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 steps:

### Step 1: Understand the concept of deciles
Deciles are values that divide a dataset into ten equal parts. The 7th decile (D7) is the value below which 70% of the data falls.

### Step 2: Identify the formula for the nth decile
The formula for calculating the nth decile (Dn) in a frequency distribution is given by:
\[ D_n = L + \left( \frac{N \cdot n}{10} - C \right) \cdot \frac{I}{f} \]
Where:
- \( L \) = lower limit of the class containing the nth decile
- \( N \) = total number of observations
- \( n \) = the decile number (for D7, \( n = 7 \))
- \( C \) = cumulative frequency of the class preceding the class containing the nth decile
- \( I \) = width of the class interval
- \( f \) = frequency of the class containing the nth decile

### Step 3: Substitute the values for D7
For the 7th decile (D7), we substitute \( n = 7 \) into the formula:
\[ D_7 = L + \left( \frac{N \cdot 7}{10} - C \right) \cdot \frac{I}{f} \]

### Step 4: Calculate the values
To calculate D7, you will need the following:
- The lower limit \( L \) of the class containing D7
- The total number of observations \( N \)
- The cumulative frequency \( C \) of the class preceding the class containing D7
- The width of the class interval \( I \)
- The frequency \( f \) of the class containing D7

Once you have these values, you can plug them into the formula to find D7.

### Step 5: Conclusion
Thus, the formula for calculating the 7th decile in a frequency distribution is:
\[ D_7 = L + \left( \frac{N \cdot 7}{10} - C \right) \cdot \frac{I}{f} \]