D1.5 Determine the range as a measure of spread and the measures of central tendency for various data sets, and use this information to compare two or more data sets.
Activity 1: Mean
Invite students to use their traditional calculators to undertake the following activities.
Guess the Number I Am Thinking of
Form teams of two students.
- The first student chooses, without revealing it, a number between 1 and 100 and asks the other student to guess it.
- On each trial, the first student indicates whether the number chosen is less than or greater than the number stated by the second student.
- Record the number of trials required to guess the chosen number.
- Repeat this exercise 20 times.
- Determine the average number (mean) of trials required to get the correct answer. (Students can switch roles and repeat the same steps.)
Guess the Number of Cubes
Fill a large container with connecting cubes and have students estimate the number of cubes in the container and write it on a sticky note.
- Collect all the sticky notes.
- Calculate the mean of the numbers written by the students.
- Check to see if the number of connecting cubes is a number close to the mean.
Popular Music
Survey students in the school and their families about the number of songs stored on their cell phones. Determine the average number of songs for various categories of people, in other words, students in the class, other students, siblings, parents, etc.
Alternative
Propose an activity to obtain several numbers, then determine the mean of the data obtained.
Source: translated from L'@telier - Ressources pédagogiques en ligne (atelier.on.ca).
Activity 2: Range of Data
Present students with the table below that compares the average monthly temperatures in degrees Celsius over the course of a year in two cities, Alpha (A) and Gamma (G).
| J | F | M | A | M | J | J | A | S | O | N | D | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | 0 | 2 | 4 | 10 | 11 | 19 | 24 | 28 | 21 | 10 | 4 | 3 |
| G | 5 | 7 | 9 | 13 | 17 | 19 | 20 | 23 | 18 | 13 | 8 | 4 |
Have students calculate the range of temperatures for each city and ask them the following questions:
- What would happen to the range of temperatures of Alpha City (A) if the three lowest temperatures were removed from the table?
- What would happen to the range of temperatures of Alpha City (A) if the three highest temperatures were removed from the table?
- What would happen to the range of temperatures of Alpha City (A) if three of the central temperatures were removed?
Source: translated from En avant, les maths!, 6e année, CM, Données, p. 3.