If 6,4,8 and 3 occur with frequencies 4,2,5 and 1 respectively, then the arithmetic mean is

Options

A. 6.15
B. 6.35
C. 6.25
D. 6.45

Answer

To find the arithmetic mean of the given data, we can follow these steps:

### Step 1: List the values and their frequencies
We have the following values and their corresponding frequencies:
- Value 6 with frequency 4
- Value 4 with frequency 2
- Value 8 with frequency 5
- Value 3 with frequency 1

### Step 2: Calculate the total of the products of values and their frequencies
We will multiply each value by its frequency and then sum these products:
- For value 6: \(6 \times 4 = 24\)
- For value 4: \(4 \times 2 = 8\)
- For value 8: \(8 \times 5 = 40\)
- For value 3: \(3 \times 1 = 3\)

Now, we sum these products:
\[ 24 + 8 + 40 + 3 = 75 \]

### Step 3: Calculate the total frequency
Next, we need to calculate the total frequency by summing all the frequencies:
\[ 4 + 2 + 5 + 1 = 12 \]

### Step 4: Calculate the arithmetic mean
Now we can calculate the arithmetic mean using the formula:
\[ \text{Arithmetic Mean} = \frac{\text{Sum of (Value × Frequency)}}{\text{Total Frequency}} = \frac{75}{12} \]

### Step 5: Simplify the fraction
Now, we divide \(75\) by \(12\):
\[ 75 \div 12 = 6.25 \]

### Conclusion
Thus, the arithmetic mean of the given data is \(6.25\).