Question 1 Foundation
Find the midpoint of the class –.
Answer.
Average the two class limits: .
Statistics II
Original questions written at exam standard. Work each one before you open the solution.
Difficulty
Question 2 Foundation
The class – records marks to the nearest whole number. State its class boundaries and width.
Answer. Boundaries to ; width
The boundaries sit half a unit outside the limits, and the width is .
Question 3 Standard
A fair die is rolled. Find the probability of scoring more than 4.
Answer.
More than 4 means 5 or 6 — two of the six outcomes, so .
Question 4 Standard
Find the median of .
Answer.
In order: . With six values the median is the mean of the 3rd and 4th: .
Question 5 Stretch
A class has cumulative frequencies of 4, 11, 23, 32 and 40 at marks of 10.5, 20.5, 30.5, 40.5 and 50.5. How many students scored between 20.5 and 40.5?
Answer.
Subtract the two cumulative frequencies: . Cumulative frequency counts everything up to a point, so a difference gives the number in between.
Question 6 Stretch
Two fair dice are rolled. Find the probability that the total is 10.
Answer.
There are 36 outcomes. Totals of 10 come from — three of them, so .