The mean height of 25 male workers in a factory is 161 cm and mean height of 35 female workers in the same factory is 158 cm. The combined mean height of 60 workers in the factory is

Options

A. `159.25`
B. `159.5`
C. `159.75`
D. `158.75`

Answer

To find the combined mean height of the 60 workers in the factory, we can use the formula for the combined mean:

\[ \text{Combined Mean} = \frac{(m_1 \cdot n_1) + (m_2 \cdot n_2)}{n_1 + n_2} \]

Where:
- \( m_1 \) = mean height of male workers
- \( n_1 \) = number of male workers
- \( m_2 \) = mean height of female workers
- \( n_2 \) = number of female workers

### Step 1: Identify the values
From the question:
- \( m_1 = 161 \) cm (mean height of male workers)
- \( n_1 = 25 \) (number of male workers)
- \( m_2 = 158 \) cm (mean height of female workers)
- \( n_2 = 35 \) (number of female workers)

### Step 2: Calculate the total height for male workers
\[ \text{Total height of male workers} = m_1 \cdot n_1 = 161 \cdot 25 \]
\[ = 4025 \text{ cm} \]

### Step 3: Calculate the total height for female workers
\[ \text{Total height of female workers} = m_2 \cdot n_2 = 158 \cdot 35 \]
\[ = 5530 \text{ cm} \]

### Step 4: Calculate the combined total height
\[ \text{Combined total height} = \text{Total height of male workers} + \text{Total height of female workers} \]
\[ = 4025 + 5530 = 9555 \text{ cm} \]

### Step 5: Calculate the combined mean height
\[ \text{Combined Mean} = \frac{\text{Combined total height}}{n_1 + n_2} = \frac{9555}{60} \]
\[ = 159.25 \text{ cm} \]

### Final Answer
The combined mean height of the 60 workers in the factory is **159.25 cm**.

---