runners, from 6 to 11 in half sizes. She wants to see how the sizes are spread. Which graph fits?
Same Kind?
Judge each one by the averaging test, without drawing anything.
Problem 14 of 15
Select every variable that is the same kind of data as the number of siblings a student has.
Problem 15 of 15
Select every variable that would be graphed the same way as eye color: a bar chart, with gaps between the bars.
Step 7: Quick Check
Show what you know.
Question 1 of 2
Hair color is which kind of data?
Question 2 of 2
Why do histogram bars touch while bar chart bars do not?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
Sam wants to invent 12 values for a histogram with four bars, 0–10, 10–20, 20–30 and 30–40, that is perfectly symmetric: the bars mirror each other about the middle. The 10–20 bar must hold 4 values. How many values go in the 0–10 bar?
values
Stretch 2 of 2
Ravi codes 20 students’ eye colors as brown = 1, blue = 2, green = 3. There are 12 brown, 5 blue and 3 green, and his average code is 1.55. Ana codes the same students as brown = 3, blue = 2, green = 1. What average does Ana get, and what does it show?
What You Learned
- Categorical data sorts; quantitative data measures.
- If averaging the values is meaningless, the data is categorical, however numeric it looks.
- Bar charts for categories, bars apart; histograms for amounts, bars touching.
- Describe a distribution by shape, center, spread and outliers.
For the grown-up
The misconception this lesson targets is "if it is written in numbers, it is quantitative." Locker numbers, area codes, ZIP codes and jersey numbers all look like amounts and are labels, and a student who sorts by appearance will happily average them and draw a histogram. The one habit that cures it is the averaging test: ask out loud whether an average would describe anyone. A quieter cousin turns up on histograms: reading the bar heights as the data, so that counts of runners get described as if they were race times. When a child describes a graph, ask which numbers are the values and which are only how many.