Question

If the mode and mean of a data are 24 and 60 respectively, then the median of the data is

• A. 49
• B. 48
• C. 47
• D. 46

Answer 1

The Correct Option is B

We can use the empirical relationship between the mean, median, and mode: $$ \text{Mode} = 3 \cdot \text{Median} - 2 \cdot \text{Mean} $$ 

The mode is 24 and the mean is 60. 

Let the median be $M$. 

Then we have: $$ 24 = 3M - 2(60) $$ $$ 24 = 3M - 120 $$ $$ 24 + 120 = 3M $$ $$ 144 = 3M $$ $$ M = \frac{144}{3} = 48 $$ 

Therefore, the median of the data is 48.