Statement-1 :`{:(x:,5,6,7,8,9),(y:,4,6,12,-,8):}` for given data mean of `x(barx)` is found to be `7.3`. The missing frequency is `10`
Statement-2: In case of a frequency distribution , `barx=(Sigmaf_ix_i)/(Sigmax_i)`

Options

A. a) Both statement I and statement II are correct. Statement II is correct explanation of statement I
B. b) Both statement I and statement II are correct. Statement II is not the correct explanation of statement I
C. c) Statement I is correct and statement II is incorrect.
D. d) Statement I is incorrect and statement II is correct.

Answer

To solve the problem step by step, we will analyze the given data and apply the formula for the mean of a frequency distribution.

### Step 1: Understand the Given Data
We have two sets of data:
- \( x_i = \{5, 6, 7, 8, 9\} \)
- \( f_i = \{4, 6, 12, c, 8\} \) (where \( c \) is the missing frequency)

We are given that the mean \( \bar{x} \) is \( 7.3 \).

### Step 2: Write the Formula for Mean
The formula for the mean of a frequency distribution is:
\[ \bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} \]
Where:
- \( \Sigma f_i x_i \) is the sum of the product of frequencies and their corresponding values.
- \( \Sigma f_i \) is the total frequency.

### Step 3: Calculate \( \Sigma f_i x_i \)
We will calculate \( \Sigma f_i x_i \) using the given values:
\[ \Sigma f_i x_i = (5 \times 4) + (6 \times 6) + (7 \times 12) + (8 \times c) + (9 \times 8) \]
Calculating each term:
- \( 5 \times 4 = 20 \)
- \( 6 \times 6 = 36 \)
- \( 7 \times 12 = 84 \)
- \( 8 \times c = 8c \)
- \( 9 \times 8 = 72 \)

So,
\[ \Sigma f_i x_i = 20 + 36 + 84 + 8c + 72 = 212 + 8c \]

### Step 4: Calculate \( \Sigma f_i \)
Now, we calculate \( \Sigma f_i \):
\[ \Sigma f_i = 4 + 6 + 12 + c + 8 = 30 + c \]

### Step 5: Set Up the Equation
Using the mean formula:
\[ 7.3 = \frac{212 + 8c}{30 + c} \]

### Step 6: Cross-Multiply to Solve for \( c \)
Cross-multiplying gives:
\[ 7.3(30 + c) = 212 + 8c \]
Expanding the left side:
\[ 219 + 7.3c = 212 + 8c \]

### Step 7: Rearranging the Equation
Rearranging the equation to isolate \( c \):
\[ 219 - 212 = 8c - 7.3c \]
\[ 7 = 0.7c \]

### Step 8: Solve for \( c \)
Now, divide both sides by \( 0.7 \):
\[ c = \frac{7}{0.7} = 10 \]

### Conclusion
The missing frequency \( c \) is \( 10 \), confirming that Statement 1 is correct.

### Step 9: Verify Statement 2
Statement 2 states that the mean formula is:
\[ \bar{x} = \frac{\Sigma f_i x_i}{\Sigma x_i} \]
This is incorrect because it should be \( \Sigma f_i \) in the denominator, not \( \Sigma x_i \).

### Final Answer
Thus, the correct option is:
**Option C: Statement 1 is correct and Statement 2 is incorrect.**