Answer all of the Questions. Show all of your working where necessary. State units for your answers where necessary. Round off decimal answers to two decimal places.

To find the mean of a set of numbers, sum all the numbers and divide by the total count of numbers.
The given numbers are: 18, 12, 15, 17, 14, 11, 17, 14.
There are 8 numbers.

$$\text{Sum} = 18 + 12 + 15 + 17 + 14 + 11 + 17 + 14 = 118$$ $$\text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{118}{8} = 14.75$$

1. What is the mean of the following set of numbers?
Answer: $\boxed{\text{14.75}}$

To find the average score, sum all the scores and divide by the total number of scores.
The given scores are: 122, 145, 144, 168, 125, 142.
There are 6 scores.

$$\text{Sum of scores} = 122 + 145 + 144 + 168 + 125 + 142 = 846$$ $$\text{Average score} = \frac{\text{Sum of scores}}{\text{Number of scores}} = \frac{846}{6} = 141$$

2. Stephen scored the following points in an online game: 122, 145, 144, 168, 125 and 142. What is his average score?
Answer: $\boxed{\text{141}}$

The value 'a' is the midpoint (M) for the class interval 16-20.
The midpoint is calculated as $\frac{\text{Lower Limit} + \text{Upper Limit}}{2}$.

$$a = \frac{16 + 20}{2} = \frac{36}{2} = 18$$

We can also verify this using the fM column: for the last row, frequency (f) is 7 and fM is 126.
So, $f \times M = 7 \times a = 126$.

$$a = \frac{126}{7} = 18$$

3. What must be the value of a in the table?
Answer: $\boxed{\text{18}}$

The value 'b' is the sum of all fM values ($\sum fM$).

$$b = 24 + 72 + 78 + 126$$ $$b = 96 + 78 + 126$$ $$b = 174 + 126$$ $$b = 300$$

4. What must be the value of b in the table?
Answer: $\boxed{\text{300}}$

The mean of grouped data is calculated using the formula: $\text{Mean} = \frac{\sum fM}{N}$.
From the table, we have $N = 30$ and we calculated $\sum fM = b = 300$.

$$\text{Mean} = \frac{300}{30} = 10$$

5. What is the mean of the grouped data in the table?
Answer: $\boxed{\text{10}}$