Calculate the total number of candidates, the median, the mode, and the mean number of subjects passed from the given frequency distribution.

Step 1: Calculate the total number of candidates.
The total number of candidates is the sum of all frequencies.

$$\sum f = 8 + 4 + 2 + 2 + 20 + 17 + 10 + 15 + 20 + 25 + 22 + 15 = 160$$

a) The total number of candidates who sat for the exam is $\boxed{\text{160}}$.

Step 2: Find the median.
The total number of candidates is $N = 160$.
The position of the median is $\frac{N+1}{2} = \frac{160+1}{2} = \frac{161}{2} = 80.5$.
We need to find the value corresponding to the 80.5th candidate. We use cumulative frequencies:

• 0 subjects: 8 candidates
• 1 subject: $8+4=12$ candidates
• 2 subjects: $12+2=14$ candidates
• 3 subjects: $14+2=16$ candidates
• 4 subjects: $16+20=36$ candidates
• 5 subjects: $36+17=53$ candidates
• 6 subjects: $53+10=63$ candidates
• 7 subjects: $63+15=78$ candidates
• 8 subjects: $78+20=98$ candidates The 80.5th candidate falls within the group of candidates who passed 8 subjects.

b) The median number of subjects passed is $\boxed{8}$.

Step 3: State the mode.
The mode is the number of subjects passed with the highest frequency.
Looking at the "Number of candidates" row, the highest frequency is 25, which corresponds to 9 subjects passed.

c) The mode number of subjects passed is $\boxed{9}$.

Step 4: Calculate the mean number of subjects passed.
The mean is given by $\frac{\sum fx}{\sum f}$.
First, calculate $\sum fx$:

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