Question:
If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is
If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is
Show Hint
Remember the important empirical relation:
\[
\text{Mode} = 3\text{Median} - 2\text{Mean}
\]
This is frequently asked in aptitude and statistics-based exams.
Updated On: Apr 30, 2026
- \(22.0\)
- \(20.5\)
- \(25.5\)
- \(23.2\)
- \(24.0\)
Show Solution
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The Correct Option is D
Solution and Explanation
Concept:
For a moderately skewed frequency distribution, the empirical relation between mean, median, and mode is:
\[
\text{Mode} = 3(\text{Median}) - 2(\text{Mean})
\]
This relation is commonly used in statistics when direct calculation of mode is difficult.
Step 1: Write the given values. Given: \[ \text{Mean} = 21 \] \[ \text{Median} = 22 \] We need to find: \[ \text{Mode} \]
Step 2: Use the empirical formula. \[ \text{Mode} = 3(\text{Median}) - 2(\text{Mean}) \] Substituting the values: \[ \text{Mode} = 3(22) - 2(21) \] \[ = 66 - 42 \] \[ = 24 \] Thus, \[ \boxed{\text{Mode} = 24.0} \] Hence, the correct option is: \[ \boxed{(E)\ 24.0} \]
Step 1: Write the given values. Given: \[ \text{Mean} = 21 \] \[ \text{Median} = 22 \] We need to find: \[ \text{Mode} \]
Step 2: Use the empirical formula. \[ \text{Mode} = 3(\text{Median}) - 2(\text{Mean}) \] Substituting the values: \[ \text{Mode} = 3(22) - 2(21) \] \[ = 66 - 42 \] \[ = 24 \] Thus, \[ \boxed{\text{Mode} = 24.0} \] Hence, the correct option is: \[ \boxed{(E)\ 24.0} \]
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