Measures of Central Tendency and DispersionPYQ Sept 25Question 4175 of 473
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Find the Coefficient of variation for the following numbers; 7, 5, 9, 3, 6

Options

A33.33
B66.66
C3
D300
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Correct Answer

✅ Option a — 33.33

All Options:

  • A33.33
  • B66.66
  • C3
  • D300

Detailed Solution & Explanation

Let us calculate the Coefficient of Variation (CV\displaystyle CV) for the given observations: X={7,5,9,3,6}\displaystyle X = \{7, 5, 9, 3, 6\}. Here, n=5\displaystyle n = 5.
1. **Calculate the Arithmetic Mean (Xˉ\displaystyle \bar{X})**:
Xˉ=∑Xn=7+5+9+3+65=305=6\bar{X} = \frac{\sum X}{n} = \frac{7 + 5 + 9 + 3 + 6}{5} = \frac{30}{5} = 6
2. **Calculate the Standard Deviation (σ\displaystyle \sigma)**:
Let us find the squares of deviations from the mean, (X−Xˉ)2\displaystyle (X - \bar{X})^2:
- For 7\displaystyle 7: (7−6)2=12=1\displaystyle (7 - 6)^2 = 1^2 = 1
- For 5\displaystyle 5: (5−6)2=(−1)2=1\displaystyle (5 - 6)^2 = (-1)^2 = 1
- For 9\displaystyle 9: (9−6)2=32=9\displaystyle (9 - 6)^2 = 3^2 = 9
- For 3\displaystyle 3: (3−6)2=(−3)2=9\displaystyle (3 - 6)^2 = (-3)^2 = 9
- For 6\displaystyle 6: (6−6)2=02=0\displaystyle (6 - 6)^2 = 0^2 = 0
Sum of the squared deviations:
∑(X−Xˉ)2=1+1+9+9+0=20\sum (X - \bar{X})^2 = 1 + 1 + 9 + 9 + 0 = 20
Variance (σ2\displaystyle \sigma^2):
σ2=∑(X−Xˉ)2n=205=4\sigma^2 = \frac{\sum (X - \bar{X})^2}{n} = \frac{20}{5} = 4
Standard Deviation (σ\displaystyle \sigma):
σ=4=2\sigma = \sqrt{4} = 2
3. **Calculate the Coefficient of Variation (CV\displaystyle CV)**:
CV=σXˉ×100CV = \frac{\sigma}{\bar{X}} \times 100
CV=26×100=1003≈33.33%CV = \frac{2}{6} \times 100 = \frac{100}{3} \approx 33.33\%
Hence, **Option A** 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.

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