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

Step 1: Understanding the problem:
We are given the mean and median of a set of data. The mean is 21 and the median is 23. We are asked to find the mode of the data.

Step 2: Relationship between mean, median, and mode:
There is a well-known empirical relationship between the mean, median, and mode in a moderately skewed distribution. This relationship is given by:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] This formula is often used when the data is approximately symmetrical, or when it follows a normal distribution.

Step 3: Applying the values:
Substitute the given values of the mean and median into the formula:
\[ \text{Mode} = 3 \times 23 - 2 \times 21 \] Simplifying the expression:
\[ \text{Mode} = 69 - 42 = 27 \]

Step 4: Conclusion:
The mode of the data is \( 27 \).