Which one of the following is the mean of the data given below?
`|{:(x_(i)" "6,10,14,18,24,28,30),(f_(i)" "2,4,7,12,8,4,3):}|`

Options

A. 17
B. 18
C. 19
D. 20

Explanation

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

### Step 1: Write down the given data
We have two sets of data: \( x_i \) (the values) and \( f_i \) (the frequencies).

- \( x_i = [6, 10, 14, 18, 24, 28, 30] \)
- \( f_i = [2, 4, 7, 12, 8, 4, 3] \)

### Step 2: Calculate \( x_i \times f_i \)
We will multiply each value of \( x_i \) by its corresponding frequency \( f_i \):

- \( 6 \times 2 = 12 \)
- \( 10 \times 4 = 40 \)
- \( 14 \times 7 = 98 \)
- \( 18 \times 12 = 216 \)
- \( 24 \times 8 = 192 \)
- \( 28 \times 4 = 112 \)
- \( 30 \times 3 = 90 \)

Now, we can summarize these products:

\[ x_i \times f_i = [12, 40, 98, 216, 192, 112, 90] \]

### Step 3: Calculate the summation of \( f_i \)
Now, we will sum the frequencies \( f_i \):

\[ \text{Sum of } f_i = 2 + 4 + 7 + 12 + 8 + 4 + 3 = 40 \]

### Step 4: Calculate the summation of \( x_i \times f_i \)
Next, we will sum the products \( x_i \times f_i \):

\[ \text{Sum of } (x_i \times f_i) = 12 + 40 + 98 + 216 + 192 + 112 + 90 = 760 \]

### Step 5: Calculate the mean
Finally, we will use the formula for the mean:

\[ \text{Mean} = \frac{\sum (x_i \times f_i)}{\sum f_i} = \frac{760}{40} = 19 \]

Thus, the mean of the given data is **19**.

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