24.3 Averages and range — Practise

1. Find the mean of 2, 4, 6, 8.

Answer: Mean $=5$.

2. Find the median of 3, 7, 2, 9, 4.

Answer: Order: 2, 3, 4, 7, 9. Median $=4$.

3. Mode of the list

Answer: The mode is $3$, which occurs twice; each other value occurs once.

4. Find the range of 5, 9, 2, 6.

Answer: Range $=9-2=7$.

5. Find the mean of 12, 15, 17, 20.

Answer: Mean $=16$.

6. Find the median of 2, 8, 5, 11.

Answer: Ordered values: 2, 5, 8, 11. Median $=(5+8)/2=6.5$.

7. The data are 2, 3, 3, 4, 18. Find the mean.

Answer: Mean $=6$. The high value pulls it upwards.

8. Set A has range 4 and set B has range 9. Which set has greater spread by range?

Answer: Set B has greater range, so its values are more spread by this measure.

9. The values 2, 4, 6 and 8 each occur once. State whether there is a mode and find the range.

Answer: There is no mode because every value occurs once. Range $=8-2=6$.