Find the mean of the first six multiples of `3. `

Options

A. `10.5`
B. `12`
C. `21`
D. none of these

Explanation

To find the mean of the first six multiples of 3, we can follow these steps:

### Step 1: Identify the first six multiples of 3.
The first six multiples of 3 are:
- 3 × 1 = 3
- 3 × 2 = 6
- 3 × 3 = 9
- 3 × 4 = 12
- 3 × 5 = 15
- 3 × 6 = 18

So, the first six multiples of 3 are: **3, 6, 9, 12, 15, 18**.

### Step 2: Calculate the sum of these multiples.
Now, we need to add these multiples together:
\[ 3 + 6 + 9 + 12 + 15 + 18 \]

Calculating step by step:
- 3 + 6 = 9
- 9 + 9 = 18
- 18 + 12 = 30
- 30 + 15 = 45
- 45 + 18 = 63

So, the sum of the first six multiples of 3 is **63**.

### Step 3: Count the number of observations.
The number of observations (multiples) we have is **6**.

### Step 4: Calculate the mean.
Using the formula for mean:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
Substituting the values we found:
\[ \text{Mean} = \frac{63}{6} \]

Calculating this gives:
\[ \text{Mean} = 10.5 \]

### Final Answer:
The mean of the first six multiples of 3 is **10.5**.

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