Find the range and mode of the data 17,18,28,19,16,18,17,29,18

A. 12 and 18

B. 13 and 18

C. 12 and 17

D. 11 and 17

Options

A. A
B. B
C. D
D. C

Answer

To find the range and mode of the given data set: 17, 18, 28, 19, 16, 18, 17, 29, 18, we will follow these steps:

### Step 1: Organize the Data
First, we need to arrange the data in ascending order.

**Data in ascending order**: 16, 17, 17, 18, 18, 18, 19, 28, 29

### Step 2: Find the Minimum and Maximum Values
Next, we identify the minimum and maximum values from the organized data.

- **Minimum value**: 16
- **Maximum value**: 29

### Step 3: Calculate the Range
The range is calculated by subtracting the minimum value from the maximum value.

\[ \text{Range} = \text{Maximum} - \text{Minimum} \]
\[ \text{Range} = 29 - 16 = 13 \]

### Step 4: Find the Mode
The mode is the number that appears most frequently in the data set.

From the organized data:
- 16 appears 1 time
- 17 appears 2 times
- 18 appears 3 times
- 19 appears 1 time
- 28 appears 1 time
- 29 appears 1 time

The number that appears most frequently is 18.

### Final Answer
- **Range**: 13
- **Mode**: 18

Thus, the answer is **B. 13 and 18**.

---