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: Understand the Empirical Formula
The empirical formula for finding the mode (Mo) based on the mean (M) and median (Me) is given by:
\[ Mo = 3 \times Me - 2 \times M \]

### Step 2: Identify the Given Values
From the question, we have:
- Mean (M) = 8.32
- Median (Me) = 8.05

### Step 3: Substitute the Values into the Formula
Now, we will substitute the values of the mean and median into the empirical formula:
\[ Mo = 3 \times 8.05 - 2 \times 8.32 \]

### Step 4: Calculate the Mode
Now, let's perform the calculations step-by-step:
1. Calculate \( 3 \times 8.05 \):
\[ 3 \times 8.05 = 24.15 \]

2. Calculate \( 2 \times 8.32 \):
\[ 2 \times 8.32 = 16.64 \]

3. Now, substitute these results back into the equation for mode:
\[ Mo = 24.15 - 16.64 \]

4. Finally, calculate the mode:
\[ Mo = 7.51 \]

### Final Answer
The mode of the distribution is \( 7.51 \).

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