Find the mean weight of 40 boys from the following data :
`{:("Weight (in kg)",27,28,29,30,31),("Number of boys",6,12,10,8,4),("(Frequency)",,,,,):}`

Answer

To find the mean weight of 40 boys from the given data, we will follow these steps:

### Step 1: Organize the Data
We have the following data:
- Weights (in kg): 27, 28, 29, 30, 31
- Number of boys (Frequency): 6, 12, 10, 8, 4

We can represent this data in a tabular form:

| Weight (X) | Frequency (F) |
|------------|---------------|
| 27 | 6 |
| 28 | 12 |
| 29 | 10 |
| 30 | 8 |
| 31 | 4 |

### Step 2: Calculate Fx
Next, we will calculate \( Fx \) for each weight, where \( Fx = X \times F \):

- For weight 27: \( 27 \times 6 = 162 \)
- For weight 28: \( 28 \times 12 = 336 \)
- For weight 29: \( 29 \times 10 = 290 \)
- For weight 30: \( 30 \times 8 = 240 \)
- For weight 31: \( 31 \times 4 = 124 \)

Now, we can add these values to form a new column in our table:

| Weight (X) | Frequency (F) | Fx |
|------------|---------------|------|
| 27 | 6 | 162 |
| 28 | 12 | 336 |
| 29 | 10 | 290 |
| 30 | 8 | 240 |
| 31 | 4 | 124 |

### Step 3: Calculate Summation of Frequency and Fx
Now we will calculate the total frequency and the total of \( Fx \):

- Summation of Frequency \( \Sigma F = 6 + 12 + 10 + 8 + 4 = 40 \)
- Summation of \( Fx \) \( \Sigma Fx = 162 + 336 + 290 + 240 + 124 = 1152 \)

### Step 4: Calculate the Mean
We will use the formula for mean:

\[ \text{Mean} = \frac{\Sigma Fx}{\Sigma F} \]

Substituting the values we calculated:

\[ \text{Mean} = \frac{1152}{40} = 28.8 \]

### Final Answer
The mean weight of the 40 boys is **28.8 kg**.

---