Question

If the mean and mode of some data are 32 and 35 respectively, then its median will be:

• A. 30
• B. 31
• C. 32
• D. 33

Hint:

Use the relation Mode = 3 × Median – 2 × Mean to quickly find any of the three measures of central tendency.

Answer 1

The Correct Option is D

Step 1: Recall the relationship between mean, median, and mode.
The empirical relation is: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Step 2: Substitute values.
\[ 35 = 3 \times \text{Median} - 2(32) \] \[ 35 = 3 \times \text{Median} - 64 \] \[ 99 = 3 \times \text{Median} \Rightarrow \text{Median} = 33 \]
Step 3: Conclusion.
Hence, the median of the data is 33.