By which formula do we compute a frequency distribution $7^{th}$?
A. ${D_7} = l + \left( {\dfrac{{\dfrac{n}{7} - C}}{f}} \right) \times c$
B. ${D_7} = l + \left( {\dfrac{{\dfrac{n}{{10}} - C}}{f}} \right) \times c$
C. ${D_7} = l + \left( {\dfrac{{\dfrac{7}{{10}}n - C}}{f}} \right) \times c$
D. ${D_7} = l + \left( {\dfrac{{\dfrac{{10}}{7}n - C}}{f}} \right) \times c$

Hint: Decile is such a method that is used to divide a dataset into 10 equal subsections with the help of 9 data points. When data is divided into deciles then a decile rank corresponds to each data point in order to sort the given data into descending or ascending order. There are 10 categorical buckets in a decile.

Formula Used:
For grouped data, ${D_n}\left( x \right) = l + \left( {\dfrac{{\dfrac{{nx}}{{10}} - C}}{f}} \right) \times c$, where $l$ is the lower boundary of the class containing the decile, $n$ is the total frequency, $x$ is the value of the decile which is to be calculated and its range is 1 to 9, $C$ is the cumulative frequency of the preceding class, $cf$ is the cumulative frequency of the entire data set.

Complete step by step solution:
In this question, the formula for the 7th decile is required.
So, here $x = 7$ and the 7th decile for a frequency distribution is denoted by ${D_7}$.
Putting $x = 7$ in the formula, we get ${D_7} = l + \left( {\dfrac{{\dfrac{7}{{10}}n - C}}{f}} \right) \times c$

Option ‘C’ is correct

Note: You should know about the definition of decile and its formula with the interpretation of each symbol used in the formula. Don’t mess up the decile with other quantiles like percentile, quartile, and quintile. They all are different types of quantiles in statistics. A decile has 10 subsections but a quartile has 4 and a percentile has 100 subsections.