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 empirical formula is to associate the larger multiplier with the longer word:
- The word "Median" has 6 letters, so its multiplier is 3.
- The word "Mean" has 4 letters, so its multiplier is 2.
Thus:
\[ \text{Mode} = 3 \text{ Median} - 2 \text{ Mean} \] This mnemonic ensures you never mix up the coefficients during an exam!
- The word "Median" has 6 letters, so its multiplier is 3.
- The word "Mean" has 4 letters, so its multiplier is 2.
Thus:
\[ \text{Mode} = 3 \text{ Median} - 2 \text{ Mean} \] This mnemonic ensures you never mix up the coefficients during an exam!
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.
The mean, median, and mode are three different measures of central tendency used in statistical analysis.
For a moderately skewed frequency distribution, there is a well-known empirical relationship that connects these three measures.
We are given the Mean of a distribution as \(43\) and its Median as \(40\).
We need to calculate the value of its Mode using the empirical formula.
Step 2: Key Formula or Approach:
The empirical relationship between Mean, Median, and Mode is given by the formula:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] We are given \(\text{Mean} = 43\) and \(\text{Median} = 40\). We will substitute these values into the formula to find the value of the Mode.
Step 3: Detailed Explanation:
• Identify the given statistical values:
\(\text{Mean} = 43\)
\(\text{Median} = 40\)
• Write down the empirical formula:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
• Substitute the given values into the formula:
\[ \text{Mode} = 3(40) - 2(43) \]
• Calculate the products:
The product of 3 and 40 is 120:
\[ 3 \times 40 = 120 \] The product of 2 and 43 is 86:
\[ 2 \times 43 = 86 \]
• Subtract the products to find the final value of the Mode:
\[ \text{Mode} = 120 - 86 \] \[ \text{Mode} = 34 \]
Step 4: Final Answer:
The value of the Mode is 34.
Therefore, the correct option is (A).
The topic of this question is Statistics.
The mean, median, and mode are three different measures of central tendency used in statistical analysis.
For a moderately skewed frequency distribution, there is a well-known empirical relationship that connects these three measures.
We are given the Mean of a distribution as \(43\) and its Median as \(40\).
We need to calculate the value of its Mode using the empirical formula.
Step 2: Key Formula or Approach:
The empirical relationship between Mean, Median, and Mode is given by the formula:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] We are given \(\text{Mean} = 43\) and \(\text{Median} = 40\). We will substitute these values into the formula to find the value of the Mode.
Step 3: Detailed Explanation:
• Identify the given statistical values:
\(\text{Mean} = 43\)
\(\text{Median} = 40\)
• Write down the empirical formula:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
• Substitute the given values into the formula:
\[ \text{Mode} = 3(40) - 2(43) \]
• Calculate the products:
The product of 3 and 40 is 120:
\[ 3 \times 40 = 120 \] The product of 2 and 43 is 86:
\[ 2 \times 43 = 86 \]
• Subtract the products to find the final value of the Mode:
\[ \text{Mode} = 120 - 86 \] \[ \text{Mode} = 34 \]
Step 4: Final Answer:
The value of the Mode is 34.
Therefore, the correct option is (A).
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