Question

The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is:

• A. 27
• B. 22
• C. 17
• D. 23

Answer 1

The Correct Option is A

Problem:
We are given:
- Mean = 21
- Median = 23
We are asked to find the mode of the data.

Step 1: Use the empirical relationship among mean, median, and mode
For a moderately skewed distribution, there is an empirical formula that relates the three central tendencies:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

Step 2: Substitute the given values into the formula
\[ \text{Mode} = 3 \times 23 - 2 \times 21 = 69 - 42 = 27 \]

Final Answer:
The mode of the data is 27.