Finding the range and median

1. Show the students slide 1 of the PowerPoint.
   What is this graph about?
   Explain what is meant by pulse rate and how it is measured. Show students a video to illustrate if necessary and ask the students to measure their own pulse rate. This might be done in relation to learning in health and physical education.
    
2. Ask students to choose a point on the graph and explain what the point represents to a partner. They should clearly explain that a chosen point represents the number of beats per minute for the heart of one person.
    
3. Together, identify the lowest and highest pulse rates. 
   How many more beats per minute does this person’s heart make than this person’s heart? (Pointing to the highest then lowest data values).
   Let students solve the problem, with a calculator if needed.
   Discuss their strategies which should include subtraction and adding on: 100 – 58 = 42 or 58 + 42 = 100.
   We call the difference between the highest and lowest values in a dataset the range. The range is a measure of how spread out the distribution is.
   You might introduce relevant te reo Māori kupu like ira (dot plot) and ine whānui (range).
    
4. Can you find the middle, or centre, of the data?
   Let students work in pairs to locate the centre of the distribution. Consider strategically pairing students to encourage tuakana-teina and productive learning conversations. 
   Watch to see how they find the centre.
   • Do they work systematically from lowest to highest, closing in, to find the median? (Between 71 and 72 beats per minute).
   • Do they find the centre visually, by halving the distance between 58 and 100? (About 79 beats per minute)
   • Do they choose the most common score, the mode? (72 beats per minute).
      
5. If you have found the centre (of the distribution), what fraction of the points should be above and below it? Look for students to say half below and half above.
   There are 30 dots representing the pulse rate of 30 different people. How can we find the middle? Look for students to say that 15 points should be either side of the centre. Work with them to count 15 points from the left and 15 points from the right. The result is the space between 71 and 72 beats per minute.
   What number shall we say is the centre? Agree that 71.5 is half-way between 71 and 72 beats per minute.
    
6. Show slides 2 and 3 of the PowerPoint (other dot plots). Note that the number of dots is given so students do not need to count them. For both distributions let students find the median and range. The correct medians are shown on slide 4.
   Discuss what the range and median mean for each distribution. Write some statements, such as:
   “There is a range of 16 points between the highest scorer and the lowest scorer.”
   “The middle number of questions correct in the basic facts test is 33 questions.”

Next steps 

1. Explore situations in which centre, as measured by the median, is significant to students. For example, “the median weight of a full school bag for ākonga your age is 3 kilograms. How does the weight of your bag compare?” or “the range in sleep time on a weeknight is 8 hours for ākonga your age. Is that true for students in your class?”
    
2. Investigate how to use the median in real life, such as house prices, income, and spending on items like food and health care. Why is the median used?