In statistics, students need to understand the different types of data that can be collected and analysed. Students are:
- introduced first to
categorical data as it is the easiest to understand;
-
numerical data is harder to understand as there are two subcategories (discrete and
continuous).
Teachers can assist students to decide whether numerical data is discrete or continuous by relating these concepts to count noun and mass (or non-count) nouns in English.
Like count nouns, discrete data can be counted as separate items (e.g. number of people). On the other hand, mass nouns cannot be counted individually (e.g. the food 'meat'. In this case you need to discuss kg of meat, or grams of meat. This variable, weight, is a continuous variable.
Understanding this strategy
This strategy has 6 steps:
- Provide students with a situation where they need to collect or analyse data.
- Ask students to decide which of the variables are categories and which are numerical.
- Ask students to find and read online sources about
count nouns and
mass nouns.
Mass nouns can also be referred to as non-count or uncountable nouns.
- Ask students to use this structure to decide which of the numerical variables are count nouns (i.e., discrete variables) and which are mass nouns (i.e., continuous variables).
- For any questions with mass nouns, ask students to re-write them using appropriate units for the question. This can be challenging for students, as they may find the distinction between count and mass nouns difficult. This is particularly the case when continuous variables, such as time (age), distance and water, are "measured". To support students to collect data for questions with mass nouns, teachers can ask students to:
Define a unit (such as year, kilometre, litre)
Use this unit to rewrite the question so a quantity can be "counted"
For example, if we measure the height of the students in centimetres (cm), then the question becomes "How
many cm tall are the students in this class?" and we end up with numbers such as 150, 151, 152, 153, etc.
- Ask students to collect data to answer their questions and determine appropriate displays and summary statistics for the data.
The example below shows how data analysis can be used in a Year 7 class where students are required to prepare a class summary to introduce the class to a new exchange student (VCMSP270).
Example of linking count nouns to variables
Situation
An exchange student from Senegal will soon be joining our class. Before she travels to Australia she would like to know more about us. Can we compile a class summary about our class?
Categorising information
In groups, students list categories of information that the exchange student might find interesting. For example, they might consider questions like:
- "What sports do they play?"
- "How many siblings do they have?"
- "How old are students in this class?"
- "How tall are the students in this class?"
- "How close to the school do students live?"
Ask students to decide which of their questions relate to categories and which are numerical. For the 5 questions above:
- "What sports do they play?" – Categorical (e.g. basketball and soccer are categories)
- "How many siblings do they have?" – Numerical
- "How old are students in this class?" – Numerical
- "How tall are the students in this class?" – Numerical
- "How close to the school do students live?" – Numerical
Explicitly teach count nouns and mass nouns
Ask students to find and read online sources, such as an online dictionary, about count nouns and mass nouns. They should find information similar to the following:
Example
Feature
|
Count nouns
|
Mass nouns
|
|---|
|
Refers to things that can be counted? | Yes
| No
|
|---|
Examples
| 'student':
1 student, 2 students …
| 'people'
|
|---|
| 'minute':
1 minute, 2 minutes … | 'time'
|
|---|
| 'biscuits':
1 biscuit, 2 biscuits …
| 'food'
|
|---|
Qualifiers
| few students,
fewer minutes,
|
less people;
little time;
|
|---|
| many biscuits
| much food |
|---|
Ask students to use this table to decide which of the numerical variables are count nouns (i.e., discrete variables) and which are mass nouns (i.e., continuous variables which come from measurement).
For questions with mass nouns, students:
- identify a relevant unit of measurement
- rewrite the question using the unit of measurement
The following table summarises the differences and demonstrates the re-writing of three questions from above:
Example
Feature
|
Count nouns
|
Mass nouns
|
|---|
|
Action | Count the items
| Measure the quantities
|
|---|
Type of variable
| Discrete variables
| Continuous variables
|
|---|
Examples from above
| "How many siblings do they have?"
| "How old are the students in this class?" (time is measured)
"How tall are the students in this class?" (height is measured) "How close to the school do students live?" (distance is measured)
|
|---|
| |
Rewritten questions: "How many years old are students in this class?" (unit of time is year) "How many cm tall are the students in this class?" (unit of height is cm) "How many km from the school do students live?" (unit of distance is km)
|
|---|
Solution
Ask students to collect data from the rest of the class to answer their questions and determine appropriate displays and summary statistics for the data.
Note: The only summary statistic for categorical data is "mode", so ensure that the students have collected some numerical data so that the following summary statistics can also be determined: