The marks of `12` students in a Math test are as follows: `8, 10, 4, 8, 5, 6, 9, 7, 6, 8, 9, 10` Find the: a maximum marks, b. minimum marks, c. range of marks, and d. mean marks.

Answer

To solve the problem step by step, we will find the maximum marks, minimum marks, range of marks, and mean marks for the given data set.

### Step 1: Arrange the Marks in Ascending Order
The marks of the students are:
`8, 10, 4, 8, 5, 6, 9, 7, 6, 8, 9, 10`

Arranging these marks in ascending order gives us:
`4, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 10`

### Step 2: Find the Maximum Marks
The maximum marks are the highest value in the arranged list.
- From the arranged list, the maximum marks are `10`.

### Step 3: Find the Minimum Marks
The minimum marks are the lowest value in the arranged list.
- From the arranged list, the minimum marks are `4`.

### Step 4: Calculate the Range of Marks
The range is calculated by subtracting the minimum marks from the maximum marks.
- Range = Maximum Marks - Minimum Marks
- Range = `10 - 4 = 6`

### Step 5: Calculate the Mean Marks
To find the mean, we first need to calculate the sum of all the marks and then divide by the number of students.

**Calculating the Sum:**
- Sum = 4 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 9 + 10 + 10
- Sum = 4 + 5 = 9
- Sum = 9 + 6 = 15
- Sum = 15 + 6 = 21
- Sum = 21 + 7 = 28
- Sum = 28 + 8 = 36
- Sum = 36 + 8 = 44
- Sum = 44 + 8 = 52
- Sum = 52 + 9 = 61
- Sum = 61 + 9 = 70
- Sum = 70 + 10 = 80
- Sum = 80 + 10 = 90

**Calculating the Mean:**
- Mean = Sum / Number of Students
- Mean = `90 / 12`
- Mean = `7.5`

### Final Answers:
a. Maximum Marks = 10
b. Minimum Marks = 4
c. Range of Marks = 6
d. Mean Marks = 7.5

---