Question:
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is
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An easy way to memorize this formula is to connect the larger coefficient with the longer word:
"Median" has 6 letters and gets multiplied by 3.
"Mean" has 4 letters and gets multiplied by 2.
\[ \text{Mode} = 3 \text{ Median} - 2 \text{ Mean} \] This prevents you from swapping the coefficients during exams!
"Median" has 6 letters and gets multiplied by 3.
"Mean" has 4 letters and gets multiplied by 2.
\[ \text{Mode} = 3 \text{ Median} - 2 \text{ Mean} \] This prevents you from swapping the coefficients during exams!
Updated On: Jul 9, 2026
- 34
- 43
- 38.5
- 41.5
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The topic of this question is Statistics.
Mean, median, and mode are the three primary measures of central tendency in a frequency distribution.
For a moderately skewed frequency distribution, there exists an empirical relationship that relates these three measures.
We are given \(\text{Mean} = 43\) and \(\text{Median} = 40\), and we need to determine the value of the Mode.
Step 2: Key Formula or Approach:
The empirical relationship between Mean, Median, and Mode is expressed by the formula:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] We will substitute the given values of the mean and median into this formula and solve for the mode.
Step 3: Detailed Explanation:
• Identify the given values from the problem statement:
\(\text{Mean} = 43\)
\(\text{Median} = 40\)
• Substitute these values into the empirical formula:
\[ \text{Mode} = 3(40) - 2(43) \]
• Perform the multiplications:
\[ 3 \times 40 = 120 \]
\[ 2 \times 43 = 86 \]
• Subtract the product of the mean from the product of the median:
\[ \text{Mode} = 120 - 86 \] \[ \text{Mode} = 34 \]
Step 4: Final Answer:
The value of the mode of the frequency distribution is 34.
Therefore, the correct option is (A).
The topic of this question is Statistics.
Mean, median, and mode are the three primary measures of central tendency in a frequency distribution.
For a moderately skewed frequency distribution, there exists an empirical relationship that relates these three measures.
We are given \(\text{Mean} = 43\) and \(\text{Median} = 40\), and we need to determine the value of the Mode.
Step 2: Key Formula or Approach:
The empirical relationship between Mean, Median, and Mode is expressed by the formula:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] We will substitute the given values of the mean and median into this formula and solve for the mode.
Step 3: Detailed Explanation:
• Identify the given values from the problem statement:
\(\text{Mean} = 43\)
\(\text{Median} = 40\)
• Substitute these values into the empirical formula:
\[ \text{Mode} = 3(40) - 2(43) \]
• Perform the multiplications:
\[ 3 \times 40 = 120 \]
\[ 2 \times 43 = 86 \]
• Subtract the product of the mean from the product of the median:
\[ \text{Mode} = 120 - 86 \] \[ \text{Mode} = 34 \]
Step 4: Final Answer:
The value of the mode of the frequency distribution is 34.
Therefore, the correct option is (A).
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