Measures of Central Tendency and DispersionPYQ Jan 26Question 4536 of 473
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If mean of 5 observations x+1,x+3,x+5,x+7\displaystyle x+1, x+3, x+5, x+7 and x+9\displaystyle x+9 is given as 125, then the value of x will be.

Options

A110
B111
C115
D120
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Correct Answer

✅ Option d — 120

All Options:

  • A110
  • B111
  • C115
  • D120

Detailed Solution & Explanation

Given the 5\displaystyle 5 observations:
(x+1),(x+3),(x+5),(x+7), and (x+9)(x+1), (x+3), (x+5), (x+7), \text{ and } (x+9)
Their arithmetic mean is given as 125\displaystyle 125.

The formula for the mean is:
Mean=Sum of all observationsTotal number of observations\text{Mean} = \frac{\text{Sum of all observations}}{\text{Total number of observations}}

Substitute the values into the formula:
125=(x+1)+(x+3)+(x+5)+(x+7)+(x+9)5125 = \frac{(x+1) + (x+3) + (x+5) + (x+7) + (x+9)}{5}
125=5x+(1+3+5+7+9)5125 = \frac{5x + (1 + 3 + 5 + 7 + 9)}{5}
125=5x+255125 = \frac{5x + 25}{5}
Divide the numerator by 5\displaystyle 5:
125=x+5125 = x + 5
x=125−5=120x = 125 - 5 = 120

Hence, **Option D** 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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