Statistics and probability: reading tables and charts, averages and spread, sampling and bias, and the probability of one event, then of two together.
Walk to this campThree questions light the next lantern. Nothing to install, no sign-up.
Eight rungs, one trail
Every camp on the mountain has the same eight rungs: the eight altitudes Alpenrise measures, read back in the words of your own school system. Rung 1 is the bottom of secondary school; rung 8 is beyond the final exam.
Rung
New Zealand
United Kingdom
Cambridge
IB
R1Explorer
Year 7
Year 7
Stage 7
MYP 1
R2Pathfinder
Year 8
Year 8
Stage 8
MYP 2
R3Voyager
Year 9
Year 9
Stage 9
MYP 3
R4Navigator
Year 10
Year 10 · GCSE yr 1
IGCSE Yr 1
MYP 4
R5Pioneer
Year 11
Year 11 · GCSE
IGCSE Yr 2
MYP 5
R6Summit
Year 12
Year 12 · AS
AS Level
DP 1
R7Apex
Year 13
Year 13 · A Level
A Level
DP 2
R8Beyond
NZ Scholarship
beyond A Level
STEP prep
DP HL+
One question from each rung
The mountain draws three questions per rung from the same slice as the free placement. Here is one from each rung of Statistics, shown without its answer.
Rung 1 · Explorer · Year 7Find the mode of: 6, 4, 4, 6, 25, 25, 6
Rung 2 · Pathfinder · Year 8The frequency table shows the number of apps downloaded last month by each student.
Number of apps (x): 4 | 5 | 6 | 7 | 8 | 9 | 10
Frequency (f): 4 | 6 | 3 | 6 | 2 | 8 | 2
Write down the range of the number of apps.
Rung 3 · Voyager · Year 9For the mass, in grams, of each bag of chips it filled, Machine 2 has a mean of 18 and a range of 16. Machine 1 has a mean of 22 and a range of 5. Machine 1 was more consistent than Machine 2. Give a reason for your answer.Machine 1 has a smaller range (5 compared with 16), so its data is less spread out. · Machine 1 has a bigger mean (22 compared with 18), so its scores are higher on average. · Machine 2 has a smaller range (16 compared with 5), so its data is less spread out. · Machine 1 has a bigger range (5 compared with 16), so its data is more spread out.
Rung 4 · Navigator · Year 10The table shows the mass of a tomato picked from the school garden (g) for 28 tomatoes.
0–5 g: 3 | 5–10 g: 7 | 10–15 g: 10 | 15–20 g: 6 | 20–25 g: 2
The cumulative frequency polygon for this data is shown below.
Estimate the interquartile range. Give your answer correct to 1 decimal place.
Rung 5 · Pioneer · Year 11A random sample of 30 mangoes from a large orchard shipment found that 5 were bruised. Estimate how many GOOD (not bruised) mangoes are in a batch of 150.
Rung 6 · Summit · Year 12Charlotte spins a spinner with 4 equal sections (only one is red) twice. What is the probability that AT LEAST ONE of the two spins lands on red? Give your answer as a fraction.
Rung 7 · Apex · Year 13A raffle sells 80 tickets at $5 each, with one prize of $40. What is the expected VALUE of buying one ticket (winnings minus cost), in dollars? Give a decimal or a fraction.
Rung 8 · Beyond · NZ ScholarshipA box holds 9 red pens and 3 blue. Two are taken without replacement. Given the first was red, what is the probability the second is also red? Give a fraction in its simplest form.