A boy scored the following marks in various class tests during a term, each test being marked out of 20.
15,17,16,7,10,12,14,16,19,12 and 16.
(i) What are his modal marks. (ii) What are his median marks?
(iii) What are his total marks? (iv) What are his mean marks?

Answer

Let's solve the problem step by step.

### Given Marks:
The boy scored the following marks in various class tests:
15, 17, 16, 7, 10, 12, 14, 16, 19, 12, and 16.

### (i) Finding the Modal Marks:
1. **Identify the frequency of each mark:**
- 7: 1 time
- 10: 1 time
- 12: 2 times
- 14: 1 time
- 15: 1 time
- 16: 3 times
- 17: 1 time
- 19: 1 time

2. **Determine the mode:**
- The mode is the number that appears most frequently. Here, 16 appears 3 times, which is more than any other number.

**Modal Marks = 16**

### (ii) Finding the Median Marks:
1. **Arrange the marks in ascending order:**
- 7, 10, 12, 12, 14, 15, 16, 16, 16, 17, 19

2. **Count the total number of marks (n):**
- n = 11 (since there are 11 marks)

3. **Find the median position:**
- Median position = (n + 1) / 2 = (11 + 1) / 2 = 12 / 2 = 6

4. **Locate the 6th term in the ordered list:**
- The 6th term is 15.

**Median Marks = 15**

### (iii) Finding the Total Marks:
1. **Add all the marks together:**
- Total Marks = 7 + 10 + 12 + 12 + 14 + 15 + 16 + 16 + 16 + 17 + 19

2. **Calculate the sum:**
- Total Marks = 154

**Total Marks = 154**

### (iv) Finding the Mean Marks:
1. **Use the formula for mean:**
- Mean = Total Marks / n = 154 / 11

2. **Calculate the mean:**
- Mean = 14

**Mean Marks = 14**

### Summary of Results:
- (i) Modal Marks = 16
- (ii) Median Marks = 15
- (iii) Total Marks = 154
- (iv) Mean Marks = 14