Question:
If the mode of the following classified data is 33.75, then what is the value of \(x\) in the table?
If the mode of the following classified data is 33.75, then what is the value of \(x\) in the table?
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For grouped data, identify the modal class first and then apply the mode formula carefully.
Updated On: Jun 15, 2026
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The Correct Option is C
Solution and Explanation
Concept:
For grouped data,
\[
\text{Mode}
=
l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h
\]
where
\[
l=30,\quad h=10,\quad f_1=8,\quad f_0=5,\quad f_2=x
\]
since the modal class is \(30-40\).
Step 1: Substitute the given values. \[ 33.75 = 30+\frac{8-5}{2(8)-5-x}\times10 \] \[ 33.75-30 = \frac{3}{11-x}\times10 \] \[ 3.75=\frac{30}{11-x} \]
Step 2: Solve for \(x\). \[ 3.75(11-x)=30 \] \[ 11-x=8 \] \[ x=3 \] 3
Step 1: Substitute the given values. \[ 33.75 = 30+\frac{8-5}{2(8)-5-x}\times10 \] \[ 33.75-30 = \frac{3}{11-x}\times10 \] \[ 3.75=\frac{30}{11-x} \]
Step 2: Solve for \(x\). \[ 3.75(11-x)=30 \] \[ 11-x=8 \] \[ x=3 \] 3
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