At a shooting competition the scores of a competitor were as given below: (i) What was his modal score?
(ii) What was his median score?
(iii) What was his total score? (iv) What was his mean score?

Answer

To solve the problem step by step, we will calculate the modal score, median score, total score, and mean score based on the given data.

### Given Scores:
Let's assume the scores and their frequencies are as follows:
- Score (X): 0, 3, 4, 6, 7, 5
- Frequency (F): 1, 2, 3, 4, 5

### Step 1: Calculate the Modal Score
The modal score is the score that occurs most frequently.

1. Identify the frequency of each score:
- 0 occurs 1 time
- 3 occurs 2 times
- 4 occurs 3 times
- 6 occurs 4 times
- 7 occurs 5 times
- 5 occurs 0 times

2. The highest frequency is 5, which corresponds to the score of 7.

**Modal Score = 7**

### Step 2: Calculate the Median Score
The median is the middle score when all scores are arranged in order.

1. Calculate the total frequency (N):
- N = 1 + 2 + 3 + 4 + 5 = 15

2. Since N is odd, the median is the score at position (N + 1) / 2:
- Position = (15 + 1) / 2 = 8

3. List the scores in order based on frequency:
- 0, 3, 3, 4, 4, 4, 6, 6, 6, 6, 7, 7, 7, 7, 7

4. The 8th score in this ordered list is 6.

**Median Score = 6**

### Step 3: Calculate the Total Score
The total score is the sum of all scores multiplied by their frequencies.

1. Calculate the total score:
- Total Score = (0 * 1) + (3 * 2) + (4 * 3) + (6 * 4) + (7 * 5)
- Total Score = 0 + 6 + 12 + 24 + 35 = 77

**Total Score = 77**

### Step 4: Calculate the Mean Score
The mean score is calculated by dividing the total score by the total frequency.

1. Calculate the mean:
- Mean = Total Score / Total Frequency
- Mean = 77 / 15 ≈ 5.13

**Mean Score ≈ 5.13**

### Summary of Results:
- (i) Modal Score = 7
- (ii) Median Score = 6
- (iii) Total Score = 77
- (iv) Mean Score ≈ 5.13