If the ratio of mode and mean is 8: 5, then the ratio of mode and median is ______

Options

A. `8:7`
B. `3 : 2`
C. `4:3`
D. `7:6`

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Understanding the Given Ratio**:
We are given that the ratio of mode to mean is 8:5. We can express this in terms of a variable \( k \):
- Mode = \( 8k \)
- Mean = \( 5k \)

2. **Using the Relationship Between Mode, Median, and Mean**:
We know the relationship between mode, median, and mean:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Substituting the expressions for mode and mean:
\[ 8k = 3 \times \text{Median} - 2 \times (5k) \]

3. **Simplifying the Equation**:
Rearranging the equation:
\[ 8k = 3 \times \text{Median} - 10k \]
Adding \( 10k \) to both sides:
\[ 8k + 10k = 3 \times \text{Median} \]
This simplifies to:
\[ 18k = 3 \times \text{Median} \]

4. **Finding the Median**:
Now, we can solve for the median:
\[ \text{Median} = \frac{18k}{3} = 6k \]

5. **Finding the Ratio of Mode to Median**:
Now we need to find the ratio of mode to median:
\[ \text{Ratio of Mode to Median} = \frac{\text{Mode}}{\text{Median}} = \frac{8k}{6k} \]
Simplifying this gives:
\[ \frac{8}{6} = \frac{4}{3} \]

### Final Answer:
The ratio of mode to median is \( \frac{4}{3} \).

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