If the difference between mean and mode is 69, then the difference betweenMean and Median will be _____(a) 63(b) 31.5(c) 23(d) None of the above

To solve the problem, we can rely on the empirical relationship known as the "Laws of Averages" which states that for a moderately skewed distribution:

$\text{Mean} - \text{Mode} \approx 3(\text{Mean} - \text{Median})$

1. Break Down the Problem

   The problem gives us the difference between the mean and mode as 69, and we need to find the difference between the mean and median using the empirical relationship.

2. Relevant Concepts

   From the relationship mentioned above, we can rearrange it to express the difference between the mean and median: $\text{Mean} - \text{Mode} \approx 3(\text{Mean} - \text{Median})$

3. Analysis and Detail

   Let $D_m = 69$ (the difference between the mean and mode). According to the formula: $69 \approx 3(\text{Mean} - \text{Median})$ We can express it as: $\text{Mean} - \text{Median} \approx \frac{69}{3} = 23$

4. Verify and Summarize

   Therefore, the difference between the mean and median is approximately 23.

Final Answer

The difference between Mean and Median will be 23 (c).