Find the mode and median of the data : 13, 16, 12, 14, 19, 12, 14, 13, 14

Answer

To find the mode and median of the data set: 13, 16, 12, 14, 19, 12, 14, 13, 14, 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:** 12, 12, 13, 13, 14, 14, 14, 16, 19

### Step 2: Find the Mode
The mode is the number that appears most frequently in the data set.

**Counting the occurrences:**
- 12 appears 2 times
- 13 appears 2 times
- 14 appears 3 times
- 16 appears 1 time
- 19 appears 1 time

Since 14 appears the most (3 times), the mode is:

**Mode = 14**

### Step 3: Find the Median
The median is the middle value of the data set when it is arranged in ascending order. Since there are 9 numbers (which is odd), we will use the formula for the median position:

**Median Position = (n + 1) / 2**

Where n is the number of observations. Here, n = 9.

**Median Position = (9 + 1) / 2 = 10 / 2 = 5**

Now, we find the 5th value in the ordered list:

**Ordered Data:** 12, 12, 13, 13, **14**, 14, 14, 16, 19

The 5th value is 14.

**Median = 14**

### Final Answer
- **Mode = 14**
- **Median = 14**

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