Mode of the data :15,14,19,20,14,15,16,14,15,18,19,15,17,15 is (i) 14 (ii) 15 (iii) 16 (iv) 17

Options

A. 14
B. 15
C. 16
D. 17

Answer

To find the mode of the given data set: 15, 14, 20, 14, 15, 16, 14, 15, 18, 19, 15, 17, 15, we will follow these steps:

### Step 1: Arrange the data in ascending order.
First, we need to sort the data from the smallest to the largest value.

**Data in ascending order:**
14, 14, 14, 15, 15, 15, 15, 15, 16, 17, 18, 19, 19, 20

### Step 2: Count the frequency of each number.
Next, we will count how many times each number appears in the data set.

- 14 appears 3 times
- 15 appears 5 times
- 16 appears 1 time
- 17 appears 1 time
- 18 appears 1 time
- 19 appears 2 times
- 20 appears 1 time

### Step 3: Identify the mode.
The mode is the number that appears most frequently in the data set. From our frequency count, we see:

- 14: 3 times
- 15: 5 times
- 16: 1 time
- 17: 1 time
- 18: 1 time
- 19: 2 times
- 20: 1 time

The number that appears the most is 15, which appears 5 times.

### Conclusion:
Thus, the mode of the data is **15**.

### Final Answer:
The correct option is (ii) 15.

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