For a frequency distribution 7th decile is computed by the formula

Options

A. `D_(7) =l+ ((n)/(7)-c))/(f) xx i`
B. `D_(7)=l+((n)/(10)-c))/(f) xx i`
C. `D_(7)=l+((7n)/(10)-c))/(f) xx i`
D. `D_(7) =l+((10n)/(7)-c))/(f) xx i`

Answer

To compute the 7th decile (D7) for a frequency distribution, we can use the following formula:

\[ D_n = L + \left( \frac{n}{10} \times N - C \right) \times \frac{i}{f} \]

Where:
- \( D_n \) = nth decile
- \( L \) = lower boundary of the class containing the nth decile
- \( N \) = total number of observations
- \( n \) = the decile to be calculated (in this case, 7)
- \( C \) = cumulative frequency of the class preceding the class containing the nth decile
- \( i \) = class width (size of the class interval)
- \( f \) = frequency of the class containing the nth decile

### Step-by-Step Solution:

1. **Identify the values needed for the formula**:
- Determine \( L \), \( N \), \( C \), \( i \), and \( f \) from the frequency distribution table.

2. **Substitute the values into the formula**:
- Since we are calculating the 7th decile, substitute \( n = 7 \) into the formula:
\[ D_7 = L + \left( \frac{7}{10} \times N - C \right) \times \frac{i}{f} \]

3. **Calculate \( \frac{7}{10} \times N \)**:
- Multiply the total number of observations \( N \) by \( \frac{7}{10} \).

4. **Subtract the cumulative frequency \( C \)**:
- Take the result from step 3 and subtract \( C \) (the cumulative frequency of the class before the class containing the 7th decile).

5. **Calculate \( \frac{i}{f} \)**:
- Divide the class width \( i \) by the frequency \( f \) of the class containing the 7th decile.

6. **Combine the results**:
- Add the lower boundary \( L \) to the product from step 4 and step 5 to find \( D_7 \).

### Final Result:
- The final result will give you the value of the 7th decile \( D_7 \).