Question

If the mean and mode of some data are 6 \& 12 respectively, its median will be:

• A. 4
• B. 6
• C. 8
• D. 10

Hint:

Memorize the empirical formula: Mode = 3(Median) - 2(Mean). It's a quick way to find one measure of central tendency if you know the other two for skewed data.

Answer 1

The Correct Option is C

For a moderately skewed distribution, there is an empirical relationship between the mean, median, and mode, which is given by the formula: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] We are given:

Mean = 6
Mode = 12
Plugging these values into the formula: \[ 12 = 3 \times \text{Median} - 2 \times 6 \] \[ 12 = 3 \times \text{Median} - 12 \] \[ 12 + 12 = 3 \times \text{Median} \] \[ 24 = 3 \times \text{Median} \] \[ \text{Median} = \frac{24}{3} = 8 \] So, the median is 8.