The arithmetic mean of 4 numbers is 15. The arithmetic mean of another 6 numbers is 12. What is the arithmetic mean of the combined 10numbers?
(a)12.2
(b)12.8
(c)13.2
(d)13.8

Options

A. 12.2
B. 12.8
C. 13.2
D. 13.8

Answer

To find the arithmetic mean of the combined 10 numbers, we can follow these steps:

### Step 1: Calculate the sum of the first group of numbers
The arithmetic mean of the first group of 4 numbers is given as 15. We can use the formula for the mean, which is:

\[ \text{Mean} = \frac{\text{Sum of numbers}}{\text{Number of observations}} \]

Rearranging the formula to find the sum gives us:

\[ \text{Sum} = \text{Mean} \times \text{Number of observations} \]

For the first group:

\[ \text{Sum}_1 = 15 \times 4 = 60 \]

### Step 2: Calculate the sum of the second group of numbers
The arithmetic mean of the second group of 6 numbers is given as 12. Using the same formula:

\[ \text{Sum}_2 = 12 \times 6 = 72 \]

### Step 3: Calculate the total sum of all numbers
Now, we can find the total sum of all 10 numbers by adding the sums of both groups:

\[ \text{Total Sum} = \text{Sum}_1 + \text{Sum}_2 = 60 + 72 = 132 \]

### Step 4: Calculate the arithmetic mean of the combined numbers
Finally, we can find the arithmetic mean of the combined 10 numbers using the formula:

\[ \text{Mean} = \frac{\text{Total Sum}}{\text{Total Number of Observations}} = \frac{132}{10} = 13.2 \]

Thus, the arithmetic mean of the combined 10 numbers is **13.2**.

### Answer:
(c) 13.2

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