Find the mode of the following data
17, 32,35,33,15,21,41,32,11,18,20,22,11,15,35,23,38,12

Answer

To find the mode of the given data set, we need to identify the number that appears most frequently. Let's go through the steps systematically.

### Step 1: List the Data
The data provided is:
17, 32, 35, 33, 15, 21, 41, 32, 11, 18, 20, 22, 11, 15, 35, 23, 38, 12

### Step 2: Count the Frequency of Each Number
We will count how many times each number appears in the data set:

- 11: 2 times
- 12: 1 time
- 15: 2 times
- 17: 1 time
- 18: 1 time
- 20: 1 time
- 21: 1 time
- 22: 1 time
- 23: 1 time
- 32: 2 times
- 33: 1 time
- 35: 2 times
- 38: 1 time
- 41: 1 time

### Step 3: Identify the Mode
The mode is the number(s) that appear most frequently. From our counting, we see that:
- 11 occurs 2 times
- 15 occurs 2 times
- 32 occurs 2 times
- 35 occurs 2 times

Since 11, 15, 32, and 35 all occur 2 times, they are all modes of the data set.

### Conclusion
The modes of the given data set are 11, 15, 32, and 35.

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