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**Hint:**So here in this question we have to find the frequency and the cumulative frequency at the place where no number is filled. The cumulative frequency is determined by adding every recurrence from a recurrence dissemination table to the number of its predecessors. And the frequency will be calculated by using the cumulative frequency.

**Complete step-by-step answer:**Since, we know the relation between the cumulative frequency and the frequency which is said determined by adding every recurrence from a recurrence dissemination table to the number of its predecessors, we will get the cumulative frequency.

Since the first term of the cumulative frequency is $15$ therefore the frequency will also be the same. Hence the first position will be filled with the number $15$ .

Now for the second position of frequency, let assume that position be $x$ . so by using the relation, we will get the equation as

$ \Rightarrow 15 + x = 28$

And on solving it we will get

$ \Rightarrow x = 13$

Hence, the second position of the frequency will be filled with the number $13$ .

Now for the third position of the cumulative frequency, we will assume that position to be $A$ .

So, by relation, the equation will be

$ \Rightarrow 28 + 21 = A$

And on solving it, we get

$ \Rightarrow A = 49$

Similarly for others position of the cumulative frequency we have

$ \Rightarrow 49 + 16 = 65$

Similarly for the fifth position of frequency,

We have the relation and it will be equal to

$ \Rightarrow 73 - 65 = 8$

And for the last position of cumulative frequency, we have the relation as

$ \Rightarrow 73 + 12 = 85$

So, by filling all these vacant spots of the table, the table will look like

Class Interval | Frequency | Cumulative Frequency |

25-34 | 15 | 15 |

35-44 | 13 | 28 |

45-54 | 21 | 49 |

55-64 | 16 | 65 |

65-74 | 8 | 73 |

75-84 | 12 | 85 |

**Hence, the option $\left( a \right)$ is the correct answer.**

**Note:**For solving this type of question the most important point is we just need to know the relation between the cumulative frequency and the frequency. By doing so we can easily find the missing numbers. So we have to memorize this type of relation to further solve such questions.

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