Question:
The median and mode of a distribution are $25.2$ and $26.1$ respectively. The mean of the distribution is :
The median and mode of a distribution are $25.2$ and $26.1$ respectively. The mean of the distribution is :
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A handy way to remember the empirical formula is by ordering the words alphabetically:
Mean, Median, Mode.
The formula is:
\[ \text{Mode} = 3 \text{ Median} - 2 \text{ Mean} \] Think of the coefficients: 3 (larger word 'Median' with 6 letters) and 2 (smaller word 'Mean' with 4 letters).
This simple mnemonic prevents you from mixing up the coefficients!
Mean, Median, Mode.
The formula is:
\[ \text{Mode} = 3 \text{ Median} - 2 \text{ Mean} \] Think of the coefficients: 3 (larger word 'Median' with 6 letters) and 2 (smaller word 'Mean' with 4 letters).
This simple mnemonic prevents you from mixing up the coefficients!
Updated On: Jul 7, 2026
- $24.75$
- $24.25$
- $24.3$
- $25.5$
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
This question is from the topic "Statistics".
We are given two measures of central tendency for a distribution: the Median ($25.2$) and the Mode ($26.1$).
We are required to find the third measure of central tendency, which is the Mean.
Step 2: Key Formula or Approach:
For any moderately asymmetrical distribution, there is an empirical relationship between Mean, Median, and Mode known as the
empirical formula:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] We can substitute the given values of Median and Mode into this equation and solve for the Mean.
Step 3: Detailed Explanation:
• Identify the given statistical values:
• $\text{Median} = 25.2$
• $\text{Mode} = 26.1$
• Write down the empirical formula relating the three measures of central tendency:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
• Substitute the given values into the formula:
\[ 26.1 = 3 \times (25.2) - 2 \times \text{Mean} \]
• Calculate the multiplication term:
\[ 3 \times 25.2 = 75.6 \]
• Rewrite the equation with this computed value:
\[ 26.1 = 75.6 - 2 \times \text{Mean} \]
• Rearrange the terms to isolate the Mean term on one side:
\[ 2 \times \text{Mean} = 75.6 - 26.1 \]
• Subtract the values:
\[ 2 \times \text{Mean} = 49.5 \]
• Divide by 2 to solve for the Mean:
\[ \text{Mean} = \frac{49.5}{2} = 24.75 \]
Step 4: Final Answer:
The mean of the distribution is $24.75$, which corresponds to Option (A).
This question is from the topic "Statistics".
We are given two measures of central tendency for a distribution: the Median ($25.2$) and the Mode ($26.1$).
We are required to find the third measure of central tendency, which is the Mean.
Step 2: Key Formula or Approach:
For any moderately asymmetrical distribution, there is an empirical relationship between Mean, Median, and Mode known as the
empirical formula:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] We can substitute the given values of Median and Mode into this equation and solve for the Mean.
Step 3: Detailed Explanation:
• Identify the given statistical values:
• $\text{Median} = 25.2$
• $\text{Mode} = 26.1$
• Write down the empirical formula relating the three measures of central tendency:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
• Substitute the given values into the formula:
\[ 26.1 = 3 \times (25.2) - 2 \times \text{Mean} \]
• Calculate the multiplication term:
\[ 3 \times 25.2 = 75.6 \]
• Rewrite the equation with this computed value:
\[ 26.1 = 75.6 - 2 \times \text{Mean} \]
• Rearrange the terms to isolate the Mean term on one side:
\[ 2 \times \text{Mean} = 75.6 - 26.1 \]
• Subtract the values:
\[ 2 \times \text{Mean} = 49.5 \]
• Divide by 2 to solve for the Mean:
\[ \text{Mean} = \frac{49.5}{2} = 24.75 \]
Step 4: Final Answer:
The mean of the distribution is $24.75$, which corresponds to Option (A).
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