Warm-up
Three quick ones from earlier work. Try each in your head or on paper before you open the answer.
- (Unit 1, lesson 1) Write nine and four hundredths as a decimal.
Answer
9.04. The 4 sits in the hundredths place and the tenths place holds a 0. - (Unit 1, lesson 7) Round 6.48 to the nearest whole number.
Answer
6. The tenths digit is 4, which is less than 5, so the 6 stays. - (Unit 2, lesson 1) What is 35% as a fraction in simplest form?
Answer
7/20. 35/100 divides by 5 on the top and the bottom.
Words used in this lesson
- categorical
- data that is words or names, sorted into groups. For example: colour of a kite.
- numerical
- data that is numbers you can add and compare. For example: goals in a match.
- qualitative
- another word for categorical: data that describes a quality. For example: kind of loaf.
- quantitative
- another word for numerical: data that gives an amount. For example: baking time.
- nominal
- categories with no natural order. For example: language spoken at home.
- ordinal
- categories that go in a natural order. For example: small, medium, large.
- discrete
- numerical data that is counted, in separate steps. For example: pages in a book.
- continuous
- numerical data that is measured, with any value in a range. For example: mass of a mango.
Words, counts and measurements
A canteen manager keeps a notebook with three columns: dish sold, plates sold and minutes the queue lasted. She wants to know which columns it makes sense to add up. Predict first: which of the three could you add up and get a total that means something? Then send the nine variables in the figure down the two questions and see how each one is sorted.
Colour of a kite: words, with no natural order. It is categorical, and nominal.
Show me the steps
- Colour of a kite: words, no natural order. Categorical, nominal.
- Goals scored in a match: numbers that are counted. Numerical, discrete.
- Time to run 100 metres: numbers that are measured. Numerical, continuous.
- Film rating, poor to excellent: words that go in an order. Categorical, ordinal.
- Number of a bus route: digits, but only a name for the route. Categorical, nominal.
Data is categorical or numerical. Categorical data (also called qualitative) is words: nominal when the words have no natural order (colours, languages), ordinal when they go in an order (small, medium, large). Numerical data (also called quantitative) is numbers: discrete when it is counted, continuous when it is measured.
Why the type matters: numbers can be added and compared; words can only be counted up, and ordinal words can be put in order but not subtracted. The type tells you which graphs and calculations make sense.
Back to the notebook: “dish sold” is nominal, so you can only count how often each dish appears. “Plates sold” is discrete and “minutes the queue lasted” is continuous, and both can be added to a total that means something.
A common mistake: “It is written with digits, so it is numerical.” A shirt number or a phone number is a number used only as a name. You would never add two shirt numbers together, so it is categorical, and nominal.
Counted has gaps, measured does not
Why are discrete and continuous different? A count jumps from one whole number to the next. A measurement can land anywhere in between, and the clock or ruler only decides how close you get. Slide the clock from coarse to fine.
A clock that reads to the nearest 0.1 s shows 14.4 s. The true time was 14.372... s, and no clock shows it exactly.
Show me the steps
- To the nearest 0.5 s: the clock shows 14.5, and there are 2 steps from 14 to 15.
- To the nearest 0.1 s: the clock shows 14.4, and there are 10 steps from 14 to 15.
- To the nearest 0.05 s: the clock shows 14.35, and there are 20 steps from 14 to 15.
- To the nearest 0.01 s: the clock shows 14.37, and there are 100 steps from 14 to 15. It is closer, but the true time 14.372... is still not shown. The goals line never gains a point between 2 and 3.
Discrete data is counted and takes separate values, usually whole numbers: you cannot have 2.5 goals. Continuous data is measured and could take any value in a range: a finer instrument gives a closer reading, and there is no gap between neighbours.
Worked example: sort four variables
A teacher records four things about each pencil case: the number of pencils in it, the length of the longest pencil, the colour of the case, and how sharp the pencils are (blunt, medium or sharp). What type of data is each?
- Number of pencils: numbers, and they are counted. Numerical, discrete.
- Length of the longest pencil: numbers, and they are measured. Numerical, continuous.
- Colour of the case: words with no natural order. Categorical, nominal.
- How sharp: words that go in an order from blunt to sharp. Categorical, ordinal.
Your go. The first step is given. A baker records four things about each loaf: the number of seeds on top, the baking time in minutes, the kind of loaf (rye or sourdough), and the crust (soft, medium or hard).
- Number of seeds: numbers that are counted. Numerical, discrete.
- Now sort the baking time, the kind of loaf and the crust yourself, then check.
Check the answer
Baking time is measured: numerical, continuous. Kind of loaf is words with no order: categorical, nominal. Crust is words in an order: categorical, ordinal.
Check before you go on
1. Which of these is continuous numerical data?
Your turn
Start at Level 1 and go as far as you can. A wrong answer gets a reason, not just a cross: read it, then try again.
Level 1 · Getting started
2. A snack bar records the flavour of crisps each customer buys: salt, paprika or cheese. What type of data is this?
3. Six things were recorded: (1) texts sent today, (2) favourite fruit, (3) wingspan of a bird, (4) grade on a test: A, B, C or D, (5) students absent, (6) house number. How many of the six are numerical data?
Level 2 · Building
4. A survey asks: “How often do you read for pleasure? Never, sometimes, often or daily.” Which description fits the answers best?
5. A form asks each student eight things: (1) height, (2) number of siblings, (3) favourite sport, (4) minutes to get to school, (5) number of pets, (6) hair colour, (7) mass of school bag, (8) hand span. How many of the eight give continuous data?
6. The number of eggs a hen lays in a week is recorded for 20 hens. Which two words describe this data?
Level 3 · Stretch
7. Zuri measures the height of 30 plants in centimetres. To save time she then records each plant only as “short”, “medium” or “tall”. What type is this second record, and what has been lost?
8. Among 25 students, the number of coins in a pocket goes from 0 up to 7. Only whole numbers of coins are possible. How many different values can the data take?
Something to think about
A person's age can be written as 12, as 12 years 4 months, or as a number of days. Is age discrete or continuous? What decides it?
One way to think about it
Time keeps running smoothly, so age is a measurement and could take any value: it is continuous. But if we only write down whole years, the recorded values go up in steps of one, a bit like a count. How the data was recorded matters as well as what was measured.
Exit ticket
9. Which pair is correctly matched?