Which one of the following measures of central tendency is based on only fifty percent (50%) of the central values?
Options
AGeometric Mean
BHarmonic Mean
CMedian
DMode
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Measures of Central Tendency and DispersionPYQ May 25Question 4376 of 473
All Questions Correct Answer
✅ Option c — Median
All Options:
- AGeometric Mean
- BHarmonic Mean
- CMedian
- DMode
Detailed Solution & Explanation
Let us analyze the definition of the Median:
1. The **Median** is defined as the middlemost value of a dataset when arranged in ascending or descending order. It divides the entire distribution into two equal halves.
2. Specifically, 50% of the observations lie below the median, and 50% lie above it. Thus, its position and value are determined based on dividing the dataset into these two 50% segments.
3. In contrast, means (Arithmetic, Geometric, Harmonic) are based on all observations in the dataset, and the mode is the value with the highest frequency.
Hence, **Option C** is the correct answer.
1. The **Median** is defined as the middlemost value of a dataset when arranged in ascending or descending order. It divides the entire distribution into two equal halves.
2. Specifically, 50% of the observations lie below the median, and 50% lie above it. Thus, its position and value are determined based on dividing the dataset into these two 50% segments.
3. In contrast, means (Arithmetic, Geometric, Harmonic) are based on all observations in the dataset, and the mode is the value with the highest frequency.
Hence, **Option C** 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 SyllabusExam 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.
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