This question tests your understanding of subject-verb agreement and participial phrases in English grammar.

Step 1: Identify the main subject and verb
The main subject of the sentence is "The statistics" and the main verb is "show".

Step 2: Check subject-verb agreement
"Statistics" can be tricky - when referring to numerical data (as in this context), it's treated as a plural noun. The verb "show" correctly agrees with the plural subject "statistics".

Step 3: Analyze the participial phrase
The phrase "having been declared with much enthusiasm to the students" is a participial phrase that modifies the subject "statistics". This phrase is correctly formed in the passive voice ("having been declared") and properly set off with commas.

Step 4: Evaluate the complete sentence structure
The entire sentence follows proper English syntax: Subject + modifying phrase + verb + object clause. All elements are correctly positioned and agree grammatically.

Final Answer: There is no error in the sentence. The correct choice is "No error".

Related Concepts

Subject-Verb Agreement: The verb must agree with its subject in number (singular/plural). Words like "statistics," "mathematics," and "news" can be confusing as they appear plural but may be singular depending on context.

Participial Phrases: These are phrases that begin with a participle (verb form ending in -ing or -ed) that modify a noun. They must be properly positioned and punctuated to avoid dangling modifiers.

Key Rules

1. Statistics (as data) = plural verb
2. Participial phrases should be set off with commas when they provide non-essential information
3. The main verb must agree with the main subject, not words in modifying phrases