Investigating data
Try these fresh problems without your notes. Explain your method before opening a solution. This practice is not a graded school assessment.
Check 1
Find the mean and median of 1, 2, 3, 4, 20.
Check 2
Equal-width histogram intervals are [0,5), [5,10), [10,15). Where does a value of 10 belong?
Challenge 1
For 2, 4, 6, 8 minutes, find the mean, median, range, IQR and MAD using medians of the lower and upper halves.
Show a hint
Find the centre, then calculate quartiles and distances from the mean.
Show the worked solution
Mean 5; median 5; range 6; IQR 4; MAD 2 minutes.
The mean and median are 5. Q1 = 3 and Q3 = 7, so IQR = 4. Distances from the mean are 3,1,1,3, averaging 2. Every summary uses minutes.
Challenge 2
A survey of six friends finds that five prefer the new lunch menu. A learner concludes that all students prefer it. Explain two problems and suggest a better investigation.
Show a hint
Consider both who was sampled and the word all.
Show the worked solution
Six friends may be unrepresentative, and one of them does not prefer the menu. Sample students across the school using a fair selection method.
Define the target group and ask the same neutral question. Report the observed counts and sample size, with uncertainty about the wider school; do not claim universal agreement.
Decide what to revisit
If a method was difficult to explain, return to that lesson and schedule a recall check. Unit-review answers are not saved as a score.
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