Question

If mode = 29, mean = 32 then median ____ .

• A. 29.5
• B. 30
• C. 30.5
• D. 31

Answer 1

The Correct Option is D

To solve the problem, we need to find the median using the given values of mode and mean.

1. Recall the Empirical Relationship:

There is an empirical relationship between mean, median, and mode for a moderately skewed distribution:

$ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} $

2. Substituting the Known Values:

Mode = 29, Mean = 32

Using the formula:

$ 29 = 3 \times \text{Median} - 2 \times 32 $

$ 29 = 3 \times \text{Median} - 64 $

3. Solving for Median:

$ 29 + 64 = 3 \times \text{Median} $

$ 93 = 3 \times \text{Median} $

$ \text{Median} = \frac{93}{3} = 31 $

Final Answer:
The median is $ {31} $