AP EAMCET · Maths · Statistics

If the arithmetic mean of the following frequency table is 50 , then
\begin{array}{|c|c|}
\hline Class & Frequency \\
\hline 0-20 & 17 \\
20-40 & f_1 \\
40-60 & 32 \\
60-80 & f_2 \\
80-100 & 19 \\
\hline & \mathbf{1 2 0} \\
\hline
\end{array}

A \(f_1=27 \quad f_2=35\)
B \(f_1=30 \quad f_2=22\)
C \(f_1=28 \quad f_2=24\)
D \(f_1=32 \quad f_2=20\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(f_1=28 \quad f_2=24\)

Step-by-step Solution

Detailed explanation

Class marks: \(x_i = \{10, 30, 50, 70, 90\}\) Total frequency: \(17 + f_1 + 32 + f_2 + 19 = 120 \Rightarrow f_1 + f_2 = 52\) Sum of \(f_i x_i\): \(17(10) + f_1(30) + 32(50) + f_2(70) + 19(90) = 3480 + 30f_1 + 70f_2\) Mean:…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If the arithmetic mean of the following frequency table is 50 , then\begin{array}{|c|c|}\hline Class & Frequency \\\hline 0-20 & 17 \\20-40 & f_1 \\40-60 & 32 \\60-80 & f_2 \\80-100 & 19 \\\hline & \mathbf{1 2 0} \\\hline\end{array}

Step-by-step Solution

If the arithmetic mean of the following frequency table is 50 , then
\begin{array}{|c|c|}
\hline Class & Frequency \\
\hline 0-20 & 17 \\
20-40 & f_1 \\
40-60 & 32 \\
60-80 & f_2 \\
80-100 & 19 \\
\hline & \mathbf{1 2 0} \\
\hline
\end{array}