Choosing Between Mean and Median for Hand Span Data
About this lesson
In this 50-minute Grade 6 lesson, students quietly measure their hand spans in centimetres, calculate the class mean and median, and write journal reflections on which measure better describes the group. They see how one unusual value changes the mean more than the median. You need rulers, notebooks, chart paper, markers and sticky notes.
- Grade
- 6
- Subject
- Math
- Time
- 50 min
Objective
Students will calculate the mean and median of a real data set and evaluate which measure of centre better represents the data when an outlier is present.
Materials
- Rulers with centimetre markings
- Math journals or lined paper
- Sticky notes
- Chart paper and markers
- Whiteboard and markers
- Calculators (optional)
Hook
Ask students to spread one hand flat on their desk and look at it closely for a moment without talking. Write this on the board: 'What is the typical hand span in our class, and how could we decide?' Give students two minutes to write their first thoughts in their journals before anyone shares.
Main Activity
Model how to measure a hand span by spreading the fingers wide and measuring from the tip of the thumb to the tip of the little finger to the nearest half centimetre. Students work in quiet pairs to measure each other, then each student writes their own measurement on a sticky note and places it on a number line on chart paper at the front of the room. Students copy the full data set into their journals, order it from least to greatest, and calculate both the mean and the median on their own, then check with a partner. Next, the teacher adds two invented values, such as 35 cm and 40 cm for 'two visiting basketball players', and students recalculate both measures and record how much each one changed. To close the activity, students write a short journal entry explaining which measure, mean or median, they think better describes a typical hand span in the room and why.
Discussion Questions
- When we added the two very large hand spans, which measure changed more, and why do you think that happened?
- If a glove maker wanted to make one standard glove size for our class, would you advise them to use the mean or the median? Explain your thinking.
- Can you think of a situation outside school where one unusual value might give a misleading picture of what is typical?
- Did the mean or median match the guess you wrote at the start of the lesson? What surprised you?
Exit Ticket
Here are five plant heights in centimetres: 12, 14, 15, 13, 46. Find the mean and the median, then write one sentence explaining which better describes a typical plant and why.
Differentiation
Support: Give struggling learners a smaller data set of 7 values taken from the class chart to work with first. Provide a step-by-step card listing the steps for mean (add all values, count them, divide) and median (order the values, find the middle, average the two middle values if there is an even count). Allow calculator use so they can focus on reasoning rather than arithmetic.
Extension: Ask advanced learners to find a value that could be added to the class data so that the mean and median become exactly equal, and explain their method. They can also calculate the range and write a journal paragraph on how spread affects how useful the mean is.
