Measures of Central Tendency and DispersionMCQMTP May 20Question 2973 of 473
All Questions

In case of an even number of observations which of the following is median?

Options

AAny of the two middle-most value
BThe simple average of these two middle values
CThe weighted average of these two middle values
DAny of these
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Correct Answer

✅ Option b — The simple average of these two middle values

All Options:

  • AAny of the two middle-most value
  • BThe simple average of these two middle values
  • CThe weighted average of these two middle values
  • DAny of these

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Detailed Solution & Explanation

In the case of an even number of observations n\displaystyle n, there is no single middle-most value. Instead, there are two middle-most values, located at positions n2\displaystyle \frac{n}{2} and n2+1\displaystyle \frac{n}{2} + 1. By convention, the median is defined as the simple arithmetic average (simple mean) of these two middle values. Hence, **Option B** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

Key Concepts to Understand

Median

The middle value of a data set when arranged in ascending or descending order. It divides the distribution into two equal halves. For even n: Median = average of (n/2)th and (n/2 + 1)th values. It is NOT affected by extreme values.

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