In a frequency distribution table the numbers 4,6 and 8 have frequencies `(x+2), x, (x-1)` respectively. If their mean is 8 then x is-

Options

A. 8
B. 0
C. 1
D. 2

Answer

To solve the problem, we need to find the value of \( x \) given the frequencies of the numbers in a frequency distribution table and that their mean is 8.

### Step-by-step Solution:

1. **Identify the values and their frequencies**:
- The numbers are 4, 6, and 8.
- Their respective frequencies are:
- For 4: \( f_1 = x + 2 \)
- For 6: \( f_2 = x \)
- For 8: \( f_3 = x - 1 \)

2. **Calculate the total frequency (\( \Sigma f_i \))**:
\[ \Sigma f_i = (x + 2) + x + (x - 1) = 3x + 1 \]

3. **Calculate the sum of the products of values and their frequencies (\( \Sigma f_i x_i \))**:
\[ \Sigma f_i x_i = (4)(x + 2) + (6)(x) + (8)(x - 1) \]
Expanding this:
\[ = 4x + 8 + 6x + 8x - 8 = 18x + 0 = 18x \]

4. **Set up the equation for the mean**:
The mean is given by the formula:
\[ \text{Mean} = \frac{\Sigma f_i x_i}{\Sigma f_i} \]
Given that the mean is 8, we can set up the equation:
\[ 8 = \frac{18x}{3x + 1} \]

5. **Cross-multiply to eliminate the fraction**:
\[ 8(3x + 1) = 18x \]
Expanding this gives:
\[ 24x + 8 = 18x \]

6. **Rearranging the equation**:
\[ 24x - 18x = -8 \]
\[ 6x = -8 \]
\[ x = -\frac{8}{6} = -\frac{4}{3} \]

### Conclusion:
The value of \( x \) is \( -\frac{4}{3} \).