83 9 73 5 20 18 82 16

Question

Examoogle · Accepted Answer

The correct answer is Option D: The sum of frequencies is $9 + 5 + 18 + 16 = 48$.. Use the weighted sum formula. Quickly calculate $f \cdot x$ for each row: $83 	imes 9 = 747$, $73 	imes 5 = 365$, $20 	imes 18 = 360$, $82 	imes 16 = 1312$. Sum = 2784. Total $f = 9+5+18+16 = 48$. Result = $2784 / 48$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the weighted sum formula. Quickly calculate $f \cdot x$ for each row: $83 	imes 9 = 747$, $73 	imes 5 = 365$, $20 	imes 18 = 360$, $82 	imes 16 = 1312$. Sum = 2784. Total $f = 9+5+18+16 = 48$. Result = $2784 / 48$.

Formula Used: $$	ext{Mean (\bar{x})} = \frac{\sum f \cdot x}{\sum f}$$

Given: Data table with Marks Obtained (x) and No. of Students (f): (83, 9), (73, 5), (20, 18), (82, 16).

Steps: Calculate the frequency sum (denominator): Sum of all students $N = \sum f = 9 + 5 + 18 + 16$.. Calculate sum of products (numerator): Calculate $\sum f \cdot x = (83 	imes 9) + (73 	imes 5) + (20 	imes 18) + (82 	imes 16)$.. Final mean calculation: Divide the total sum of marks by the total number of students.

Answer: D is correct because the calculated mean of the distribution is 58.

Exam Tip: This concept of weighted averages is fundamental for calculating overall class performance or solving mixture and alligation problems in competitive exams.

Examoogle · Answer

Option A: Calculate the weighted mean based on the provided data table.

Examoogle · Answer

Option B: The mean is calculated as $\frac{\sum (f_i \cdot x_i)}{\sum f_i}$.

Examoogle · Answer

Option C: Identify the correct mean value from the choices once calculated.

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