Measures of Central Tendency and DispersionMCQPYQ June 19Question 2952 of 473
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For the distribution, The value of median is x: 1, 2, 3, 4, 5, 6; f: 6, 9, 10, 14, 12, 8

Options

A3.5
B3
C4
D5
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Correct Answer

✅ Option c — 4

All Options:

  • A3.5
  • B3
  • C4
  • D5

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Detailed Solution & Explanation

We are given the following frequency distribution: - x\displaystyle x: 1,2,3,4,5,6\displaystyle 1, 2, 3, 4, 5, 6 - f\displaystyle f: 6,9,10,14,12,8\displaystyle 6, 9, 10, 14, 12, 8 1. Compute the cumulative frequencies (cf\displaystyle cf): - For x=1\displaystyle x = 1: cf=6\displaystyle cf = 6 - For x=2\displaystyle x = 2: cf=6+9=15\displaystyle cf = 6 + 9 = 15 - For x=3\displaystyle x = 3: cf=15+10=25\displaystyle cf = 15 + 10 = 25 - For x=4\displaystyle x = 4: cf=25+14=39\displaystyle cf = 25 + 14 = 39 - For x=5\displaystyle x = 5: cf=39+12=51\displaystyle cf = 39 + 12 = 51 - For x=6\displaystyle x = 6: cf=51+8=59\displaystyle cf = 51 + 8 = 59 2. Total number of observations: N=∑fi=59\displaystyle N = \sum f_i = 59. 3. The median position is N2=592=29.5\displaystyle \frac{N}{2} = \frac{59}{2} = 29.5. 4. The cumulative frequency just greater than 29.5\displaystyle 29.5 is 39\displaystyle 39, which corresponds to the class x=4\displaystyle x = 4. Thus, the median value is 4\displaystyle 4. Although the textbook key lists Option D, the mathematically correct choice is Option C. 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 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.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

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