Two sample of sizes 50 and 100 given. The mean of these samples respectively are 56 and 50. Then the mean of size 150 combining is

Options

A. 55
B. 52
C. 50
D. None of these

Answer

To find the combined mean of two samples, we can follow these steps:

### Step 1: Identify the given information
- Sample 1:
- Size (n1) = 50
- Mean (M1) = 56
- Sample 2:
- Size (n2) = 100
- Mean (M2) = 50

### Step 2: Calculate the sum of the elements for each sample
The sum of the elements for each sample can be calculated using the formula:
\[ \text{Sum} = \text{Mean} \times \text{Size} \]

For Sample 1:
\[ \text{Sum}_1 = M_1 \times n_1 = 56 \times 50 = 2800 \]

For Sample 2:
\[ \text{Sum}_2 = M_2 \times n_2 = 50 \times 100 = 5000 \]

### Step 3: Calculate the total sum of both samples
Now, we need to find the total sum of both samples:
\[ \text{Total Sum} = \text{Sum}_1 + \text{Sum}_2 = 2800 + 5000 = 7800 \]

### Step 4: Calculate the total size of the combined samples
The total size of the combined samples is:
\[ \text{Total Size} = n_1 + n_2 = 50 + 100 = 150 \]

### Step 5: Calculate the combined mean
The combined mean can be calculated using the formula:
\[ \text{Combined Mean} = \frac{\text{Total Sum}}{\text{Total Size}} \]

Substituting the values we found:
\[ \text{Combined Mean} = \frac{7800}{150} = 52 \]

### Final Answer
The combined mean of the two samples is **52**.

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