Find the mode of the following data:
(i) 7,9,8,7,7,6,8,10,7 and 6 (ii) 9,11,8,11,16,9,11,53,11,17 and 8

Answer

To find the mode of the given data sets, we will follow these steps:

### Part (i): Data Set: 7, 9, 8, 7, 7, 6, 8, 10, 7, and 6

**Step 1: Arrange the data in ascending order.**
- The given data is: 7, 9, 8, 7, 7, 6, 8, 10, 7, 6
- Arranging in ascending order gives us: 6, 6, 7, 7, 7, 7, 8, 8, 9, 10

**Step 2: Count the frequency of each number.**
- 6 occurs 2 times
- 7 occurs 4 times
- 8 occurs 2 times
- 9 occurs 1 time
- 10 occurs 1 time

**Step 3: Identify the number that occurs the most frequently.**
- The number 7 occurs the maximum number of times (4 times).

**Step 4: State the mode.**
- Therefore, the mode of the first data set is **7**.

### Part (ii): Data Set: 9, 11, 8, 11, 16, 9, 11, 53, 11, 17, and 8

**Step 1: Arrange the data in ascending order.**
- The given data is: 9, 11, 8, 11, 16, 9, 11, 53, 11, 17, 8
- Arranging in ascending order gives us: 8, 8, 9, 9, 11, 11, 11, 11, 16, 17, 53

**Step 2: Count the frequency of each number.**
- 8 occurs 2 times
- 9 occurs 2 times
- 11 occurs 4 times
- 16 occurs 1 time
- 17 occurs 1 time
- 53 occurs 1 time

**Step 3: Identify the number that occurs the most frequently.**
- The number 11 occurs the maximum number of times (4 times).

**Step 4: State the mode.**
- Therefore, the mode of the second data set is **11**.

### Final Answers:
- Mode of the first data set: **7**
- Mode of the second data set: **11**