Using the empirical formula, find the mode of a distribution whose mean is 8.32 and the median is 8.05.

Answer

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

### Step 1: Write down the empirical formula for mode
The empirical formula to find the mode (Mo) is given by:
\[ Mo = 3 \times \text{Median} - 2 \times \text{Mean} \]

### Step 2: Substitute the given values
We have:
- Mean (M) = 8.32
- Median (Me) = 8.05

Substituting these values into the formula:
\[ Mo = 3 \times 8.05 - 2 \times 8.32 \]

### Step 3: Calculate \(3 \times \text{Median}\)
Calculating \(3 \times 8.05\):
\[ 3 \times 8.05 = 24.15 \]

### Step 4: Calculate \(2 \times \text{Mean}\)
Calculating \(2 \times 8.32\):
\[ 2 \times 8.32 = 16.64 \]

### Step 5: Substitute the results back into the formula
Now, substitute these results back into the mode formula:
\[ Mo = 24.15 - 16.64 \]

### Step 6: Perform the subtraction
Now, perform the subtraction:
\[ Mo = 24.15 - 16.64 = 7.51 \]

### Final Answer
Thus, the mode of the distribution is:
\[ \text{Mode} = 7.51 \]