The mean and standrad deviation of 100 items are 50, 5 and that of 150 items are 40, 6 respectively.
What is the combined mean of all 250 items?

Options

A. 43
B. 44
C. 45
D. 46

Explanation

To find the combined mean of all 250 items, we can follow these steps:

### Step 1: Calculate the total sum of the first group of items
The mean of the first group of 100 items is 50. To find the total sum of these items, we use the formula:
\[ \text{Total Sum} = \text{Mean} \times \text{Number of Items} \]
For the first group:
\[ \text{Total Sum}_{100} = 50 \times 100 = 5000 \]

### Step 2: Calculate the total sum of the second group of items
The mean of the second group of 150 items is 40. Similarly, we calculate the total sum:
\[ \text{Total Sum}_{150} = 40 \times 150 = 6000 \]

### Step 3: Calculate the combined total sum
Now, we combine the total sums of both groups:
\[ \text{Combined Total Sum} = \text{Total Sum}_{100} + \text{Total Sum}_{150} = 5000 + 6000 = 11000 \]

### Step 4: Calculate the combined mean
The total number of items is:
\[ \text{Total Number of Items} = 100 + 150 = 250 \]
Now, we can find the combined mean using the formula:
\[ \text{Combined Mean} = \frac{\text{Combined Total Sum}}{\text{Total Number of Items}} = \frac{11000}{250} = 44 \]

### Final Answer
The combined mean of all 250 items is **44**.

---