Find the mode of the data using an empirical formula when it is given that mean is 30 and median is 25.

Answer

To find the mode of the data using the empirical formula, we can follow these steps:

### Step 1: Identify the given values
- Mean (M) = 30
- Median (Me) = 25

### Step 2: Write down the empirical formula for mode
The empirical formula to find the mode (Mo) is given by:
\[ Mo = 3 \times Me - 2 \times M \]

### Step 3: Substitute the values into the formula
Now, we will substitute the values of the mean and median into the formula:
\[ Mo = 3 \times 25 - 2 \times 30 \]

### Step 4: Calculate the first part of the equation
Calculate \( 3 \times 25 \):
\[ 3 \times 25 = 75 \]

### Step 5: Calculate the second part of the equation
Calculate \( 2 \times 30 \):
\[ 2 \times 30 = 60 \]

### Step 6: Substitute the calculated values back into the equation
Now, we will substitute these calculated values back into the equation:
\[ Mo = 75 - 60 \]

### Step 7: Perform the final calculation
Now, perform the subtraction:
\[ Mo = 15 \]

### Conclusion
Thus, the mode of the data is:
\[ \text{Mode} = 15 \]

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