Six faces of a balanced die are numbered from integers 1 to 6. This die is tossed 60 times and the frequency distriction of the integers obtained is given below. Then the mean of the grouped data is
`{:("Integer",1,2,3,4,5,6),("Frequency",8,9,10,16,9,8):}`

Options

A. 3.25
B. 3.55
C. 3.45
D. 3.35

Answer

To find the mean of the grouped data from the frequency distribution of the die rolls, we will follow these steps:

### Step 1: Organize the Data
We have the following frequency distribution:

| Integer (xi) | Frequency (fi) |
|--------------|----------------|
| 1 | 8 |
| 2 | 9 |
| 3 | 10 |
| 4 | 16 |
| 5 | 9 |
| 6 | 8 |

### Step 2: Calculate the Product of Each Integer and Its Frequency
Next, we calculate the product of each integer (xi) and its corresponding frequency (fi):

| Integer (xi) | Frequency (fi) | xi * fi |
|--------------|----------------|---------|
| 1 | 8 | 8 |
| 2 | 9 | 18 |
| 3 | 10 | 30 |
| 4 | 16 | 64 |
| 5 | 9 | 45 |
| 6 | 8 | 48 |

### Step 3: Sum the Frequencies and the Products
Now, we sum the frequencies and the products:

1. **Sum of Frequencies (Σfi)**:
\[ Σfi = 8 + 9 + 10 + 16 + 9 + 8 = 60 \]

2. **Sum of Products (Σxi * fi)**:
\[ Σ(xi * fi) = 8 + 18 + 30 + 64 + 45 + 48 = 213 \]

### Step 4: Calculate the Mean
The mean (x̄) is calculated using the formula:
\[ \bar{x} = \frac{Σ(xi * fi)}{Σfi} \]
Substituting the values we calculated:
\[ \bar{x} = \frac{213}{60} = 3.55 \]

### Final Answer
The mean of the grouped data is **3.55**.

---