Part A — Mean, Median, Mode & Range
Part A — Mean, Median, Mode & Range
These four measures summarise a data set. The mean shares the total equally; the median is the middle value in order; the mode is the most common; the range is the highest minus the lowest.
1
For the data set 3, 7, 7, 8, 10, find the mean, median, mode and range.
Mean: Median: Mode: Range:
2
Five test scores are 12, 15, 15, 18, 20. Find the mean, median, mode and range.
3
The mean of four numbers is 10. What is their total? A fifth number, 20, is added. What is the new mean?
4
Find the missing value. Four numbers have a mean of 9. Three of them are 7, 8 and 12. What is the fourth number?
5
Reasoning. A shoe shop wants to know which size to stock most of. Which average — mean, median or mode — is most useful here? Why?
6
Open challenge. Create a set of five whole numbers that has a mean of 6 and a mode of 4.
Part B — Investigating & Critiquing Data
Part B — Investigating & Critiquing Data
A statistical investigation follows a cycle: ask a question, collect data, display it, then interpret it. Good data detectives also spot when a graph has been drawn to mislead.
1
Write a statistical question you could investigate in your class (one with answers that will vary). What data would you collect to answer it?
2
Sort each into categorical (groups) or numerical (numbers) data: favourite colour, height in cm, type of pet, number of siblings.
3
Spot the trick. A column graph’s vertical axis starts at 90 instead of 0, so a change from 92 to 96 looks enormous. Why is this misleading?
4
A survey asks only 5 people whether they like a new drink, and 4 say yes. Why might it be unwise to claim “80% of people like it”?
5
Choose the display. For each, name a sensible graph: (a) how a plant’s height changes over 6 weeks; (b) favourite lunch of the class.
6
Plan an investigation. Choose a question from question 1 (or a new one) and outline: the data you would collect, how you would display it, and what conclusion you expect to draw.